McPhee etal 2013

McPhee etal 2013
JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 1–15, doi:10.1002/jgrc.20261, 2013
Creation and tidal advection of a cold salinity front in Storfjorden:
2. Supercooling induced by turbulent mixing of cold water
Miles G. McPhee,1 Ragnheid Skogseth,2 Frank Nilsen,2,3 and Lars H. Smedsrud4
Received 13 December 2012; revised 19 March 2013; accepted 29 May 2013.
[1] Measurements near the edge of fast ice in Freemansundet, Svalbard, reveal mixing
processes associated with tidal advection of a sharp front in salinity, including possible
supercooling induced by double diffusion in a fully turbulent water column. The front
translated back and forth with the semidiurnal tide between an area of mobile (drifting) ice
in Storfjorden proper, and the narrow sound covered by fast ice. Water on each side of the
front was near its salinity-determined freezing temperature. Instruments deployed about 400
m into the sound from the fast ice edge measured current, temperature, conductivity, and
turbulence quantities through several tidal cycles. Turbulence data illustrate that as the steep
horizontal salinity (density) gradient advected past the measurement site, vertical shear near
the fast-ice base induced marked flood/ebb asymmetry in turbulent mixing. As fresher water
entered the sound on the flood phase, inward transport of denser water near the upper
boundary was retarded, leading to statically unstable conditions and enhanced turbulence.
The opposite occurred during ebb tide, as denser water underran lighter. Transient episodes
of supercooling accompanied frontal passage on both flood and ebb phases. The most likely
explanation for a zone of supercooled water within the strongly mixed frontal region is that
during mixing of fresher, slightly warmer (but still at freezing) water from outside with
saltier, colder water in the sound, the former constituent lost heat faster than gaining salt.
This interpretation (differing turbulent diffusivities for heat and salt) challenges strict
application of Reynolds analogy for highly turbulent shear flow.
Citation: McPhee, M. G., R. Skogseth, F. Nilsen, and L. H. Smedsrud (2013), Creation and tidal advection of a cold salinity front in
Storfjorden: 2. Supercooling induced by turbulent mixing of cold water, J. Geophys. Res. Oceans, 118, doi:10.1002/jgrc.20261.
1.
salinity front past our instruments, with fresher, slightly
warmer water from outside replacing saltier, colder water on
the flood, and vice versa on the ebb. As shown later, in the
Eulerian frame of our instrument site, the tidally varying
component of salinity appeared as a rectified wave with
peak-to-peak excursion of about 0.4 on the practical salinity
scale (hereafter expressed as practical salinity units, psu).
[3] At cold temperatures, salinity controls density.
Advection of a horizontal salinity gradient past a solid surface thus provides a mechanism for altering the vertical
static stability of the water column, as shear induced by turbulent stress retards flow near the boundary. Consequently,
when salinity is decreasing (flood), we expect statically
unstable conditions (lighter water underrunning heavier)
and the opposite effect on the ebb. Crawford et al. [1999]
reported measurements from Barrow Strait, NWT, showing
a sevenfold difference in turbulence scale and eddy viscosity during tidal advection of a salinity gradient under fast
ice, with considerably higher drag when salinity was
decreasing. The phenomenon is related to a similar effect
seen in open estuaries, termed tidal straining [Rippeth
et al., 2001].
[4] Of particular interest during the FMS measurements
was intermittent appearance of what we interpret as supercooled water (water in liquid state at temperatures below
its in situ freezing point), apparently associated with the
Background
[2] One component of the 2007 Storfjorden project
described in a companion paper [Skogseth et al., 2013] was
measurement of mean and turbulent flow properties under
fast (stationary) ice near the mouth of Freemansundet
(FMS), a narrow sound separating Edgeïya and Barentsïya
in the eastern part of the Svalbard Archipelago. Tidal flow
in the sound was relatively energetic, comprising a nearly
rectilinear tidal oscillation with amplitude of about 0.8 m
s1 superimposed on residual flow of about 0.12 m s1 into
the sound (i.e., to the northeast from Storfjorden proper)
[see Figure 1 in Skogseth et al., 2013]. A notable feature of
the flood/ebb cycle was back-and-forth advection of a sharp
Companion to Skogseth et al. [2013] doi:10.1002/jgrc.20231.
1
McPhee Research Co., Naches, Washington, USA.
2
Department of Arctic Geophysics, The University Centre in Svalbard,
Longyearbyen, Norway.
3
Geophysical Institute, University of Bergen, Bergen, Norway.
4
Uni Research, Bjerknes Centre for Climate Research, Bergen, Norway.
Corresponding author: R. Skogseth, The University Centre in Svalbard,
PO Box 156, NO-9171 Longyearbyen, Norway. ([email protected]
unis.no)
©2013. American Geophysical Union. All Rights Reserved.
2169-9275/13/10.1002/jgrc.20261
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 1. (a) One-minute averages of salinities measured by TIC2 (unpumped, no corrections), TIC1
(pumped), and RDCP both corrected for conductivities as described in Appendix A. (b) Departure of
water temperature from freezing at surface pressure. RDCP temperature has been adjusted upward by 8
mK, with conductivity adjusted downward by 0.013 S m1. Numbers refer to ‘‘supercooling’’ events discussed in the text.
[5] A different mechanism for producing supercooling
is the so-called ‘‘ice pump’’ where water in contact with
ice at depth (e.g., beneath a floating glacial shelf) is
cooled to its pressure-dependent freezing point by latent
exchange at the ice/water interface and then circulates
adiabatically to a higher level, where its temperature is
well below the in situ freezing point [e.g., Lewis and Perkin, 1983]. Near the Antarctic continental margins, the ice
pump can produce large amounts of frazil ice [Foldvik
and Kvinge, 1974] and platelet ice that may constitute a
sizable portion of the sea ice cover near glacial shelves
[Dempsey et al., 2010; Robinson et al., 2010]. It is also
the likely source of extensive supercooled water found
annually near the surface in McMurdo Sound, Antarctica
[Leonard et al., 2011].
[6] Supercooling mechanisms described earlier depend
in some sense on water column boundary conditions: e.g.,
intense heat loss to the atmosphere at the surface, or ice/
ocean exchange under variable pressure conditions.
[7] Based on measurements from an ice camp on fast
ice, we suggest here a novel mechanism for producing
frontal passage. Supercooled water can form in various
ways. For example, seawater in contact with cold air in
leads and polynyas can become supercooled when (i) the
net heat loss from the water is large and (ii) the supercooled
water is transported away from existing ice before any
crystallization can take place [e.g., Coachman, 1966]. Frazil crystals form when supercooled water encounters suitable nucleation sites, releasing latent heat and rapidly
restoring water temperature toward freezing. Most commonly, frazil ice forms in regions of open water where
blowing snow and other atmospheric contaminants provide
plentiful nucleation opportunities. Laboratory experiments
show maximum levels of supercooling of 20–40 mK,
where the supercooling level is created and varied with the
heat flux and limited by the frazil ice growth [Daly, 1984;
Smedsrud, 2001]. Theoretically, congelation growth of sea
ice can also create supercooled water by a double-diffusive
mechanism [Mellor et al., 1986; Steele et al., 1989], but a
controlled study of turbulence under growing fast ice
showed this effect to be of minor importance [McPhee et
al., 2008].
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
iance spectra. For reasons described later we settled on calculating scalar fluxes (hw 0 T 0 i and hw 0 S 0 i) by combining
their variance spectra with turbulent kinetic energy (TKE)
dissipation rates.
supercooled water : one that depends directly on turbulent
mixing between water masses with differing salinities,
when both are near their salinity controlled freezing temperatures. The measurements were collected between 22
and 24 March 2007, at an ice camp established with support from the Norwegian Coast Guard icebreaker, K/V
Svalbard, about 400 m into the sound from a boundary
with less compact, drifting sea ice typical of Storfjorden.
Skogseth et al. [2013] describe general conditions in Storfjorden prior to establishment of the ice camp, the instrumentation and setup of the ice camp, as well as
documentation of the abrupt salinity front described earlier.
[8] This paper is organized as follows. Section 2
describes measurements and techniques, including discussion of unexpected drops in conductivity observed at different times with different instruments, and turbulent
momentum and scalar exchanges near the ice/ocean boundary. Section 3 discusses the measurements in the context of
an abrupt salinity (density) front advected past the instruments, including transient supercooling events. Results are
summarized in section 4.
2.
2.2. Odd Behavior of Conductivity Sensors During
FMS Deployment
[11] After reconciling differences in conductivity as
described in Appendix A, time series of salinity and departure of temperature from freezing (Figure 1) during the
short FMS deployment reveal (i) substantial tidal changes
in salinity superimposed on an overall freshening trend,
and (ii) that during the first day, water temperature
remained very near freezing, except for large negative
excursions in conductivity lasting for tens of minutes that
appeared at times on the SBE4 (standard) and Aanderaa
RDCP sensors (but not on the mC instrument). These had
no counterpart during the other two on-ice deployments
(Van Mijenfjorden, Barents Sea) during the 2007 K/V Svalbard exercise, when water temperatures were generally
warmer. Taken at face value they implied measurements in
water supercooled to temperatures ranging from a few centikelvins to more than 0.1 K below freezing. We at first suspected one of two sources (or a combination of both) for
this behavior: (i) patches of significantly supercooled
water, transported from outside the fast-ice zone by the
tide; or (ii) a high concentration of frazil crystals blocking
the instruments, altering their conductivity. Upon further
analysis, however, neither explanation appears to be
entirely satisfactory.
[12] Salinity evolution during the FMS deployment is
shown in Figure 2a, in which we have replaced the anomalously low-conductivity events in the RDCP record with
data from TIC2 where available (or by interpolation for
event 5). By removing a linear trend from the salinity record and combining the result with velocity along the major
tidal axis [Skogseth et al., 2013], we can put the events (the
shaded bars in Figure 2b) in the context of the tidal cycle.
In Figure 2b, positive velocities indicate flow into FMS
from Storfjorden, i.e., the flood side of the cycle. The tidal
part of the salinity record appears as a rectified wave and
represents advection of a relatively sharp salinity front
back and forth across the instrument site. We have identified this feature with a salinity front observed offshore
from the FMS fast ice in the afternoon of 23 March [Skogseth et al., 2013, Figures 14 and 16]. Anomalous lowconductivity events (indicated by shaded areas in Figure
2b) apparently occur (i) when current speed is near maximum and (ii) during times of rapid salinity change, i.e.,
frontal passage. In the RDCP record they occur on both the
flood and ebb phases. Their absence on day 83 (24 March)
is not surprising, as the water warmed to above freezing
(Figure 1b).
[13] We examined the anomalous events in more detail
by considering the response of the SBE4 conductivity
meters in the first few hours of 23 March (Figure 3). Temperatures measured at TIC1 (1 m from ice) and TIC2 (3 m)
agree to within about a millikelvin (mK) and showed a
rapid, albeit small rise beginning about 02:15 (UT) at about
the same time that salinity began to decrease at all TIC sensors, marking the arrival of fresher water from outside the
fast-ice zone. Salinity time series are shown in Figure 3b
Measurements
2.1. Methods
[9] During the FMS ice-camp phase of the 2007 K/V
Svalbard exercise, we deployed two turbulence instrument
clusters (TICs) under fast ice about 400 m from the boundary with loosely consolidated, mobile pack ice near the entrance to the sound. Each TIC comprised a three-axis
acoustic Doppler velocimeter (ADV, Sontek ADVOcean—
5 MHz), with the measurement volume in the same horizontal plane as temperature and conductivity sensors manufactured by Sea-Bird Electronics. TIC1, mounted 1 m
below the ice/ocean interface on a rigid rod, included a
pumped temperature/conductivity pair (SBE3F/SBE4) plus
a SBE7 microstructure conductivity (mC) sensor, also
mounted in the same plane. TIC2 was similarly mounted 3
m below the ice/water interface but differed from TIC1 in
that there was no mC component, and the standard SBE4
conductivity meter was not pumped but instead relied on
the mean current to flush the small cylindrical duct housing
the electrodes. The instrument was aligned with the major
tidal axis to provide maximum flushing. In addition to the
TICs, we obtained data from a downward oriented, Aanderaa recording Doppler current profiler (RDCP) deployed
approximately 100 m away, which included temperature
and conductivity from sensors in the RDCP housing suspended just below the 50 cm thick, level ice.
[10] Turbulence data from the two TICs were processed
using standard procedures developed for these instruments
over several previous projects [McPhee, 2008; Sirevaag et
al., 2010]. Data were divided into 15 min ‘‘realizations,’’
and deviatory values were calculated by removing a linear
trend from each series, e.g., u0 ¼ u hui where u is the
measured velocity in a direction aligned with the mean
realization streamline, and hui is a least-squares linear fit to
the measured velocity over the realization period. Turbulent Reynolds stress was estimated by two methods: first
by calculating the covariance of the vertical velocity with
the horizontal deviatory velocity components; and second
by considering the area-preserving vertical velocity var3
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 2. (a) Corrected salinity from the RDCP (black) and TIC1 (red), with linear trend indicated by
the dashed line. (b) Salinity anomaly plotted together with barotropic tidal velocity along the major tidal
axis (positive into FMS). Light shading indicates times of conductivity drops in the RDCP record. Heavier shading indicates drops in the TIC standard C records, corresponding to events 1 and 2 as identified
in Figure 3b.
lower. Both events occurred during a time of high currents
and vigorous turbulent mixing. Because of boundaryinduced shear from the fast-ice cover, we expect water with
lower salinity to appear first at the lower site, as discussed
later. Given the levels of turbulence in the flow, it also
seems quite unlikely that separate, low-aspect lenses of
supercooled water at different depths in the upper 3 m
could persist long enough after encountering the fast-ice
boundary to produce the observed events.
[15] It is perhaps less easy to dismiss the idea that advection of frazil ice crystals from elsewhere could account for
the events; however, several factors argue against this
interpretation. Whereas it is plausible that during the flood
tide, frazil crystals generated by air-sea fluxes in low concentration pack in Storfjorden proper could be swept past
our instrument sites and in fact might sustain a vertical gradient that would cause them to appear first at the shallower
site, it is difficult to imagine a source well within the limits
of the solid fast ice that would produce similar behavior on
from three instruments with calibration adjustments as
explained in Appendix A: the pumped SBE4 instrument on
TIC1 (C1, blue); the SBE7 microstructure conductivity
instrument on TIC1 (mC, red), and the standard (not
pumped) SBE4 instrument on TIC2 (C2, green), 2 m lower.
Events 1 and 2, and a similar dropout in RDCP conductivity (Figure 1), all occur within an hour and a half after flood
maximum, during a time of intense mixing. Event 1, sensed
by the C1 sensor (pumped), lasted for about 40 min, and
then reverted to values near those sensed by the other two
instruments. About 15 min later, event 2 occurs in the other
standard SBE4 instrument, 2 m lower, and lasts for about
half an hour. Significantly, neither event is evident in the
mC salinity.
[14] These observations are difficult to reconcile with the
possible sources identified earlier. If, for example, a mass
of water supercooled to 50 mK had indeed advected under
the fast ice from outside the sound, it is difficult to see how
it would appear at the upper TIC almost an hour before the
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
rection in the UNESCO formula is applied (Figure 5b),
Tp begins positive at both levels, but the positions are
reversed, with minimum Tp at TIC1 (1.5 dbar) coinciding
closely with event 1, and similarly, event 2 begins near the
time that TIC2 (3.5 dbar) Tp decreases to within about
0.5 mK of freezing. Consequently, it seems reasonable to
infer that the time lag between events 1 and 2 is related to
the pressure dependence of freezing temperature. Starting
at about 02:15, water temperature increase (Figure 3a)
coincides with the arrival of fresher water (still near freezing) from offshore of the fast ice. Note that during the period of rapid temperature rise lasting for about the next half
hour Tp continues to decrease at TIC2 until it reaches a
value very close to freezing.
[17] These observations suggest that the dropouts
observed in both the standard SBE4 conductivity meters
occurred as the water reached a transient supercooled state
and nucleated on the small glass ducts housing their
resistance-measuring electrodes, in effect decreasing their
diameter and increasing apparent resistivity. We think similar nucleation on the electrode surface of Aanderaa RDCP
conductivity sensor accounts for its sudden drops in conductivity, and that events 1–5 are in fact localized, transient
supercooling episodes.
Figure 3. (a) TIC temperatures measured during dropout
events early on day 82. (b) Adjusted salinity at TIC1
(pumped, blue; mC, red) and TIC2 (green).
the ebb tide. There are instrumental considerations as well.
Typically, with SBE4 instruments, it is readily apparent
when ice blockage occurs, because conductivity drops to
values near zero. Here the inferred salinity values remain
within somewhat plausible ranges. The mC instrument,
mounted quite close to the intake of the pumped T/C pair
on TIC1, did not indicate lower conductivity during event 1
and showed little evidence of crystals striking or passing
between the small exposed dual electrodes. We also examined the echo intensity of the Sontek ADVOcean acoustic
backscatter velocimeters (Figure 4). We would expect a
cloud of frazil crystals appearing for 20 min at TIC1 (event
1) and later for 15 min at TIC2 to induce quite different
echo amplitudes from the respective velocimeters, but the
differences are minimal. Even in the 1 min average time series, they are often highly correlated, which would be
expected from ‘‘normal’’ turbulence during both events.
[16] There is reasonably convincing evidence that the
low-conductivity events are indeed linked to supercooling,
even if the magnitudes seem far too large. Using our best
estimates for temperature and salinity at levels 1 and 3 m
below the ice undersurface, the departure of water temperature from freezing at surface pressure (T0) indicates (Figure 5a) slight (1–2 mK) supercooling at both levels. Two
factors need to be considered in discussing this result: first,
the magnitude of T0 is comparable to the uncertainty in
SBE3 thermometer calibration ; and second, it is smaller
than the uncertainty cited by Gill [1982] in the United
Nations Educational, Scientific and Cultural Organization,
Paris (UNESCO) freezing temperature formula, which we
have used here and is given by
2.3. Stress, TKE Production, and Dissipation
[18] Three-axis Sontek ADVOcean current data provided
estimates of turbulent stress along with TKE production
and dissipation as follows. Friction speed (square root of
the local kinematic turbulent stress) was calculated directly
from the covariance of the deviatory velocity components
using 1 h bin averages of the 15 min turbulence
realizations :
u ¼ ðhu0 w02 i þ hv0 w02 iÞ1=4
ð1Þ
[19] We also calculated area-preserving vertical velocity
variance spectra following the procedure described by
McPhee [1994, 2008], which provides estimates of two important turbulence parameters : (i) the dominant turbulence
scale (mixing length), l ¼ cl/kmax, where kmax is the angular
wave number at the peak of the area-preserving (weighted)
vertical velocity variance spectrum [kSww(k)] and cl 0.85; and (ii) the dissipation rate, estimated from the
Tf ðS; pÞ ¼ 0:0575S þ 1:710523 103 S 3=2
2:154996 104 S 2 7:53 103 p
where S is the salinity on the practical salinity scale and p
is the pressure in bars (105 Pa). Despite these uncertainties,
it is clear that T0 decreases in the first half hour, with a
slightly lower value at 3 m. When the small pressure cor-
Figure 4. ADV echo amplitude during the two dropout
events in TIC conductivity. Light traces are the 1 min average amplitude of three beams for each ADVOcean instrument. Heavy traces are 5 min running average.
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 5. (a) T calculated at surface pressure (p ¼ 0) for salinities from TIC1 mC (red) and TIC2
standard C (green). (b) T corrected for pressure (1.5 dbar for TIC1, 3.5 dbar for TIC2).
spectral level at a wave number, k", in the 2/3 (inertial)
subrange of the area-preserving log-log vertical velocity
(w) spectrum
"¼
3
Sww ðk Þk"5=3
4"
inferred from the spectral peaks (Figure 7a) often
approaches the geometric scale (jzj, where is Karman’s
constant) for TIC1 but is consistently smaller for the 3 m
cluster, indicating that other factors in the flow influenced
turbulence scales fairly close to the interface. TKE production (Figure 7b; based on the covariance estimate of u )
accentuates the asymmetry between flood and ebb, particularly at the 3 m level. TKE dissipation, based on w spectral
levels, also illustrates this marked asymmetry. At the 1 m
level during flood episodes, dissipation exceeds production,
which suggests a source of turbulence in addition to local
shear. The opposite holds during the ebb tide. At 3 m, this
pattern is not so clear, although overall dissipation slightly
exceeds production.
[23] Assuming that the 1 m level satisfies surface-layer
criteria (as indicated by the correspondence between l and
jzj), hydraulic roughness is obtained from the ‘‘law of
the wall’’:
ð2Þ
where " ¼ 0.51 is the Kolmogorov constant for the alongstream spectrum.
[20] If local stress and shear are related by local eddy
viscosity, u l, TKE shear production is estimated as
u3
@u
@z ¼ l . In a turbulent regime where the TKE shear production is approximately balanced by dissipation, the vertical velocity spectrum then by itself provides an
independent estimate of friction velocity
uð"Þ ðl"Þ1=3
ð3Þ
[21] Conversely, by using the covariance estimate of
friction speed, TKE production may be estimated instead
1=3
by PS ¼ uðcovÞ =l.
[22] Maximum values of about 0.8 m s1 during both
flood and ebb are shown from hourly averages of current
speed (Figure 6) at 3 m. As expected, there is significant
shear between the two clusters. The two estimates of friction speed (covariance, spectral) are reasonably similar
overall (Figures 6b and 6c), although there are periods of
significant difference, the largest of which occurs during
the ebb tide. Then uð"Þ values for both clusters are smaller
than during the two flood events, while this holds only for
TIC2 in the uðcovÞ time series. The master turbulence scale
log z0 ¼ u
þ log ð1Þ
u0
ð4Þ
[24] Average values for log z0 are 10.7 and 11.4
using uðcovÞ and uð"Þ , respectively, with corresponding z0
values: 2.2 105 and 1.1 105 m. These are very
small, but not widely different from hydraulic roughnesses
observed under fast ice elsewhere [e.g., Crawford et al.,
1999; McPhee et al., 2008].
2.4. Scalar Fluxes
[25] Estimating turbulent heat flux Hf ¼ cp hw0 T 0 i ,
where is water density and cp is specific heat
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 6. (a) Hourly average current speed 1 m (TIC1, circles) and 3 m (TIC2, red squares) below the
ice. Bars represent 61 standard deviation from the mean. (b) Friction velocity from Reynolds stress estimated from covariance statistics. Bars represent confidence limits for the hourly average covariance estimates. (c) Friction velocity estimated from dissipation and mixing length, both obtained from vertical
velocity spectra.
0
(approximately 4.1 103 J kg1 for cold seawater) during
the FMS deployment presented a difficult challenge
because (i) deviations in temperature were often very small
despite the intense turbulence, and (ii) when changes in
temperature occurred (e.g., Figure 3a), they were associated
with the passage of the advected front. These were often
very abrupt, as illustrated by the arrival at the turbulence
mast of relatively cold, more saline water with the ebb (outward) tide in the morning of 23 March (Figure 8a), and the
later arrival of fresher, warmer water with the afternoon
flood tide (Figure 8b) as the front separating the two water
types advected back into the sound. In each case, the
change in ‘‘mean’’ temperature between minutes 9 and 12
is larger than the turbulent fluctuations yet occurs at a comparable time scale. Such events were not uncommon during
the frontal passages, which often included smaller-scale
structure embedded in the front (e.g., Figure 2). In these
circumstances, covariance statistics are sensitive to removal of the ‘‘mean’’ flow. Using the example for TIC2 in
Figure 8b, the covariance calculated by our standard
method of removing a linear trend over the 15 min segment
is cp w0 T linear ¼ 42 W m 2 , whereas if we instead
remove a quadratic fit (allowing more realistic curvature),
the result is 8 W m2, a fivefold difference. For comparison if we use the same procedure for comparing friction velocity during the same data segment, the difference
between removing a linear fit of the horizontal velocity
components versus a quadratic fit is minimal : uðlinearÞ ¼
0:030 m s 1 ; uðquad Þ ¼ 0:029 m s 1 . The reason, of
course, is that there is no abrupt change in momentum of
the flow comparable to the change in temperature.
[26] Since direct covariance estimates of heat flux
seemed questionable, we instead considered spectral estimates of heat flux magnitude, obtained from a combination
of thermal variance dissipation from spectral density in the
inertial subrange [e.g., McPhee, 1994, 2008]
"T ¼
STT "1=3 k 5=3
ð5Þ
[27] ( ¼ 0.81 is the thermal Kolmogorov constant),
and the conservation equation for thermal variance
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 7. (a) Mixing length l inversely proportional to the wave number at the peak in the areapreserving w spectrum. Dashed lines indicate the geometric scale jzj. (b) Shear production rate of
TKE from the covariance estimates of u . (c) Dissipation estimated from spectral density in the inertial
subrange of the w spectrum.
0 0 @T kmax hw0 T 0 i2
hw T i
¼
¼ "T
c u
@z and larger heat flux in the second flood is slight heating
from solar insolation in lower concentration ice offshore
from the fast-ice edge (local solar zenith was at approximately 10:45 UT). Despite this warming and large friction
velocity, the water remained near enough freezing that
basal heat flux calculated according
to a bulkformulation
for sea ice: Hbulk ¼ cp cH u0 Tml Tf ðSml Þ with cH ¼
0.0057 [McPhee et al., 2008] never exceeded 3.2 W m2.
For the bulk relation we calculated u0 from current speed
at 1 m using (4).
[29] As indicated earlier, problems with the pumped
TIC1 conductivity meter precluded using its record for covariance estimates of salinity flux, and even after accounting for its lag in response ; we noticed at times fairly large
deviation from the other sensors during the FMS deployment. These differences were not present during the other
two deployments. Having used the low-pass filtered TIC2
conductivity to establish a time-dependent intercept for the
linear mC calibration (see Appendix A), we were unable to
determine small differences in salinity at the two levels.
The rapidly changing frontal structure apparent in
ð6Þ
l [28] Our reasoning in choosing the spectral method is
that in a rapidly moving, heterogeneous flow (i.e., with significant horizontal gradients in mean quantities) turbulence
characteristics in the inertial subrange would be more representative of the actual flux magnitudes. We made the following assumptions to extract heat flux magnitude from (5)
and (6): first, that eddy heat diffusivity is nearly the same
as eddy viscosity (i.e., KH Km ¼ u l), and second that
the wave number, k", used to evaluate TKE dissipation
from (2) is the same for thermal dissipation. To specify
heat flux direction, we considered the sign of the difference
between temperatures measured at 1 and 3 m. Since these
differences were often very small, we adjusted T1 so that it
agreed with T2 during times of small heat flux magnitude.
Results (Figure 9) indicate relatively small vertical heat
flux except at 3 m during the second flood event, which
coincides with a rapid rise in temperature beginning shortly
after 82.6. A possible explanation for higher temperatures
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MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 8. Temperature measurements at 1 and 3 m below the ice for 15 min data segments during (a)
ebb and (b) flood events on 23 March 2007. In each, a small correction to T1 (<1 mK) has been added so
that mean temperatures in the first 8 min coincide.
Figure 9. (a) Hourly average heat flux estimates from spectral characteristics at 1 m (blue) and 3 m
(red). Error bars represent 61 standard deviation of the spectral magnitude estimates. The green trace indicates interface (basal) heat flux based from bulk parameterization. (b) Temperatures at the two TIC levels
(left scale), with the 1 m thermometer adjusted downward by 1.3 mK, determined at times when the heat
flux magnitude was small. Shaded area indicates the temperature difference in kelvins (right scale).
9
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
Figure 10. Same as Figure 8, except for salinity, with mC salinity adjusted so that mean values agree
in the first 8 min of both records.
current shear near the interface induces substantial changes
to the turbulent flow structure, in a manner similar to estuarine tidal straining as described by Rippeth et al. [2001].
Results described earlier illustrate the importance of this
process in FMS, even relatively close to the boundary in a
highly turbulent environment. Consider first the short T and
S time series in Figures 8 and 10. On the ebb tide (Figures
8a and 10a), the front is exiting the sound, and interior
(saltier, colder) water appears first at the lower cluster on
the TIC mast. At low temperature, density is controlled
almost exclusively by salinity, so when the front is outbound, the effect is to vertically stabilize the water column.
During the flood (lower panels), positions are reversed,
with slightly fresher, warmer water from outside the fastice zone underrunning the colder, saltier water mass of the
temperature was even more pronounced in salinity (Figure
10), so we also utilized the spectral method for estimating
salinity flux, i.e., the haline equivalents of (5) and (6),
assuming that the thermal Kolmogorov constant was suitable for salinity. As suggested by Figures 8 and 10, we
assigned direction based on the negative of the thermal gradient, which combined with the spectral magnitude estimates, provided a time series of salinity flux at the two
levels (Figure 11). Two factors argue against considering
results of Figure 11 as quantitatively correct. First, in addition to the assumptions implicit in the thermal spectral flux
magnitude calculation, the standard TIC2 conductivity meter depends on mean flow for flushing (its duct was oriented
along the major tidal axis); hence, the impact of time lag
between the conductivity sensor and thermometer is not
well known (which affects salinity), perhaps exacerbating
the horizontal homogeneity problem mentioned earlier.
Second, as discussed later, there is reason to believe that
eddy diffusivities for heat and salt differ, implying different
scalar Kolmogorov constants. Nevertheless, estimates from
the two different sensors are qualitatively consistent and
suggest fairly strong downward salinity flux during the
flood events and a weaker upward flux during the ebb. At
these low temperatures, buoyancy is controlled almost
exclusively by salinity. The downward salinity maximum
at time 82.667 corresponds to a destabilizing buoyancy flux
of about 2 107 m2 s3.
3.
Discussion
3.1. Turbulence in a Moving Horizontal Density
Gradient Near a Solid Boundary
[30] Crawford et al. [1999] showed that when a horizontal gradient in density advects under a fast-ice boundary,
Figure 11. Hourly average salinity flux estimates from
spectral characteristics at 1 m (blue) and 3 m (red). Error
bars represent 61 standard deviation of the spectral magnitude estimates.
10
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
inner sound. The impact then is to create a statically unstable water column, gravitationally enhancing the sheargenerated turbulence. This qualitative description of the
impact on turbulence of the horizontal density gradient is
borne out by the measurements presented in Figures 6 and
7. In the former, current speeds during flood (centered
around times 82.1 and 82.65) are similar to the ebb, but
there is a marked reduction in friction velocity, especially
at the lower level, 3 m from the interface. At TIC1 (1 m
below the interface) this flood/ebb asymmetry also carries
over to the TKE shear production (PS) and dissipation "
(Figure 7). During flood events both PS and " are larger
than ebb values. Furthermore, during flood events dissipation exceeds shear production, suggesting
a positive TKE
0 0
buoyancy source (i.e., Pb ¼ hw b i), whereas during the
ebb event, PS > ", which would be expected with a negative
buoyancy source (sink). At TIC2, shear production and dissipation appear to be more closely balanced.
[31] These observations are consistent with the echo amplitude data from the RDCP [Figure 13b in Skogseth et al.,
2013]. Assuming echo amplitude reflects in some way turbulent intensity in the water column, the higher amplitudes
penetrate much farther down in the water column on the
flood (freshening, statically unstable) than on the ebb
(increasing salinity, statically stable).
[32] As described in section 2.4, the accuracy of our scalar flux estimates (hw0 T 0 i and hw0 S0 i) is highly questionable
because during the frontal passages, mean values of temperature and salinity change rapidly on time scales comparable to the time scale of the energy containing eddies.
Generally, a condition for invoking conservation of scalar
variance (6) to estimate fluxes is horizontal homogeneity,
which is clearly violated here. Still, the qualitative sense of
the estimates is consistent with shear-induced mixing as
described earlier : during the two flood events salt is mixed
downward as fresher water underruns saltier, and heat is
mixed upward because the introduced fresher water, being
near freezing, is slightly warmer than the water above,
which is also near freezing. In the single ebb event during
which fluxes were estimated, the opposite holds.
Figure 12. Conductivity measured in late winter in
McMurdo Sound near Erebus Glacier Tongue. Mast 1 conductivity meters (1 and 3 m below the ice/water interface)
were in supercooled water. The Mast 2 TIC was at 40 m, in
water about 20 mK above its in situ freezing temperature.
The arrow shows the difference in salinity (practical salinity scale) indicated by the conductivity difference at the
end of the period. The conductivity meter at 1 m was
pumped; the meter at 3 m was not.
entists (NIWA project K132). In late October 2010, we
deployed a mast identical to the FMS mast about 140 m
from the glacier tongue with TICs 1 and 3 m below the ice,
along with a second mast nearer the tongue that could be
lowered to depths exceeding 60 m. The water column was
close to isothermal in the upper 60 m, reaching its pressuredependent freezing temperature at a depth of about 15 m,
above which the water was supercooled. This was confirmed by platelet ice growth to that level on the cable suspending the second mast. After a few days, nucleation of
ice on the mast 1 (shallow) ADVs degraded performance
enough to warrant its recovery ; however, during the
deployment period one of the SBE4 conductivity meters
(not pumped) exhibited behavior somewhat reminiscent of
the experience at FMS (Figure 12). Conductivity at 3 m
decreased by steps, apparently related to the dominant diurnal tidal cycle at Erebus Glacier Tongue. By DOY 303 (30
October 2010), its conductivity indicated salinity about 0.2
psu less than 2 m higher, which is physically untenable.
None of the other conductivity sensors at the station
showed a similar drop: e.g., a TIC stationed at 40 m depth
for about 3 days, approximately 100 m away (þ symbols),
is slightly greater than at 1 m, consistent with a small salinity gradient observed in the upper 50 m. As before, we attribute the drop in conductivity of the 3 m instrument to
slow accretion of a layer of ice on the duct housing the
SBE4 electrodes, slowly reducing its diameter and increasing measured resistivity. Unlike FMS, there was no source
of above freezing water to remove the ice layer. It might be
appropriate to point out that, had the 3 m conductivity cell
been our only source of salinity data, a reasonable but false
inference would have been that each tidal cycle brought
slightly fresher water into the local region.
3.2. Conductivity Measurements in Supercooled
Seawater
[33] Given the premise that the low-conductivity events
indicate nucleation on the instrument electrode surfaces
and thus signal the presence of supercooling, Figures 1 and
2 show that nucleation occurred on the RDCP sensor in
four different episodes encompassing both flood and ebb of
two tidal cycles, whereas it appeared on the two SBE4
standard conductivity sensors only during the first flood
cycle, early on day 82. The SBE7 microstructure instrument never exhibited a sustained dropout in the same way.
A possible explanation for this difference among the sensors might be variations in surface curvature of the electrodes: the flatter the surface, the less resistance to developing
an ice coating. Mixing intensity might also play a role: the
TICs were deployed under very smooth ice, while the
RDCP was closer to highly deformed areas.
[34] Subsequent to the 2007 Storfjorden project, one of
us (M.G.M.) had an opportunity to again deploy TICs in a
supercooled seawater environment, near Erebus Glacier
Tongue, Antarctica, in collaboration with New Zealand sci-
3.3. Supercooling by Mixing: Double-Diffusion
Hypothesis
[35] The low-conductivity events occurred (Figure 2)
near peak tidal flow when a sharp front in salinity passed
our measurement site as it rode the tide in and out of the
11
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
tude smaller than scales associated with convection
measured at the edge of a freezing lead [McPhee and Stanton, 1996]. Third, the only plausible source for replenishing
melted frazil would be advection from outside (flood), yet
the supercooling appears on both the flood and ebb cycles.
Finally, a conductivity-temperature-depth (CTD) station
taken at the edge of the fast ice near slack tide, in the water
mass representative of the interior sound [Skogseth et al.,
2013, Figure 18], shows no evidence of water with temperature below the surface-pressure freezing point, a requirement for the heat pump mechanism.
entrance to FMS. Given our interpretation of the events as
signaling the presence of supercooled water (but not its true
magnitude), it thus appears that zones of local supercooling
were embedded within the front. In what follows we examine the hypothesis that this supercooling resulted mainly
from vertical mixing of heat and salt characteristics of the
two different water masses separated by the front, and that
the supercooling occurred because heat was transferred
locally faster than salt. In other words, we are suggesting a
process by which supercooling occurs by double-diffusive
mixing processes within the water column, and not from
direct surface or boundary heat and salt transfer.
[36] The hypothesized process involves two elements:
first that the frontal passage induced significant vertical
gradients in T and S, and consequent turbulent mixing; and
second, that double-diffusive mixing caused localized
supercooling in the water masses that were separately very
close to their salinity controlled freezing temperatures. The
former is a fairly straightforward consequence of vertical
shear near the fast-ice boundary acting upon the horizontal
gradients, as demonstrated earlier. The latter is less
obvious, and in fact requires some violation of Reynolds
analogy, i.e., that eddy viscosity and scalar eddy diffusivities are all about equal in highly turbulent flow. If turbulent diffusivities are the same for all scalars (Reynolds
analogy), then combining two water masses with different
salinities, each at its in situ freezing temperature, would
result in a mixture still at its freezing temperature (departure from freezing due to the miniscule curvature in the
UNESCO freezing formula was found to be negligibly
small), i.e., there would be no supercooling. However, in
the mixing process, if thermal eddy diffusivity exceeds haline eddy diffusivity, then heat would transfer from the
fresher, warmer water type to the saltier, colder water faster
than salt moved in the opposite direction, in effect supercooling the fresher constituent. Note that this process could
occur regardless of the flow direction; only the mixing intensity would change depending on the direction of the salinity flux.
[37] We considered an alternative hypothesis, based on
the ‘‘heat pump’’ concept. Suppose that at slack tide the
water column was isothermal at its surface-pressure freezing temperature, and that a layer of frazil crystals had collected near the ice/water interface. As the tide
strengthened, turbulent eddies generated by shear would
mix the frazil downward. At depth, the frazil would encounter water above its in situ freezing temperature and
melt, thereby producing water that would appear supercooled as it was mixed back toward the surface, accounting
for the transient events observed at shallow depths during
the flood and ebb tides. In this view, supercooling near the
surface would result from large-scale vertical mixing,
rather than mixing associated with sheared horizontal temperature and salinity gradients during frontal passage. Their
only impact would be in changing the turbulent forcing as
described in section 2.2. Our data posit several objections
to this scenario. First, there is little evidence in either the
conductivity or ADV records of frazil either collecting or
passing through levels 1 and 3 m below the interface, during the supercooling events. Second, the vertical turbulence
scales inferred from flow statistics (Figure 7a) do not suggest deeply penetrating eddies. They are an order of magni-
4.
Summary
[38] Despite its short duration, our measurement program near the edge of fast ice in FMS provided a fascinating look at processes that occurred when a relatively
narrow front separating water masses with different salinities and temperatures near freezing encountered a fixed
upper boundary as it rode on a strong tidal current. Turbulence measurements near the ice/water boundary confirmed
that vertical shear of the horizontal density gradient had
significant impact on stress and TKE production and dissipation (section 2.3). These results were confirmed by turbulent flux of scalar quantities, at least qualitatively (section
2.3).
[39] The FMS measurements also provided an opportunity to observe concurrently the performance of multiple
conductivity meters when conditions hovered near the in
situ freezing temperature. Our preferred explanation for
sudden drops in conductivity observed at different times on
the various instruments is that when the sensors encountered supercooled water, ice accreted on surfaces housing
the electrodes, increasing apparent resistivity. In our interpretation, small modifications to sensor geometry induced
changes to resistivity that implied transient events of large,
but not wholly unrealistic supercooling (Figure 1b). Considered in isolation without the context provided by other
nearby measurements, it would have been natural to accept
these at face value. This suggests caution in interpreting
conductivity data from an isolated instrument in water that
may be potentially supercooled.
[40] Despite the rather strange response of our conductivity measuring instruments during passage of the salinity
front, we believe they indicated transient supercooling
events, and that double diffusion provides a plausible
mechanism for their occurrence. A drawback to this explanation for the supercooling events is that it directly challenges strict application of Reynolds analogy for scalar and
momentum transfer in a flow with very high turbulent
Reynolds number [e.g., Hinze, 1975]. There are, of course,
well-known examples of double diffusion in the ocean, but
most are associated with low turbulence levels. An exception is an event reported by McPhee et al. [2005], who
showed that heat had been extracted from the upper pycnocline faster than salt, when an upwelling episode apparently
forced by Ekman pumping during horizontal ice shear,
encountered a highly turbulent boundary layer. These
results are not inconsistent with a laboratory study reported
by Krylov and Zatzepin [1992], who found evidence of
double diffusion at relatively high turbulence levels in a
12
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
ability. There were two aspects to this. First, there were
short periods when dramatic drops in conductivity (and
inferred salinity) occurred, which we view as artifacts of
supercooling behavior as discussed in section 2. Excluding
these periods, it is clear that a sizable offset between the
SBE sensors and the RDCP sensor persisted throughout the
deployment. Although at the scale shown, the SBE4 conductivity sensors agree reasonably well, the higherfrequency response of the pumped TIC1 SBE4 instrument
is suspect as described later. For this reason we placed priority on carefully calibrating the microstructure (SBE7)
instrument mounted with TIC1. The SBE7 mC time series
calculated using the factory calibrations is included to illustrate that although the mean value is obviously biased low
compared with the others, its deviations from the mean are
comparable in magnitude to the others.
[44] Based on previous experience, we anticipated that
the pumped apparatus in TIC1 would provide adequate frequency response for calculating salinity and buoyancy
flux; however, we found upon analysis that the TIC1 conductivity record showed much less high-frequency variation than either the mC or TIC2 (standard SBE4,
unpumped) sensors. Furthermore, its response to rapid variation in salinity appeared to noticeably lag in comparison
stirred, salt-stratified tank and suggested that it was important in frazil ice production.
[41] If our hypothesis for how supercooling can result
from mixing at a boundary between cold water masses with
differing salinities withstands further observational scrutiny, it suggests a novel mechanism that depends only on
mixing within the water column and requires neither surface heat and salt exchange as in latent heat polynyas
[Skogseth et al., 2008], nor large changes in pressure as
encountered in ice shelf cavities.
Appendix A: Adjustments to T and S Time Series
[42] The combination of two TICs plus the nearby
RDCP sensors provided three independent temperature
time series and four separate conductivity records (Figure
A1), all taken relatively near the ice-ocean interface. In
general, the TIC (Sea-Bird Electronics SBE3) temperatures
agreed well (within 1–2 mK). Both have higher resolution
and read somewhat warmer than the RDCP temperature
(Figure A1a). We reconciled the RDCP temperature with
the SBE sensors by applying a constant correction of
0.008 C.
[43] Time series of conductivity from the standard SBE4
and RDCP sensors (Figure A1b) showed much greater vari-
Figure A1. (a) One-minute average raw temperature records from TICs 1 and 2, plus the RDCP. (b)
Conductivity from standard (SBE4) conductivity meters for TICs 1 and 2, and RDCP (solid traces), and
for the microstructure conductivity sensor with factory calibrations (dashed).
13
MCPHEE ET AL.: SUPERCOOLING INDUCED BY TURBULENT MIXING
sudden shifts in mC output, we found that the slope of the
linear relation between mC frequency and conductivity at
TIC2 was not significantly different from the factory calibration, but that the intercept (i.e., actual calibration) varied
more or less predictably over the deployment period (Figure A2), as illustrated by the polynomial fit with time. Consequently, we estimated the actual conductivity at TIC1 as
C1 ¼ mfC þ bðtÞ, where b(t) is from the cubic fit.
[46] Apart from the ‘‘dropout’’ events discussed in section 2, there was an obvious offset between the RDCP and
TIC2 conductivities (Figure A1). Again assuming CTIC2 to
be correct, we applied a constant correction to CRDCP
(0.013 S m1) so that mean values over a common measurement period when there was little change agreed with
CTIC2.
[47] Acknowledgments. We thank A. Sirevaag for suggesting
improvements to this manuscript. Support for this research was provided
by National Science Foundation grants ARC-0856214 and ANT-0739371
(M.G.M.) and by the IPY project Bipolar Atlantic Thermohaline Circulation (BIAC) and the Storfjorden Polynya Air Sea Ice Exchange Experiment (POLRES grant 196145) from the Norwegian Research Council
(R.S., F.N., and L.H.S.). We thank two anonymous reviewers for helpful
comments. We will also thank the captain and crew at the Norwegian
coastguard vessel K/V Svalbard for superb service and invaluable help
during the FMS field campaign.
Figure A2. Polynomial fit to mC intercept b ¼ mfC CTIC2 , where fC is the realization-average mC frequency, m
is the factory calibration slope, and CTIC2 is the average
conductivity at TIC2, assumed correct.
with the others. For practical purposes, at low temperatures
conductivity of both the standard and mC SBE instruments
is proportional to the frequency output. By normalizing departure of instrument frequency from the mean by its standard deviation over a suitable averaging interval, we were
able to show that maximum lagged correlation between the
pumped and mC instruments occurred with a lag of about
25 s. Shifting the pumped time series forward in time by 25
s resulted in reasonably good correspondence with the other
two sensors, except for damping of higher-frequency fluctuations. While it is not obvious why the response of the
pumped SBE4 instrument lagged both the collocated SBE7
(mC) and the lower (unpumped) SBE4 instruments, we note
that in the pumped pair, the plumbing that routes fluid from
the thermometer to the conductivity cell includes two rightangle bends. It is possible that enough ice formed and
remained in these constrictions to retard flow past the conductivity sensor by the observed lag. During the 2007 exercise, similar deployments were made at two other sites with
water temperatures slightly above freezing, both before the
FMS study (in Van Mijenfjorden) and after (Barents Sea).
In those conditions, we found no evidence of similar lag
between the standard SBE4 instrument and collocated mC
instruments on TIC1, nor with timing of larger-scale features observed at TIC2, 2 m lower.
[45] The SBE7 mC instruments produce a signal frequency that is related linearly to conductivity over the limited range of conductivities encountered in the study. In
previous deployments, mC instruments used in combination
with the standard SBE4 conductivity meters have often
shown significant drift in absolute calibration [McPhee and
Stanton, 1996; McPhee et al., 2008; Sirevaag et al., 2010],
in addition to occasional sudden shifts in output frequency.
This presents an obvious interpretation problem, particularly in our case where the collocated SBE4 (pumped) conductivity time series appeared to lag the other instruments
as described earlier, possibly associated with icing problems. By examining 15 min segments of data during which
salinity varied significantly, and for which there were no
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