1. Introduction
The sea ice environment of the Arctic Ocean has been rapidly changing over the past few decades. Near-continuous satellite observations, which began in the late 1970s, indicate that sea ice extent is decreasing, multiyear sea ice is disappearing, and the duration of the annual ice growth season is getting shorter (Carmack et al. 2015; Comiso 2012; Stammerjohn et al. 2012). Models predict that the Arctic will have nearly ice-free summers sometime in this century (Overland and Wang 2013). Warming atmospheric temperatures have largely contributed to these changes (Maykut and McPhee 1995), but oceanic heat stored year-round from summertime warming also plays a significant role in melting sea ice (Jackson et al. 2010; Carmack et al. 2015).
In the Arctic Ocean, where density is largely controlled by salinity, a salinity-driven layering of water masses allows reservoirs of ocean heat originating from the Atlantic and the Pacific to sit beneath the surface. Atlantic water enters through Fram Strait, between Greenland and Svalbard and reaches the Canada Basin at depths below 300 m with temperatures above 0.5°C (Coachman et al. 1975). The only exchange of mass, heat, and salt between the Arctic and Pacific Oceans is through a small channel, Bering Strait, which separates Asia and North America (Fig. 1). The strait is only 50 m at its deepest and 85 km wide with two islands occupying about 9 km of distance in the center. After transiting through Bering Strait, Pacific water is modified on the Chukchi shelf and reaches the Canada Basin with densities between those of Arctic surface waters and Atlantic-origin water, creating a subsurface temperature peak (Jackson et al. 2010). Strong salinity-driven stratification acts as a barrier on either side of the Pacific water: it limits the upward flux of heat from Atlantic water into the surface layer and it constrains the depth over which convection occurs in the upper ocean (Coachman and Barnes 1961; Toole et al. 2010; Timmermans et al. 2017). This strong halocline prevents mixing of warm Pacific water into the upper ocean even during energetic storms (Lincoln et al. 2016). However, the warm halocline is ventilated during the summer when warm Chukchi Sea waters migrate north into the basin—wind-driven Ekman convergence and subduction create a pathway of heat transport from the Chukchi shelf to the warm halocline (Timmermans et al. 2017). In this way the temperature and salinity characteristics of Chukchi Sea summer water are influential in setting upper Arctic stratification.
Map of the study area. The red box outlines the boundaries of the map shown in Fig. 3, below. Bathymetry is shown in colors, and black contours denote the 50-, 100-, and 1000-m isobaths.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
Chukchi seawater properties are influenced by the properties of water entering through Bering Strait. Despite its small size, Bering Strait provides significant heat and freshwater fluxes to the Arctic Ocean: Pacific water comprises 30% of the freshwater flux into the Arctic (Serreze et al. 2006), and the heat flux through Bering Strait is enough to account for one-third of the Arctic sea ice retreat every year (Woodgate et al. 2010). Between 1990 and 2015, heat and freshwater fluxes through Bering Strait increased notably (Woodgate 2018), and these changes are reflected in the increasing heat and freshwater content of the Pacific summer water layer in the central Canada Basin (Timmermans et al. 2014). Some of this heat triggers summer ice melt by opening up the ice pack and allowing more solar radiation to be absorbed by areas of open water (Serreze et al. 2016): via this mechanism, April–June heat flux through Bering Strait explains 68% of the variance in the timing of sea ice retreat in the Chukchi Sea. Some of the Pacific water subducts under cooler, fresher Arctic surface waters and it remains a subsurface heat source throughout the year (Woodgate et al. 2010), sometimes in the form of mesoscale eddies, which have been observed with core temperatures as high a 6°C (Fine et al. 2018). Transport through Bering Strait, therefore, has important effects on the sea ice and stratification conditions of the Chukchi Sea and the Pacific sector of the Arctic Ocean.
Schematic representation of the three-term balance among the pressure gradient force, wind stress, and bottom stress used to describe transport in Bering Strait.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
The along-strait wind stress drives an across-strait Ekman transport fu, which is small relative to the along-strait terms but leads to a cross-strait sea surface height difference ηx [Eq. (1b)]. Northward flow in Bering Strait is known to be largely in geostrophic balance with the cross-strait pressure gradient that results from ηx (Spaulding et al. 1987; Woodgate 2018).
In this paper, we will present the first measurements of TKE dissipation reported in Bering Strait and use them to compute a bottom drag coefficient. Bottom drag plays a first-order role in the momentum balance that regulates transport through Bering Strait. In their transport model, Coachman and Aagaard (1966) used a drag coefficient of 3.3 × 10−3 following Sternberg (1965), who made stress measurements over a bottom similar in roughness to that in Bering Strait. Subsequent studies followed this precedent. Here, we compute a value from friction velocities derived from measured velocity profiles and measured dissipation rates of TKE in the bottom boundary layer.
Turbulent mixing controls the modification of Pacific water as it transits from the Bering to the Chukchi Sea. Modeling studies have shown that there is significantly elevated eddy kinetic energy in Bering Strait when compared with the Bering and Chukchi shelves and that eddy kinetic energy is often associated with areas of active mixing in the physical world (Clement et al. 2005). Between 1990 and 2015, transport through Bering Strait increased at an average rate of ~0.01 Sv yr−1 (1 Sv ≡ 106 m3 s−1) (Woodgate 2018). The increase in transport led to a 150% increase in kinetic energy, which has presumed but unknown consequences on bottom mixing rates (Woodgate 2018). We employ an advection–diffusion model to examine the transformation of water properties associated with the mixing rates we observed in Bering Strait.
We begin, in section 2, by summarizing the efforts that have been made until now to understand the balance of forces controlling transport through Bering Strait. We describe our observational methods in section 3. In section 4 we present our hydrographic observations, including microstructure measurements made in Bering Strait. We present a bottom drag coefficient computed from these observations. In section 5, we discuss the effect of bottom drag on the momentum balance in the strait and comment on the watermass modification driven by the observed mixing. We conclude with a summary and outlook for future studies.
2. Drivers of transport in Bering Strait
Estimates of transport through Bering Strait have been made since the 1930s when Ratmanov (1937) measured current velocities for up to 25 h at anchor stations in both the western and eastern channels (Barnes 1938; Ratmanov 1937). These early observations indicated that the average flow was northward and that it was stronger during summer than during winter. Shtokman (1957) was the first to suggest that the generally northward flow through Bering Strait was driven by a downward sloping sea surface height difference between the Pacific and Arctic Oceans. He assumed a model in which the pressure gradient force caused by the sea surface slope balanced the wind stress and the bottom stress created by friction between the seafloor and the flow.
In the succeeding decades, similar models were used to predict transport from wind speed and to estimate the magnitude of the pressure gradient (Coachman and Aagaard 1966, 1988; Spaulding et al. 1987; Woodgate et al. 2005b). Using a two-dimensional, vertically averaged model of the region surrounding Bering Strait, Spaulding et al. (1987) found that velocity and transport scaled linearly with the imposed sea surface slope. A consensus grew that flow through Bering Strait is dominantly controlled by the pressure difference between the Bering Sea and the Arctic, and that the winds modify the flow. Linear regressions between monthly averages of current velocities and wind speeds have been used to estimate the influence of the pressure head (which is assumed to be relatively constant on these time scales) and the wind on transport (Aagaard et al. 1985; Coachman and Aagaard 1988; Woodgate et al. 2005b). In an oversimplified view, a steric height difference of ~0.7 m (Aagaard et al. 2006; Stigebrandt 1984) leads to a sea surface slope of ~10−6 (Coachman and Aagaard 1966; Coachman et al. 1975; Shtokman 1957) that maintains an annual average northward transport of ~0.8 Sv (Coachman and Aagaard 1988; Coachman et al. 1975; Ratmanov 1937; Roach et al. 1995; Shtokman 1957; Woodgate et al. 2005a).
These regressions explain about one-half of the transport variance during winter and a quarter during summer, when flows are stronger and when the seasonal Alaskan Coastal Current (ACC) is present (Danielson et al. 2014). The ACC is a surface-intensified warm and fresh current that is generally coastally trapped east of the 40-m isobath (Woodgate and Aagaard 2005). Transport through the strait is variable on hourly to interannual time scales (Aagaard et al. 1985; Coachman and Aagaard 1966, 1988; Coachman et al. 1975; Roach et al. 1995; Woodgate et al. 2005a,b). Annual transport anomalies are as large as 30% of the long-term average (Woodgate et al. 2012). Variations on hourly to monthly time scales are attributed to local winds (Aagaard et al. 2006) and continental shelf waves that are generated far from the strait by nonlocal winds (Danielson et al. 2014). In addition to seasonal and annual variability, there has been a long-term increase in transport. Two-thirds of this change can be attributed to an increase in the far-field pressure gradient (Woodgate et al. 2012).
The cause of the pressure gradient is still unknown. Gudkovich (1962) theorized that it was driven by wind patterns over the Arctic. It is now more commonly assumed to be steric in origin (Aagaard et al. 2006; Stigebrandt 1984; Wijffels et al. 1992), but there is no consensus on the causes of long-term change in sea surface height difference. For example, model results from Danielson et al. (2014) suggest that the increase in transport through Bering Strait can be explained by increasing sea surface height in the Bering Sea, while satellite observations analyzed by Peralta-Ferriz and Woodgate (2017) indicate that ocean bottom pressure in the Arctic is strongly correlated with the northward flow through the strait.
Arctic models are still in need of improvement in order to satisfactorily match observational data. There are still significant discrepancies between modeled and observed heat, salt, and volume fluxes through Bering Strait (Clement Kinney et al. 2014). In addition to uncertainty about the source of the pressure head, models suffer from uncertainty in the choices of wind stress parameterization, bottom drag coefficient, and the treatment of sea ice, stratification, and tides (Danielson et al. 2014). In this paper, we attempt to reduce some of the uncertainty in the bottom drag coefficient.
3. Methods
The ArcticMix project was a National Science Foundation–funded cruise on the R/V Sikuliaq during September of 2015. Its overall goal was to understand the physical processes that control the distribution of heat and salt in the Beaufort Sea and how they may be affecting the rate of Arctic sea ice loss. The Bering Strait was sampled during 24 and 25 September at high spatial resolution using towed instruments across three transects. The Modular Microstructure Profiler (MMP) measured turbulence across the middle of the strait, from Cape Prince of Wales to the Diomedes Islands at the center of the channel, marking the border between U.S. and Russian waters (Fig. 3, subplots labeled ii). The Shallow Water Integrated Mapping System (SWIMS) measured temperature, salinity, and density along cross-strait transects ~45 km to the north and ~19 km to the south of the middle transect (Fig. 3, subplots labeled i and iii, respectively).
Hydrographic data collected during the cruise (24–25 Sep 2015): (a) wind vectors from the ship’s masthead—red, yellow, and green shading respectively mark the time periods when the north, middle, and south sections were occupied [as shown with the thick lines in corresponding colors in (b)], (b) wind (dark blue), depth-averaged currents (light blue), and the A2 (blue; western midchannel), A3 (orange; northernmost), and A4 (green; eastern midchannel) moorings maintained by the Applied Physics Laboratory at the University of Washington, (c) northward current speed, (d) eastward current speed, (e) temperature, and (f) salinity. Potential density contours are shown in (c)–(f) at 0.2 kg m−3 intervals between 1024.8 and 1026.2 kg m−3, with 1025.2 and 1025.8 kg m−3 as thicker lines. Map contours show the 10-, 20-, 30-, 40-, and 50-m isobaths, and geographic features are labeled DI (Diomedes Islands) and CPW (Cape Prince of Wales). Colored arrows in (c) show the ship’s direction of travel.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
a. SWIMS
The SWIMS package is a towed frame equipped with a CTD and upward- and downward-looking ADCPs. This instrument package was winched up and down while being towed behind the ship at approximately 5 kt (1 kt ≈ 0.51 m s−1) along the northern and southern transects (Fig. 3). Profiling to within 5 m of the seafloor, this led to profiles separated by less than 100 m. Unfortunately, the downward-looking ADCP stopped functioning earlier in the cruise before sampling in Bering Strait began. Since it tracks the bottom, which allows the velocities from both instruments to be transformed into Earth coordinates, this meant losing functionality of the upward-looking ADCP as well. Only the CTD data are used from this package. The CTD sampled at 24 Hz, and data were binned to 0.5 m.
b. MMP
The MMP is a loosely tethered, free-falling instrument package with redundant pairs of temperature and shear probes mounted facing downward to sample undisturbed water as it falls through the water column (Alford and Gregg 2001; MacKinnon and Gregg 2003). The instrument is allowed to fall freely, slowed by drag screens interspaced with foam at the top to achieve an optimal downward speed for resolving vertical velocity shear. The shear spectra from velocity fluctuations measured at centimeter scales are used to estimate rates of TKE dissipation ε (Wesson and Gregg 1994). A pumped CTD is also mounted to the MMP to measure temperature, salinity, and density at scales similar to SWIMS. The horizontal spacing between MMP profiles was about 200 m.
c. Shipboard velocity
A 300-kHz RDI ADCP was mounted in an open well in the ship’s centerboard. Velocity data were averaged from 1-Hz pings at 1-min intervals between 10-m depth and within 5 m of the seafloor at a vertical spacing of 2 m. They were smoothed in time over 10 min to reduce noise variance (Alford and Gregg 2001) and linearly interpolated to the locations of the SWIMS and MMP profiles.
d. Surface heat fluxes
Surface heat fluxes were calculated using the COARE 3.0 bulk flux algorithm (Fairall et al. 1996, 2003). Sea surface temperature measurements came from the ship’s pyrometer, at 0.05-m depth. Cool skin temperature was taken from the ship’s intake at 6-m depth. Both cool skin and warm layer corrections were applied; cool skin had a ±0.2°C effect and the warm layer had a negligible effect. Uncertainty in net surface heat flux is 10 W m−2 (Fairall et al. 2003; Cronin et al. 2006).
e. Contextual data sources
Wind reanalysis, and data from three nearby moorings are included in the analyses to put our shipboard observations in context of larger spatial and temporal scales (Fig. 4). The 10-m wind reanalysis data are taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) 10-m reanalysis product, which is gridded to 2.5° × 2.5° and computed as instantaneous values four times daily (Kalnay et al. 1996); 10-m winds were also measured from the ship’s masthead. When ship data are interpolated to the 6-h interval of the reanalysis data, the sources are in good agreement (correlation coefficient R > 0.9, Fig. 4).
Time series of (a) northward and eastward components of NCEP–NCAR reanalysis wind velocity (black) and wind velocity measured on the ship’s masthead (purple) and (b) northward current speed, (c) eastward current speed, (d) temperature, and (e) salinity from the bottommost measurements at the A2 (blue), A3 (orange), and A4 (green) moorings and the bottommost observations from ship measurements (purple). Ship wind and current data were low-pass filtered at 1 h. The timing of the shipboard measurements made on the north (N), middle (M), and south (S) sections is indicated by gray shading.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
Temperature, salinity, and current velocity data are taken from three moorings, which were deployed and serviced by the High Latitude Dynamics group at the University of Washington (Woodgate et al. 2015; Woodgate 2018). Currents were measured throughout the water column by upward-looking ADCPs while temperature and salinity were measured at single point locations near the bottom: 49, 43, and 41 m at moorings A2, A3, and A4, respectively (Fig. 3). Accuracy of the current data above 10 m is unreliable, so we focus on the data below this depth.
4. Results
a. Hydrographic observations
The properties of potential temperature θ and salinity S in our observations cluster around two endpoints in θ–S space with a mixing line between them (Fig. 5). A warmer, fresher endpoint is centered at θ = 3.7°C, S = 32.7. This water fills the eastern side of the channel and the surface waters. A cooler saltier endpoint is centered at θ = 5.3°C, S = 31.5 and fills the western side of the channel and the lower half of the water column. The entire population of water properties spans a potential density range of 1.3 kg m−3.
The θ–S diagrams overlaid with contours of potential density σθ of three sections colored by section; θ–S from moorings A2 and A4, at depths of 49 and 41 m, respectively, is shown at 6-h intervals for 15–23 Sep. They decrease in temperature and increase in salinity over that time period.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
The θ–S properties of all the water observed along the three shipboard sections fall within the range of seasonally warmed Pacific summer water, which, itself, consists of two water masses, Alaskan coastal water and summer Bering seawater (Timmermans et al. 2014). Alaskan coastal water, which we find on the eastern side of the channel, is a late-summer water mass that originates near the Alaskan coast south of Bering Strait and enters the Chukchi Sea with temperatures above 3°C (Gong and Pickart 2015). It is formed from colder, more saline Bering Sea winter water that has been warmed by solar radiation and diluted by freshwater runoff from the Alaskan coast (Coachman et al. 1975). summer Bering seawater, which we find on the western side of the channel, is saltier and cooler and originates from the Gulf of Anadyr (Coachman et al. 1975; Timmermans et al. 2014).
About a week prior to shipboard sampling a warmer, saltier water mass was observed at moorings A2 and A4 at depths of 49 and 41 m, respectively (Fig. 5). This water mass can be seen in θ–S space on the southern and middle lines, and it appears to have been eroded away on the northern section.
The three sections were sampled from north to south over 42 h on 24 and 25 September 2015. At the beginning of sampling, winds were predominantly from the south, but they had been blowing moderately from the north for two days prior (Fig. 4). During this time, the current at all depths flowed northward and the water column was strongly stratified except very near the Alaskan coast (Fig. 3). Between the middle and southern transects, the winds reversed and began blowing strongly from the north. Almost immediately, the current reversed and began flowing to the south at all depths.
During sampling of the northern section, a rapid warming and freshening of the bottom water occurred at mooring A4, closest to the Alaskan coast (Figs. 4d,e). The cause of this abrupt change in watermass properties is unknown but could be explained by a meander of the front defining the edge of the ACC. This physical context is important to keep in mind as we evaluate the effect of mixing rates in later sections—the observations were made during a transition period. The influx of warm, freshwater, followed by the wind and current reversal, preclude us from considering the three sections as a snapshot view of the strait.
b. Observed rates of energy dissipation
Our observations of ε, N2, and Kρ are shown in Figs. 6 and 7 along with shear squared
Section plots of (a) wind and bottom stress, (b) TKE dissipation rate, (c) diapycnal diffusivity, (d) squared buoyancy frequency, (e) squared vertical shear, and (f) inverse Richardson number. Contours of potential density difference are shown at 0.2 kg m−3 intervals between 24.8 and 26.2 kg m−3. Data were measured by the MMP and ADCP along the middle section between the Diomedes Islands and the Alaskan coast (yellow bar in Fig. 3b and middle row in Fig. 3c).
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
Profiles of (left) density and velocity, (left center) squared buoyancy frequency and squared vertical shear, (center) inverse Richardson number, (right center) turbulent kinetic energy dissipation rate, and (right) diapycnal diffusivity. Data were measured by the MMP and ADCP at points (top) on the west side, (middle) in the center, and (bottom) on the east side of the middle section across Bering Strait (Fig. 3). Gray shading shows the bottom boundary layer height, defined by the approximation of the ε profile to a 1/z fit. Black shading shows bathymetry.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
High stratification in the middle of the channel coincided with an area of low dissipation. On the western side, velocities were slower, but stratification was very low and dissipation rates were high. Dissipation rates were elevated near the bottom, particularly on the eastern side of the channel where the depth is shallower and current velocities are stronger due to the presence of the Alaskan Coastal Current. Average dissipation rates near the bottom boundary were 10−7–10−6 W kg−1 with values as high as 3 × 10−5 W kg−1. Near the Alaskan coast, the highest measured values were 10−3 W kg−1. These rates are high for the coastal ocean (e.g., Moum et al. 2002; MacKinnon and Gregg 2003; Shao et al. 2018) but not uncommon (e.g., Simpson et al. 1996; Shao et al. 2018). They are similar in magnitude to dissipation rates observed at flow constrictions or over shallow banks and sills where the acceleration of flow approaching an obstacle is known to create turbulence (e.g., Wesson and Gregg 1994; Polzin et al. 1996; Moum and Nash 2000; Nash and Moum 2001; Jarosz et al. 2014). The diapycnal diffusivities observed here, however, are elevated above those observed in other regions of strong turbulence. Using section averages denoted by the overbars, we computed the average diapycnal diffusivity,
c. Sources of boundary layer turbulence
The surface and bottom boundary layers of the ocean are characterized by turbulent eddies that impact the buoyancy and momentum fluxes within those layers. At the seafloor, stress is exerted by the rigid boundary on the current flowing above it and the resulting vertical velocity shear can lead to shear instabilities and overturns. In Bering Strait, the current velocity is largely driven by large-scale pressure gradients (Peralta-Ferriz and Woodgate 2017), with a small contribution from tides. Using “t_tide” (Pawlowicz et al. 2002), tidal frequencies were isolated from a year-long along-strait velocity time series measured near the bottom at mooring A2 between July 2015 and July 2016 (Figs. 3, 4). Over the course of the year, the strongest current velocities were ~80 cm s−1. Combined diurnal (K1, O1) and semidiurnal (M2, S2) tidal variance had maximum amplitudes of ~4 cm s−1 and explained less than 1% of the total variance in along-strait velocity. Little of the velocity shear in Bering Strait can be attributed to tides.
Lateral processes associated with vertical velocity shear can work to move light water under dense, creating convective or gravitational instabilities. For example, when flow is northward along a continental shelf that slopes upward to the east with density decreasing to the east, as we find on our middle section, bottom Ekman transport is directed westward and the vertical shear acting on the lateral density gradient can pull lighter water under dense in the boundary layer leading to an increase in convectively driven turbulence and a thickening of the layer (Moum et al. 2004). Shear can also be generated where there are lateral constrictions due to topography causing the flow to accelerate. We see evidence of this flow constriction and acceleration in the cross-strait component of velocity on the middle section across Bering Strait (Fig. 3) and in the fact that along-strait current speeds are almost always stronger at mooring A2 (at the narrowest part of the strait) than those at mooring A3 (north of the strait; Fig. 4).
At the surface, wind stress creates turbulence through shear instability, while ocean–atmosphere temperature gradients drive convective fluxes at the surface. Because of contamination of data by the ship’s wake, we do not have enough near-surface measurements of ε to evaluate the relative importance of convection and wind stress on turbulence in the surface layer. We focus, instead, on the bottom boundary layer and the extent to which bottom drag affects turbulence and the watermass modification.
d. Estimating the bottom drag coefficient
Equation (5) represents the dissipation method for estimating friction velocity within the boundary layer (Dewey and Crawford 1988; Perlin et al. 2005b; Wijesekera et al. 2014). For each profile, we determine the values of u* using a least squares fit to our measurements of ε from the deepest observation to the height above the boundary where ε can no longer be approximated by a 1/z profile. This height ranged from 7 to 27 m, with an average value of 12 m.
Several studies have shown that the profile method tends to predict much higher friction velocities than the dissipation method (Dewey and Crawford 1988; Johnson et al. 1994; Taylor and Sarkar 2008). When stratification in the BBL is sufficiently large, the stratification becomes the factor that limits the size of turbulent eddies rather than the distance from the boundary, and the logarithmic decay occurs in two distinct layers (Perlin et al. 2005b). For this reason, Perlin et al. (2005b) introduced a modified profile method, which simultaneously fits both log layers and improves the agreement with u* computed using the dissipation method. They found that the median ratio of the friction velocities calculated using the profile method to those calculated using the dissipation method,
For each profile, we have estimates of u* using both the dissipation method and the modified profile method. We then compute a single value of Cd for each method by minimizing the least squares difference between
Dissipation method for computing u* and Cd. Three example dissipation profiles are shown from the east, center, and west of the middle section. A least squares fit of Eq. (5) to ε data in the bottom boundary layer (black horizontal line) is shown in green. Also shown are (left) individual estimates of
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
As in Fig. 8, but for the profile method. Three example logarithmic velocity profiles are shown, and a least squares fit of Eq. (8) to velocity data in the bottom boundary layer (black horizontal line) is shown in green.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
Individual values of Cd were also computed for each profile as
Histograms of Cd calculated from individual estimates of u0 and u* using the dissipation method (red) and the profile method (blue).
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
5. Discussion
a. Evaluating a new bottom drag coefficient for Bering Strait
Typical values of Cd used in Bering Strait are 3 × 10−3–3.3 × 10−3 (Coachman and Aagaard 1966; Danielson et al. 2014; Spaulding et al. 1987), an estimate that was based on observations of stress in a tidal channel within Puget Sound (Sternberg 1965). Here, we estimated Cd in Bering Strait using our direct measurements of TKE dissipation and velocity and determined a bottom drag coefficient of 2.3 × 10−3. This value is ~30% smaller than the value generally assumed for bottom drag in Bering Strait but is well within the range of global estimates of Cd (Feddersen et al. 2003).
A second possibility for the discrepancy is that our estimates of Cd are not representative of all conditions in Bering Strait. To evaluate this possibility, we consider the tide and wind conditions during our observations. Turbulence grows as the cube of near-bottom velocity [Eq. (6)], so turbulent dissipation rates can be expected to be elevated during the strongest tidal flows. However, since tidal variance only explains 1% of the variance in near-bottom flow in Bering Strait, we expect the tides to be an insignificant control on turbulence here. The turbulence and velocity measurements were made during a transition period when the wind changed from moderately strong northward to weakly southward, slowing the current as a result. Repeating the dissipation method [Eq. (6)] with subsets of the data binned by u0, we find that the least squares fit consistently replicates values of Cd within the 95% confidence intervals (Table 1) with the exception of the −6–0 m s−1 wind speed range, during which only two profiles were measured.
Drag coefficients measured using the dissipation method during different wind conditions.
With minimal contribution from form drag and tidal currents and an insensitivity of Cd to wind speed over several ranges, it is likely that the bottom stress environment of Bering Strait is in fact different from that of the Puget Sound tidal channel and that an appropriate value of Cd is lower than what has typically been used. Our estimate is based on observations of ε that we assume are created by bottom stress [Eqs. (5) and (6)]. As noted earlier, depending on the direction of flow, bottom Ekman layer advection of the cross-strait buoyancy gradient could work to increase ε by increasing bottom instability or suppress ε by increasing stratification. Since bottom Ekman transport would have been to the west (and therefore destabilizing) during our sampling of the middle line, we expect our estimate of Cd to be an upper limit.
In a model that included across-strait terms and a time-varying pressure head Danielson et al. (2014) predicted along-strait velocities that underestimated observed variance by a factor of 2. Some of the discrepancy between the model and observations may be explained by their choice of Cd. For a range of typical along-strait wind speeds between −20 and 20 m s−1, when we use a drag coefficient of Cd = 2.3 × 10−3, we predict a range of northward velocities through the strait that is 1.2 times greater than the range predicted when Cd = 3.3 × 10−3.
b. Estimates of watermass transformation in Bering Strait
The high rates of TKE dissipation measured in Bering Strait have the potential to significantly modify the watermass properties of Pacific water as it transits through the strait. The average diapycnal diffusivity measured on the middle section was 2 × 10−2 m2 s−1 (Fig. 11). The distribution was patchy with higher rates near the seafloor and in the weakly stratified western part of the section, and low rates in strongly stratified regions (Fig. 6).
(a) Example θ–S profiles from the western side of the south section (red) and the north section (blue). Orange, yellow, and green curves show the results of the advection–diffusion model for λ = 10, 20, and 30 m, respectively. (b) Transit times and diapycnal diffusivities predicted by λ = 10, 20, and 30 m. The shaded gray box indicates the range of values that would collapse the original (red) profile to a straight line in the time it took for water to transit from the south section to the north section. (c) Histogram of diapycnal diffusivities observed along the middle section.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
A temperature peak on midwater column density surfaces can be seen in the profiles collected on the south section, but is not present in the data collected on the north section (Fig. 5). Such a change can be modeled with a simple advection–diffusion model to estimate the diapycnal diffusivity required to cause the change over a given amount of time (e.g., Hautala et al. 1996; Voet et al. 2015). In our case, the complete reversal of flow direction precludes us from considering our southern section the “upstream” condition and our northern section the “downstream” condition. However, it is instructive to estimate the average diapycnal diffusivity that could account for the disappearance of the middepth temperature maximum during a northward transit through the strait.
Wind had been blowing steadily to the north for over a day before sampling began. The depth-averaged velocity at mooring A2 during this time period was used to determine the travel time required for a parcel beginning at the latitude of the southern line to arrive at the latitude of the northern line, assuming it transited at the speed measured by the mooring. Velocity fluctuated between 0.25 and 0.66 m s−1 for an average transit time of 36.6 h. The outer time bounds in Fig. 11 indicate the transit times that would result from the slowest and fastest speeds measured at the mooring during this time period being sustained.
The transformed profile becomes a straight mixing line between the surface and bottom water properties when λ is between 20 and 30, which corresponds to a diffusivity range of Kρ = 0.1 × 10−2 –1 × 10−2 m2 s−1. This agrees well with the values observed on the middle section (Fig. 11c) and is slightly less than their average value of 2 × 10−2 m2 s−1. This analysis shows that these diffusivities are capable of cooling Pacific summer water over a distance of 60 km by 0.1°C along isopycnals.
The turbulent vertical heat flux is estimated as Jq = ρCpKρdθ/dz and describes the magnitude and direction of heat that is transported vertically in the ocean as a result of turbulence. Here, Cp is the specific heat of seawater, equal to 4000 J kg−1 K−1, and negative values of Jq refer to downward flux. Since ε was only directly measured on the middle line, our best approximation of the Kρ profile experienced by the profile that initialized our advection–diffusion model is calculated with data from two profiles just to the west of the highest stratified section on the middle line (Fig. 12). One of the profiles had a depth-averaged Kρ of 1.3 × 10−2 m2 s−1 and fairly uniform diffusivities throughout the measured water column. The other had a depth-averaged Kρ of 2.7 × 10−3 m2 s−1 with the highest diffusivities found in the upper water column and values an order of magnitude lower near the bottom.
Profiles of vertical temperature gradient, diapycnal diffusivity, temperature, and vertical heat flux due to turbulent mixing measured just to the west of the highest stratified section on the middle line (the locations are noted in the left panels). Flux is downward for Jq < 0. Net surface heat flux of −20 ± 10 W m−2 (into the ocean) is shown with black line at 0–2 m.
Citation: Journal of Physical Oceanography 50, 3; 10.1175/JPO-D-19-0154.1
Where vertical heat flux is divergent, a water parcel is losing more heat out the bottom than it is gaining from the top, which leads to local cooling. Convergent heat flux means the parcel is gaining more heat from above than it is losing below and is thus warming. Net surface heat flux during the two days we occupied Bering Strait averaged −20 ± 10 W m−2 indicating a net warming of the surface ocean by the atmosphere. The pattern of divergent heat flux at the top of the water column and convergent heat flux at middepths is consistent with a cooling of the surface layer by moving heat from lighter to denser isopycnals. A similar pattern of divergence followed by convergence near the bottom suggests a similar transfer of heat to the densest isopycnals. This redistribution of heat between water masses can lead to the flattening of mixing lines described in Fig. 11a. Higher stratification and stronger turbulence in the first profile lead to a greater cumulative downward heat flux (Fig. 12).
During the time between sampling of the northern (first) and southern (a day later) sections, the bottom temperature measured at the A2 and A4 moorings warmed by 0.3°C and the salinity increased by 0.1. A similar difference is seen between the theoretical θ–S profile transformed from the southern profile by the advection–diffusion model and the observed northern profile (Fig. 11, the green line as compared with the blue dots). While the observed rates of turbulent dissipation can account for much of the difference in water properties between these locations, advection was also clearly important during the sampling period.
6. Summary
The first reported turbulence measurements made in Bering Strait reveal that rates of turbulent kinetic energy dissipation here are comparable to values observed over shallow banks and at flow constrictions in the deep ocean. The high turbulence was associated with high diffusivities, even during a period of moderate wind stress. Water cooled by up to 0.1°C and freshened by as much as 0.01 “practical salinity unit” (psu) over a distance of 60 km. Estimates of diffusivity from a simple advection–diffusion model predict vertical diffusivities on the order of 10−2 m2 s−1 to cause the observed watermass modifications. We observed diapycnal diffusivities matching and exceeding these inferred values along a cross section of the strait between the Diomedes Islands and the Alaskan coast.
We used our observations of turbulence within the bottom boundary layer to make an improved estimate of the bottom friction coefficient. We suggest that an appropriate value for the strait is 2.3 × 10−3, which is smaller than the value typically used and may help to improve models of transport in the region.
Surface observations of turbulent kinetic energy dissipation used in this study were contaminated by the ship’s wake because the instruments were deployed directly off the stern (the rear of the ship where the propellers create the most turbulence). Recently, efforts have been made to minimize this effect by making measurements off the port or starboard quarter (near the rear but to the side). Following similar methods as those presented in this paper for computing the bottom drag coefficient, these types of observations could be helpful in better estimating the surface drag coefficient should they become available in Bering Strait.
Acknowledgments
This work was supported by NSF Award PLR-1303791 and ONR Award N00014-12-1-0917. Suggestions from the editor and two anonymous reviewers were a great help in improving the paper. We thank the captain and crew of R/V Sikuliaq and the engineers and scientists of the Scripps Multiscale Ocean Dynamics group for all their efforts that made this project possible. We gratefully acknowledge Mike Gregg and Dave Winkel for their support in moving the MMP and SWIMS from the Applied Physics Laboratory at the University of Washington to their new home at the Scripps Institution of Oceanography.
Data availability statement: Shipboard (http://www.rvdata.us/catalog/SKQ201511S) and microstructure (https://microstructure.ucsd.edu) data are available for download. University of Washington mooring data were obtained online (http://psc.apl.washington.edu/BeringStrait.html) and are also available from the National Centers for Environmental Information (https://www.nodc.noaa.gov).
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