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  • View in gallery
    Fig. 1.

    Bathymetric map of the observation area. The depth contours are in meters. Tracks of the submarine corresponding to the legs in November 2001 (labeled legs A1–A3) and November 2002 (labeled leg B1) are indicated. Small arrows on the tracks indicate mean direction of the wind during the legs.

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    Fig. 2.

    Locations of the sensors. (a) Sketch, not to scale, of the F. A. Forel, showing relative positions of the sensors on the bow; TP shows the location of the turbulence package. Also shown are relative positions of the sensors during (b) legs A1–A3 in November 2001 and (c) leg B1 in November 2002 viewed from ahead of the submarine. The PME thermistors are labeled S1–S8.

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    Fig. 3.

    Variation of the rate of dissipation with depth in the mixed layer: (a) the logarithm of the mean rates of dissipation as a function of depth and (b) the number of samples in each depth bin, during the period of observations in November 2002. The dashed line in (a) represents the law-of-the-wall variation.

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    Fig. 4.

    Average time sections of the measured values through conditionally sampled cold-water events in legs A1, A2, and A3: (a) the temperature recorded by the reference thermistor S4, (b) the vertical velocity corrected for submarine motion and detrended using the temporal averages over the leg durations, and (c) the rate of dissipation.

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    Fig. 5.

    Average time sections of the temperature data recorded by the vertical array of thermistors through cold-water events in legs A1, A2, and A3. The events are identified using (a) thermistor S1 and (b) thermistor S8 as references. The temperatures plotted at times relative to the time, t = 0, of event encounter, are, top to bottom, from the S1 to the S8 sensors on the vertical array. The temperature decreases slowly with depth with a mean gradient of about 1.7 mK m−1 in the mixed layer.

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    Fig. 6.

    Contour plots of cold-water events, or filaments, derived from the temperature data presented in Fig. 5. Isotherm contours are drawn at 1-mK intervals. The events are shown as time series derived (as in Figs. 5a and 5b) using (a) S1 and (b) S8 as conditional references. (c), (d) Expanded sections of the events in distance along the submarine track. Distance is derived using the mean submarine speed. Dashed lines are drawn at 60° to the horizontal direction and indicate the approximate mean slope of the filaments. The lowest thermistor is at a mean depth of 6.7 m, about 3.3 m above the base of the mixed layer.

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    Fig. 7.

    Contour plots of the cross-correlation coefficients during leg B1. Cross-correlation coefficients in the direction x of the submarine path are determined from the time series assuming the Taylor frozen field hypothesis. (a) Isocontours in the xy plane. There is no significant slope. (b) Isocontours in the x–z plane. Structure is tilted in a direction consistent with the wind-driven shear flow in the mixed layer.

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    Fig. 8.

    Contour plots of the cross-correlation coefficients in the x–z plane during legs A1 and A3. Cross-correlation coefficients in the direction of the submarine path, x, are determined from the time series, assuming the Taylor frozen field hypothesis, and correlation distances are measured using sensor S1 as one of the locations. Isocontours during (a) legs A1 and (b) A3. Leg A3 is in a direction opposite to that of A1, and upwind, as in leg B1 of which the corresponding correlation diagram is shown in Fig. 7b. The correlation structure is tilted in a direction consistent with the wind-driven shear flow in the mixed layer.

  • View in gallery
    Fig. 9.

    Contour plots of the cross-correlation coefficients of cold-water events. Isocontours in the (a) xy and (b) x–z planes during leg B1, which may be compared with those of the full dataset shown in Fig. 7. As in that figure, cross-correlation coefficients in the direction x of the submarine path are determined from the time series, assuming the Taylor frozen field hypothesis. Correlation values are greater than in the corresponding plots in Fig. 7. Tilt is evident in the 0.6 correlation contour in (b). (c) Isocontours in the x–z plane during leg A1, which may be compared with the full data plot of Fig. 8a.

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    Fig. 10.

    Sketch showing the cold-water filaments in the mixed layer. They are tilted in the wind direction, typically 25 m apart in the downwind direction, and 1.5 m wide, although tapering upward in width. Both the temperature and the rate of dissipation within the filaments are less than in the surrounding water, and there is vertically upward motion at speeds of about 5 cm s−1.

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Cold-Water Events and Dissipation in the Mixed Layer of a Lake

B. OzenLaboratoire d’Hydraulique Environnementale, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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S. A. ThorpeSchool of Ocean Sciences, University of Bangor, Menai Bridge, Bangor, United Kingdom

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U. LemminLaboratoire d’Hydraulique Environnementale, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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T. R. OsbornDepartment of Earth and Planetary Science, The Johns Hopkins University, Baltimore, Maryland

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Abstract

Measurements of temperature, velocity, and microscale velocity shear were made from the research submarine F. A. Forel in the near-surface mixed layer of Lake Geneva under conditions of moderate winds of 6–8 m s−1 and of net heating at the water surface. The submarine carried arrays of thermistors and a turbulence package, including airfoil shear probes. The rate of dissipation of turbulent kinetic energy per unit mass, estimated from the variance of the shear, is found to be lognormally distributed and to vary with depth roughly in accordance with the law of the wall at the measurement depths, 15–20 times the significant wave height. Measurements revealed large-scale structures, coherent over the 2.38-m vertical extent sampled by a vertical array of thermistors, consisting of filaments tilted in the wind direction. They are typically about 1.5 m wide, decreasing in width in the upward direction, and are horizontally separated by about 25 m in the downwind direction. Originating in the upper thermocline, they are characterized in the mixed layer by their relatively low temperature and low rates of dissipation of turbulent kinetic energy and by an upward vertical velocity of a few centimeters per second.

Corresponding author address: B. Ozen, EPFL–ENAC–ICARE–LHE, GC A1.365, Station 18, CH-1015, Lausanne, Switzerland. Email: baris.ozen@epfl.ch

Abstract

Measurements of temperature, velocity, and microscale velocity shear were made from the research submarine F. A. Forel in the near-surface mixed layer of Lake Geneva under conditions of moderate winds of 6–8 m s−1 and of net heating at the water surface. The submarine carried arrays of thermistors and a turbulence package, including airfoil shear probes. The rate of dissipation of turbulent kinetic energy per unit mass, estimated from the variance of the shear, is found to be lognormally distributed and to vary with depth roughly in accordance with the law of the wall at the measurement depths, 15–20 times the significant wave height. Measurements revealed large-scale structures, coherent over the 2.38-m vertical extent sampled by a vertical array of thermistors, consisting of filaments tilted in the wind direction. They are typically about 1.5 m wide, decreasing in width in the upward direction, and are horizontally separated by about 25 m in the downwind direction. Originating in the upper thermocline, they are characterized in the mixed layer by their relatively low temperature and low rates of dissipation of turbulent kinetic energy and by an upward vertical velocity of a few centimeters per second.

Corresponding author address: B. Ozen, EPFL–ENAC–ICARE–LHE, GC A1.365, Station 18, CH-1015, Lausanne, Switzerland. Email: baris.ozen@epfl.ch

1. Introduction

The processes in the near-surface mixed layer of lakes and oceans that contribute to the vertical transfer of momentum, heat, and gases within the layer, into and from the underlying thermocline and between the water and the overlying atmosphere, are, as yet, poorly known. It appears that turbulence generated by breaking surface waves may dominate mixing within a few significant wave heights of the surface but that, at greater depths, processes associated with Langmuir circulation and with the instability of the mean shear flow within the layer, or with thermal convection under conditions of strong heat flux to the atmosphere, are mainly responsible for the vertical transfer of heat from the surface. These processes may be identified by the presence of large-scale coherent structures in the thermal or velocity field, for example, by temperature anomalies and vertical velocities in the case of Langmuir circulation, temperature ramps or microfronts in the case of processes related to the mean shear, and plumes in convective conditions. Studies of the structure of the temperature field within Langmuir circulation are described by Thorpe and Hall (1982) and Thorpe et al. (2003). Temperature ramps, and related changes in rates of dissipation, are investigated by Soloviev (1990), Thorpe and Hall (1982), and Thorpe and Osborn (2005) and convective plumes by Stips et al. (2003) and Thorpe et al. (1999).

While it is sometimes possible to identify individual structures using pattern recognition processing or conditional sampling, more general methods of structural analysis have been applied including, for example, time-lagged cross-correlation analysis. Study of the thermal field measured by a small (1.8 m × 1.35 m × 1.5 m) moored three-dimensional array of thermistors in the mixed layer of Loch Ness by Thorpe and Hall (1977) during a period of lake heating showed that, while the Taylor frozen field hypothesis was valid in the flow direction (time-lagged correlations exceeding 0.85 over periods of 7 s or over distances of about 1.75 m at a mean flow speed of 0.25 m s−1), a time lag between temperatures measured at vertical separations suggested that there are structures in the temperature field that are tilted at a mean angle of about 53° to the horizontal plane (intermittent abrupt increases in temperature, or temperature ramps, at intervals of some several hundred seconds were identified as being associated with instability of the shear flow in the layer at a scale much larger than the array). Similar tilted structures have been observed by Keller and van Atta (2000), whose studies of a stably stratified homogeneous turbulent shear flow in a laboratory wind tunnel include analysis by cross-correlation methods.

The processes by which water is entrained into the mixed layer from the underlying thermocline are, at best, poorly known, in spite of it being a fundamental process assumed in models of mixed layer deepening [e.g., the one-dimensional model of Turner and Kraus (1967)]. According to laboratory experiments by Strang and Fernando (2001), Kelvin–Helmholtz or Holmboe instability may be important. The dominant instability is dependent on the magnitude of the bulk Richardson number characterizing the flow and stratification at the base of a turbulent upper layer.

Our objective here is to describe observations made with arrays of thermistors and a turbulence package, including airfoil shear probes, from a moving platform in the mixed layer of a lake that provide evidence of entrainment into the mixed layer of cold water filaments from the underlying thermocline, structures that appear not to have been identified in previous observations. (The form of the filaments is shown in Fig. 6 and is illustrated in Fig. 10. Both figures are described in later sections.)

The paper is arranged as follows: After describing the methods of measurement in section 2 and observations of the mean rates of dissipation of turbulent kinetic energy in section 3, conditional analysis is used in section 4 to show that the temperature field in the mixed layer contains coherent filaments of cold water with relatively low rates of dissipation. These originate in the thermocline. The filaments are tilted in a sense consistent with the mean wind-driven shear in the mixed layer. Their contribution to the vertical flux of heat in the mixed layer is assessed in section 5. Correlation and coherence techniques are applied to the measured temperature field in sections 6 and 7 and show that, like the filaments, the mean field has a tilted structure. Our conclusions about the source and role of the filaments are summarized in section 8.

2. Platform and sensors

Measurements were made in Lake Geneva from the three-person research submarine F. A. Forel (Thorpe et al. 1999) operating off the northern shore of the lake in the vicinity of Ouchy (46°31′N, 6°37′E), south of Lausanne, Switzerland. The bathymetry of the site and submarine dive tracks are shown in Fig. 1. Data were obtained on single days in November 2001 and 2002, with four legs on each day although, for clarity and simplicity of presentation, reference is only made to three, referred to as A1–A3, in 2001 and one, referred to as B1, in 2002. These were made at a uniform speed of about 0.4 m s−1 at constant depth along the tracks shown in Fig. 1. (A GPS, installed on the surface support ship combined with an underwater tracking system, allowed the horizontal position of the submarine to be determined every 1 min with 2-m accuracy.)

The submarine was equipped with arrays of high-precision fast response thermistors manufactured by Precision Measurements Engineering, a 10-MHz Nortek acoustic Doppler velocimeter (ADV), and a turbulence package. Locations of the sensors are shown in Fig. 2.

The thermistor arrays are used to obtain information about the vertical and horizontal field of temperature through which the submarine is passing. Much of the following text uses data collected with the vertical array shown in Fig. 2b. The thermistors have a time response of 2 × 10−2 s and provided measurements of temperature with a resolution of 1 mK at frequencies of 10 or 25 Hz. They were mounted on a frame about 2.2 m ahead of the bow of the submarine. An intercalibration accuracy of approximately ±1 mK was achieved by the now standard means of first applying a sensor calibration obtained in the laboratory, and then by adjusting the temperatures of sensors so that the mean temperatures of the individual sensors on a vertical array over all legs made on a single day lie on a smooth curve, and the mean value of those at the same level in an array are equal.

The ADV was mounted about 0.15 m ahead of the thermistor arrays and measured with ±1% accuracy in the range of ±1 m s−1 at the same sampling frequency.

The turbulence package, described by Thorpe et al. (2003), included two airfoil probes (Osborn and Crawford 1980) for sensing the vertical and horizontal velocity shear and a fast response thermistor, which measured temperature at a frequency of 512 Hz. Figures 2b and 2c show the positions of the airfoil probes and the fast response thermistor in the turbulence package (marked as TP), relative to the different arrays of thermistors (labeled S1, S2, . . . , S8) used during the observations in the two respective years.

In addition to the aforementioned instruments, a pressure transducer, two accelerometers, and a compass on the submarine provided measurements of depth, pitch, roll, and heading at frequencies of 10 or 25 Hz with resolutions of 0.1 m and 1°.

Meteorological data were obtained from the nearest meteorological station located at Pully (46°31′N, 6°40′E), which is part of the automatic online monitoring network of MeteoSwiss. The station is equipped with sensors of air temperature, wind speed and direction, atmospheric pressure, vapor pressure, relative humidity, and global radiation carrying out measurements automatically every 10 minutes. Data from this station were supplemented by the records of a meteorological mast located in the vicinity of Buchillon (46°28′N, 6°23′E), approximately 100 m away from the shore where the water is 3 m deep. The mast, described by Graf et al. (1984), is operated by the Laboratoire d’Hydraulique Environnementale of the Ecole Polytechnique Fédérale de Lausanne and provides hourly measurements of air temperature, wind speed, wind direction, atmospheric pressure, net radiation, relative humidity, and surface water temperature. In November 2002, additional data were obtained at 10-min intervals by using air temperature, wind speed, and wind direction sensors, installed on the quay of Ouchy.

The legs in November 2001 were run under a relatively steady wind blowing from the northeast at a speed of about 7 m s−1. The depth of the weakly stratified mixed layer (buoyancy frequency is estimated to be about 1.56 × 10−3 s−1), known from a preliminary dive of the submarine, was about 10 m, and all data were recorded in the mixed layer. Windrows were visible on the lake surface, 4–5 m apart, indicative of the presence of Langmuir circulation. During the observations in November 2002, the wind blew from the southeast at a mean speed of 6.9 m s−1. The depth of the mixed layer, weakly stratified with a buoyancy frequency of about 0.7 × 10−3 s−1, exceeded 20 m at the site, and leg B1 was above this depth. Navigational and meteorological data and submarine depths averaged over the legs are summarized in Table 1.

The net heat flux HN into the lake through the water surface (see section 5) during observations in November 2001 (legs A1–A3) was 170 ± 50 W m−2. The corresponding heat flux in November 2002 (leg B1) was 90 ± 25 W m−2. The mean thermal compensation depth (Woods 1980) dc, estimated using meteorological data and transparency measurements made using a Secchi disk, was about 0.6 m. On both days the significant wave height hs, estimated from visual observations, was about 0.3–0.4 m. Both dc (above which there is a net cooling of the water because the sum of the latent, sensible, and longwave radiative heat loss at the water surface exceeds the incoming, mainly shortwave, radiative heating, so that convection may occur) and hs are smaller than the mean depths, about 2–8 m, at which observations in the mixed layer are obtained.

3. Rate of dissipation of turbulent kinetic energy

The rate of dissipation ε of turbulent kinetic energy per unit mass is estimated from the variance of the shear using the relation for isotropic turbulence,
i1520-0485-36-10-1928-e1
where υ is the transversal velocity, w is the vertical velocity, ν is the water viscosity, and the overbar denotes a spatial or temporal average.

The variance of the shear in Eq. (1) is calculated from the data obtained with the airfoil probes. The recorded shear spectrum is corrected for spatial averaging of the probe and integrated. A second correction is then applied to account for the use of finite integration limits following the “Nasmyth universal shape” (Oakey 1982). The depth of observation, about 15–20hs, is well beyond the region affected by breaking surface waves. The rate of dissipation of turbulent kinetic energy is found to be lognormally distributed, consistent with observations by Thorpe et al. (2003). Some variations in the submarine depth during single legs occurred unavoidably and are indicated by the deviations to depth shown in Table 1. These, and successive legs at different depths, however, allowed the depth variation of ε to be examined: the depth of the turbulence sensors zTP was divided into 0.1-m-thick bins and mean values εmb of the rates are calculated within them. Logarithmic values of the mean estimates in each bin obtained in November 2002 are shown in Fig. 3a, and the number of samples in each depth bin is shown in Fig. 3b.

A comparison is made in Fig. 3a with the relation predicted by the law of the wall,
i1520-0485-36-10-1928-e2
where u* is the friction velocity in the water, k is von Kármán’s constant (taken as 0.41), and the friction velocity is estimated from the observed wind speed using the relation
i1520-0485-36-10-1928-e3
obtained by assuming the continuity of wind stress at the water surface. In Eq. (3), ρa and ρw are the air and water densities, respectively, W10 is the wind speed at 10-m height, and CD is the drag coefficient given by Merzi and Graf (1988) as
i1520-0485-36-10-1928-e4
derived using long-term data records of the mast located in the vicinity of Buchillon. The dashed line in Fig. 3a is the rate of dissipation predicted by the law of the wall, using the wind speed W10 averaged over the observation period. The upper and lower ends of the depth range are relatively undersampled. In the depth bins with a substantial number of samples (e.g., >100), the values of logεmb decrease as depth increases, roughly in accordance with the law of the wall. This is consistent with observations in the mixed layer by Agrawal et al. (1992) at depths greater than 2 × 105 u2*g−1, which here is about 1.8 m, and by Thorpe et al. (2003) at depths exceeding 1.55hs. Rates of dissipation taken from these limited, but well sampled, depth ranges are found to be lognormally distributed, having properties similar to those of the full record with wider depth sampling.

4. Conditional analysis of temperature

Temperature data recorded during legs in the mixed layer have a negative skewness in the majority of the legs and show many instances when the temperature descends rapidly to values below the local average, suggesting the presence of filaments of water being entrained from the upper thermocline. To investigate the structure of these cold-water events, and their effect on the dissipation of turbulent kinetic energy and the water motion, an analysis is carried out using conditional sampling.

Cold-water events through which the submarine is moving are identified using the temperature measured by one of the thermistors selected as reference. Each thermistor record is averaged over 1-s intervals (about 0.4 m along the submarine track) and detrended by removing a running mean over 1 min. To provide a basis for event identification or a “conditional” to identify events, a threshold level is chosen as
i1520-0485-36-10-1928-e5
where T ′ is the detrended temperature at the reference thermistor, σT ′ is the standard deviation of the detrended record, the overbar denotes a temporal average, and the constant C is taken to be equal to 1.5. (The value of C is chosen arbitrarily. About 7.4% of temperature values are below the threshold if C is equal to 1.5. Reduction leads to more events being identified and, as described below, to their carrying a greater negative heat flux.) In the mixed layer, instances when the temperature recorded by the reference thermistor remains below this threshold level are recognized as cold-water events. The times of passage of the minimum values during these events are selected as times of the events. Intervals centered on the times of events are extracted from the data, and averaged together to obtain average time sections of these quantities across events at the reference thermistor.

A total of 133 cold-water events are identified in legs A1–A3 (Table 2) and 36 in leg B1, using S4 as the reference. The mean distance between events is about 25 m but with the large standard deviation of 30 m. Their mean width (the mean distance moved by the submarine when the temperature remained less than the threshold value) is about 1.6 m with standard deviation of 1 m at the observation depths.

Figure 4 shows average time sections of the temperature recorded by the reference thermistor, here chosen as S4 (see Fig. 2b), together with the vertical velocity of the water measured by the ADV but corrected for the vertical motion of the submarine and the rate of dissipation, across events in legs A1–A3. The reference temperature decreases on average by about 20 mK at times of events. Rate of dissipation in the relatively cold water shows a pronounced minimum, reaching values about 50% lower than the mean at the mean depth of the submarine. At the same time, the vertical water velocity is seen to increase, indicating that, on average, the events are associated with the upward transport of cold water with relatively low turbulence levels from below the level of sampling. Using the observed inverse proportionality of the rate of dissipation with depth, the decrease in the rate of dissipation is found to correspond to a vertical displacement of water of about 2 m, giving a rough estimate of the mixing length in the mixed layer.

Figure 5 shows average time sections of the temperature across events in legs A1–A3 and gives further information about the nature of the cold-water events. (Legs A1 and A2 are toward the south, roughly in the wind direction. Time is reversed in the analysis of data from leg A3, made in the northerly direction, to preserve the tilted temperature structure in the vertical plane.) Selection of the uppermost thermistor, S1, as the reference reveals a pronounced temperature decrease that is replicated in all thermistors of the array without much reduction in strength but with minima values that tend toward earlier times, indicating that the mean event has a tilted structure (Fig. 5a). When the lowest thermistor, S8, is selected as the reference, the cold-water signal is only weakly detected at the top thermistor, although a trend toward an increase in the time of the temperature minima is visible in the shallower thermistors (Fig. 5b). The difference between these two conditional sets of temperatures detected relative to the top or the lowest thermistor is consistent with cold-water events that are produced by filamentary structures moving upward from levels below the submarine but which may not span the totality of the array. Only those detected at S1 (Fig. 5a) extend to the top of the array.

The temperature anomaly in the events of Fig. 5a is about 20 mK. The mean temperature gradient in the mixed layer (estimated from measurements during preliminary submarine dives and from binning the observed temperatures as were dissipation rates in producing Fig. 3a) is about 1.7 mK m−1. This implies that a vertical scale of some 12 m may be associated with the temperature anomalies: the source of the cold water is therefore in the upper thermocline below the mixed layer since the submarine is only about 3.3 m above the base of the mixed layer.

A more vivid picture of the cold-water, low dissipation events is obtained by contouring the mean temperature field through events as in Fig. 6. Figures 6a and 6b are the contours from the data of Figs. 5a and 5b, respectively. The events stand out as strong cold water features, reaching the top thermistor in Fig. 5a but only marginally so in Fig. 5b. The filaments appear to decrease in width by a factor of about 3 over the vertical span, 2.38 m, of the sampling array. Figures 6c and 6d show expanded versions of the data of Figs. 6a and 6b, plotted against distance rather than time using the mean speed of the submarine. The dashed line indicates a slope of 60° to the horizontal plane, roughly the mean slope of the cold events. (This tilt is discussed further in sections 6 and 7.) The inversion in the temperature contours to the right of the event in Fig. 6c and the larger than average vertical gradients between 0.34-m and 0.68-m depth (the locations of the S2 and S3 thermistors) appear to be artifacts caused by slight errors in sensor calibration, errors at 1-mK level, which is the resolution of the thermistors.

A variety of other conditionals were adopted to detect features of the temperature and dissipation fields, such as maximum temperatures (rather than the minima used above) or high dissipation, but none produced signals that provided such well-defined patterns and correlations between temperature and dissipation.

5. Role of cold-water events in the transfer of heat

The net heat flux HN into the lake through the water surface is estimated from the records of the meteorological mast located in the vicinity of Buchillon using the relation
i1520-0485-36-10-1928-e6
where RN is the net radiation, HL is the latent heat flux across the air–water interface, defined as
i1520-0485-36-10-1928-e7
and HS is the sensible heat flux across the air–water interface, defined as
i1520-0485-36-10-1928-e8

In Eqs. (7) and (8), L is the latent heat of water at a given temperature, cpa is the specific heat at constant pressure for dry air, ρa is the air density, ua is the friction velocity in the air, and q* and θ* are the surface-layer humidity and temperature scales, respectively.

Here q* (depending on the coefficient of water vapor exchange, drag coefficient, and on the difference between the saturation specific humidity and specific humidity) and θ* (depending on the coefficient of heat exchange, drag coefficient, and on the difference between the water and air temperatures) are estimated following a procedure based on the equations given by Kantha and Clayson (2000), Large and Pond (1981, 1982), and Liu et al. (1979).

The vertical flux of heat associated with events is compared with that through the water surface to assess their importance in the heat budget of the mixed layer at the time of observation. The mean vertical heat flux HE carried by the cold-water events averaged over a leg is estimated as
i1520-0485-36-10-1928-e9
where n is the number of events in the leg, wc is the vertical velocity measured by the ADV and corrected for submarine motion, ρw is the water density, cp is the specific heat of water at constant pressure, T ′ is the detrended temperature at the reference thermistor, D is the duration of the leg, and the overbar denotes the temporal averaging made over the leg duration. The term in the braces is the flux carried by a single event, estimated over an interval (−t; t) selected to characterize the event.

Estimates made using the data recorded in legs A1–A3 are presented in Table 2. The mean (negative) upward flux of heat HE carried by the events is about 15% of the 170 W m−2 of heat entering the mixed layer from the atmosphere (HN), or some 25 W m−2. [Reducing the threshold value coefficient C in Eq. (5) to 1.0 results in a moderate increase in the mean cold water flux to about 20% of HN.] The table also shows that the events last, on average, for about 7% of the total record length. It would have been desirable to compare the flux carried by the cold-water filaments with the net vertical heat flux at the observation depth. Except during events, however, estimates of the latter cannot be made with sufficient confidence. This is because of the uncertainty in the measurement of small vertical speeds by the ADV and in their correction for submarine motion.

6. Correlation of temperature data

The structure of the temperature field has been investigated by cross-correlation techniques following those used by Thorpe and Hall (1977) and, in the laboratory, by Keller and van Atta (2000). Cross-correlation coefficients with time lags τ between pairs of thermistors at relative positions I and J (XIJ) are calculated using 1-s-averaged records to obtain a further estimate of the mean inclination of the coherent structures in the mixed layer. The time-lagged cross-correlation values allow two-dimensional diagrams to be constructed in x–z and xy planes, where x is directed along the submarine path in the travel direction, y is across path, and z is vertically upward. Distances in the x direction are derived using Taylor’s hypothesis and the mean submarine speeds.

Leg B1 is the only one of the four legs with measured values of temperature in the across-track, y, direction. Figure 7a shows sections of constant XIJ surfaces in the xy plane obtained from the temperature data recorded in this leg. There is no evidence of a tilted structure although the structure is slightly asymmetrical, with greater correlations in the y than in the x direction. The x–z correlation diagram (Fig. 7b), however, shows enhanced correlations on a direction inclined at an angle of about 60° to the horizontal, consistent with that obtained using the phase differences, which will be discussed in section 7.

Figure 8 shows the constant XIJ surfaces in the x–z plane for legs A1 and A3, obtained using correlations between thermistor S1 and the others down the array. Both diagrams show tilted structures but in opposite directions, consistent with Fig. 7b and the direction of the legs relative to the wind direction. The roughly elliptical correlation contours are tilted at about 60° to the horizontal.

The tilted correlation structures shown in Figs. 7 and 8 refer to all of the temperature data collected in the respective legs; the events are not singled out. To examine their correlation structure, cross-correlation coefficients have been calculated using the detrended temperature data during intervals selected to characterize the events. To limit the effect of the variances of the temperature data, which are used to normalize the cross-correlation coefficients, estimates are made using 3-s-long intervals, centered on the times of events at the reference thermistor.

The main feature of the correlation diagrams constructed in this way is that they have greater correlation scales in all directions and, being based on smaller sets of data, are less regular in shape. The examples shown in Fig. 9 are in the xy plane of leg B1 and the x–z plane of legs B1 and A1 based on correlations using thermistor S1. In comparison with the contours derived from the full dataset (Figs. 7a, 7b and 8a, respectively), the correlations are generally greater. The correlation in the y direction in Fig. 9a is less than in x (differing from those in Fig. 7a), indicating that the filaments are relatively narrow in the across-wind direction. The tilt of features is however less obvious than in Figs. 7b and 8.

7. Coherence and phase differences of temperature data

The mean structure of the temperature field has also been studied using standard spectral techniques to investigate coherence CIJ and relative phase of temperatures recorded at 10 and 25 Hz at pairs of thermistors, I and J. The coherence CIJ decreases as the vertical separation of thermistors increases. Using the Taylor frozen field hypothesis and the mean submarine speed of 0.43 m s−1 for legs A1 and A3, coherence of sensors separated at 0.34, 0.68, and 1.02 m is significant (>0.6) only to horizontal distances of about 4.8, 8.1, and 15.5 m, respectively. Small-scale horizontal eddies or fluctuations are less coherent at greater vertical separations. The phase differences between vertically separated pairs of thermistors in these two legs made in opposite directions through the mixed layer, A1 downwind and A3 upwind (Fig. 1), differ in sign for frequencies where the temperature data are found to be coherent, implying that coherent structures are tilted in the downwind direction. Phase differences between thermistors mounted on the vertical spar in leg B1, a leg run in the upwind direction, indicate a tilt of the temperature structures similar to that in A3.

The sense of the tilt of the temperature structure is consistent with that which would be produced by a wind-driven shear in the mixed layer as it distorts and rotates vertically mixed patches of water. A measure of the inclination of the structures to the horizontal is obtained using the phase differences and the mean submarine speed, and assuming the validity of Taylor’s hypothesis. This angle is estimated to be about 78° ± 8° for legs A1 and A3 (somewhat greater than the tilt angles found by correlation techniques in section 5) and 62° ± 12° for leg B1.

8. Conclusions

Observations made from the research submarine F. A. Forel, operating in the mixed layer of Lake Geneva at depths of 15–20 times the significant wave height and the middepth of the mixed layer, have identified large-scale coherent structures, events in which the relatively cold water originating in the thermocline is transferred vertically upward and entrained into the mixed layer. A sketch of these cold-water events is shown in Fig. 10. They consist of filaments tilted in the wind direction and, on average, about 25 m apart in the downwind direction and roughly 1.5 m wide, although on average narrower in the across-wind direction and tapering upward in width. Within the filaments both the temperature and the rate of dissipation are less than in the surrounding water, and there is vertically upward motion at speeds of about 5 cm s−1.

Both the mean temperature field and the filaments are found to be tilted in a sense consistent with the mean wind-driven shear in the mixed layer. The filaments have similar tilt angles to those reported for temperature ramps in Loch Ness by Thorpe and Hall (1980). This suggests that the two structures may be part of a single process. No connection has, however, been established and other mechanisms may be proposed for the generation of temperature fronts, especially near the water surface (Thorpe and Osborn 2005). It is tempting to suggest that the filaments are a manifestation of Holmboe instability occurring at the upper boundary of the thermocline as observed in the laboratory experiments of Strang and Fernando (2001). However, the nature of turbulent flow in the laboratory may differ substantially from that in the lake or ocean mixed layer because, for example, the forcing by breaking waves or Langmuir circulation (present at least in legs A1–A3) is lacking. The thin tilted structures strongly resemble those seen in visualizations of the disturbed density field resulting from Holmboe instability, but without a definite linkage to their source it is impossible to be certain. Further investigations with thermistors and velocimeters, capable of sampling the upper thermocline and the mixed layer at the same time, would be worthwhile to identify the presence and structure of the mixing processes, to quantify the contribution of the filaments to the heat content of the mixed layer, and to understand better the dynamics of this presently undersampled region of entrainment into the mixed layer—one that is vital in the process of ocean mixing and heat transfer.

When scaled with the estimate of the mixing length, about 2 m (see section 4), the correlation contours of temperature fluctuations in the mixed layer shown in Figs. 7b and 8 are similar to those observed in the laboratory by Keller and van Atta (2000) although the tilts are greater; Keller and van Atta find values of about 30°, decreasing as the stratification increases (or as a gradient Richardson number increases), rather than the angle of 60° to the horizontal direction, or greater, found here. Conditions, however, differ substantially. Keller and van Atta’s stratified flow in a wind tunnel is made turbulent in passing through a grid and there is no underlying thermocline, where shear and stratification may result in shear flow instability, as in the lake.

Acknowledgments

We thank Dr. J. Piccard and his sponsors for use of the submarine F. A. Forel and for the friendly and constructive help given by the submarine pilots. Financial support for this project is provided by the Swiss National Science Foundation, Grant 2000-066637. Authors S. A. Thorpe and T. R. Osborn are grateful for support by the Ecole Polytechnique Fédérale de Lausanne, which allowed them to take part in this study.

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Fig. 1.
Fig. 1.

Bathymetric map of the observation area. The depth contours are in meters. Tracks of the submarine corresponding to the legs in November 2001 (labeled legs A1–A3) and November 2002 (labeled leg B1) are indicated. Small arrows on the tracks indicate mean direction of the wind during the legs.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 2.
Fig. 2.

Locations of the sensors. (a) Sketch, not to scale, of the F. A. Forel, showing relative positions of the sensors on the bow; TP shows the location of the turbulence package. Also shown are relative positions of the sensors during (b) legs A1–A3 in November 2001 and (c) leg B1 in November 2002 viewed from ahead of the submarine. The PME thermistors are labeled S1–S8.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 3.
Fig. 3.

Variation of the rate of dissipation with depth in the mixed layer: (a) the logarithm of the mean rates of dissipation as a function of depth and (b) the number of samples in each depth bin, during the period of observations in November 2002. The dashed line in (a) represents the law-of-the-wall variation.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 4.
Fig. 4.

Average time sections of the measured values through conditionally sampled cold-water events in legs A1, A2, and A3: (a) the temperature recorded by the reference thermistor S4, (b) the vertical velocity corrected for submarine motion and detrended using the temporal averages over the leg durations, and (c) the rate of dissipation.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 5.
Fig. 5.

Average time sections of the temperature data recorded by the vertical array of thermistors through cold-water events in legs A1, A2, and A3. The events are identified using (a) thermistor S1 and (b) thermistor S8 as references. The temperatures plotted at times relative to the time, t = 0, of event encounter, are, top to bottom, from the S1 to the S8 sensors on the vertical array. The temperature decreases slowly with depth with a mean gradient of about 1.7 mK m−1 in the mixed layer.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 6.
Fig. 6.

Contour plots of cold-water events, or filaments, derived from the temperature data presented in Fig. 5. Isotherm contours are drawn at 1-mK intervals. The events are shown as time series derived (as in Figs. 5a and 5b) using (a) S1 and (b) S8 as conditional references. (c), (d) Expanded sections of the events in distance along the submarine track. Distance is derived using the mean submarine speed. Dashed lines are drawn at 60° to the horizontal direction and indicate the approximate mean slope of the filaments. The lowest thermistor is at a mean depth of 6.7 m, about 3.3 m above the base of the mixed layer.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 7.
Fig. 7.

Contour plots of the cross-correlation coefficients during leg B1. Cross-correlation coefficients in the direction x of the submarine path are determined from the time series assuming the Taylor frozen field hypothesis. (a) Isocontours in the xy plane. There is no significant slope. (b) Isocontours in the x–z plane. Structure is tilted in a direction consistent with the wind-driven shear flow in the mixed layer.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 8.
Fig. 8.

Contour plots of the cross-correlation coefficients in the x–z plane during legs A1 and A3. Cross-correlation coefficients in the direction of the submarine path, x, are determined from the time series, assuming the Taylor frozen field hypothesis, and correlation distances are measured using sensor S1 as one of the locations. Isocontours during (a) legs A1 and (b) A3. Leg A3 is in a direction opposite to that of A1, and upwind, as in leg B1 of which the corresponding correlation diagram is shown in Fig. 7b. The correlation structure is tilted in a direction consistent with the wind-driven shear flow in the mixed layer.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 9.
Fig. 9.

Contour plots of the cross-correlation coefficients of cold-water events. Isocontours in the (a) xy and (b) x–z planes during leg B1, which may be compared with those of the full dataset shown in Fig. 7. As in that figure, cross-correlation coefficients in the direction x of the submarine path are determined from the time series, assuming the Taylor frozen field hypothesis. Correlation values are greater than in the corresponding plots in Fig. 7. Tilt is evident in the 0.6 correlation contour in (b). (c) Isocontours in the x–z plane during leg A1, which may be compared with the full data plot of Fig. 8a.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Fig. 10.
Fig. 10.

Sketch showing the cold-water filaments in the mixed layer. They are tilted in the wind direction, typically 25 m apart in the downwind direction, and 1.5 m wide, although tapering upward in width. Both the temperature and the rate of dissipation within the filaments are less than in the surrounding water, and there is vertically upward motion at speeds of about 5 cm s−1.

Citation: Journal of Physical Oceanography 36, 10; 10.1175/JPO2946.1

Table 1.

Navigational and meteorological data averaged over the legs.

Table 1.
Table 2.

Ratios of the vertical flux of heat by the cold-water filaments identified as “events” divided by the net surface heat flux, HE/HN, for legs A1, A2, and A3. Events are identified with C = 1.5 in Eq. (5).

Table 2.
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