Enthalpy Transfer across the Air–Water Interface in High Winds Including Spray

Dahai Jeong Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Brian K. Haus Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Mark A. Donelan Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Abstract

Controlled experiments were conducted in the Air–Sea Interaction Saltwater Tank (ASIST) at the University of Miami to investigate air–sea moist enthalpy transfer rates under various wind speeds (range of 0.6–39 m s−1 scaled to equivalent 10-m neutral winds) and water–air temperature differences (range of 1.3°–9.2°C). An indirect calorimetric (heat content budget) measurement technique yielded accurate determinations of moist enthalpy flux over the full range of wind speeds. These winds included conditions with significant spray generation, the concentrations of which were of the same order as field observations. The moist enthalpy exchange coefficient so measured included a contribution from cooled reentrant spray and therefore serves as an upper limit for the interfacial transfer of enthalpy. An unknown quantity of spray was also observed to exit the tank without evaporating. By invoking an air volume enthalpy budget it was determined that the potential contribution of this exiting spray over an unbounded water volume was up to 28%. These two limits bound the total enthalpy transfer coefficient including spray-mediated transfers.

Corresponding author address: Brian K. Haus, RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. E-mail: bhaus@rsmas.miami.edu

Abstract

Controlled experiments were conducted in the Air–Sea Interaction Saltwater Tank (ASIST) at the University of Miami to investigate air–sea moist enthalpy transfer rates under various wind speeds (range of 0.6–39 m s−1 scaled to equivalent 10-m neutral winds) and water–air temperature differences (range of 1.3°–9.2°C). An indirect calorimetric (heat content budget) measurement technique yielded accurate determinations of moist enthalpy flux over the full range of wind speeds. These winds included conditions with significant spray generation, the concentrations of which were of the same order as field observations. The moist enthalpy exchange coefficient so measured included a contribution from cooled reentrant spray and therefore serves as an upper limit for the interfacial transfer of enthalpy. An unknown quantity of spray was also observed to exit the tank without evaporating. By invoking an air volume enthalpy budget it was determined that the potential contribution of this exiting spray over an unbounded water volume was up to 28%. These two limits bound the total enthalpy transfer coefficient including spray-mediated transfers.

Corresponding author address: Brian K. Haus, RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. E-mail: bhaus@rsmas.miami.edu

1. Introduction

Fluxes of water vapor, heat, and momentum at the air–sea interface play an important role in the formation and mixing of water and air masses, and are responsible for much of the thermodynamic and dynamic forcing of the ocean and atmosphere. Knowledge of these fluxes is essential in a wide range of oceanographic and marine meteorological studies. Air–sea fluxes, however, being relatively difficult to measure, are rarely available outside dedicated studies. It is thus desirable to parameterize the fluxes in terms of more readily available mean conditions of the boundary layers.

For the purpose of obtaining the parameterizations of the fluxes in terms of bulk transfer coefficients, a relatively large number of measurements of the water vapor and heat fluxes over the sea (e.g., Anderson 1993; Anderson and Smith 1981; DeCosmo et al. 1996; Drennan et al. 2007; Friehe and Schmitt 1976; Geernaert 1990; Large and Pond 1982; Smith 1980, 1988; Smith and Anderson 1988) have been made. There is a general agreement on the average values of the bulk coefficients obtained from such measurements. Nonetheless, some basic questions still exist regarding the dependence of the exchange coefficients on wind speed, which is obscured because of considerable scatter in the data. In particular, bulk parameterizations have been unreliable due to the lack of direct flux measurements at wind speeds above 20 m s−1. These uncertainties are due not only to the difficulties in flux measurements such as contamination by flow distortion, ship or buoy motion, and the marine environment (e.g., Blanc 1983; Businger 1986; Panofsky and Dutton 1984; Wucknitz 1980; Wyngaard 1990), but also to mechanisms that may affect fluxes but cannot be isolated without great difficulty in the field (Donelan 1982; Kitaigorodskii et al. 1973; Wu 1969a,b). In particular, the effects of spray have been difficult to directly observe, requiring existing spray flux formulations to be based on extrapolation to wind speeds beyond the range for which data are available (e.g., Andreas 2010). These circumstances suggest the need for complementing field measurements with laboratory experiments, where the variables governing the transfer phenomena can be adjusted and controlled.

The purpose of this work is to advance our knowledge of the nature of the enthalpy (total heat) transfer process across the air–water interface. This was accomplished by measuring the wind speed dependence of the moist enthalpy exchange coefficient over a wide range of wind speeds in the Air-Sea Interaction Saltwater Tank (ASIST) wind-wave facility at the University of Miami.

These experiments were conducted in freshwater, which is known to produce a different spray droplet spectrum than seawater because of larger and less concentrated bubble production in breaking waves. The net effect of this difference cannot be directly determined, but it is the smallest droplet scales (diameters < 25 μm) that are produced by bursting bubbles. The larger droplets that contribute most significantly to the reentrant spray are robustly produced in freshwater in the ASIST facility and have been observed to scale similarly with wind as in field observations (Toffoli et al. 2011). Available field observations also do not contradict the observed trends in the enthalpy transfer coefficient with wind speed.

2. Bulk parameterization with stability-dependent transfer coefficients

Moist enthalpy flux HK (W m−2) is defined as
e1
where k′ is the turbulent fluctuation of the specific moist enthalpy k (J kg−1) of the binary (air and water vapor) mixture, defined as
e2
Here q is the specific humidity, cp is the specific heat of air (J kg−1 K−1), Lυ is the latent heat of vaporization of water (J kg−1), T is the air temperature, and is the specific heat of water vapor (J kg−1 K−1). The enthalpy flux thus represents total energy transfer including that energy associated with the liquid-to-water-vapor phase change at the air–water interface. By convention, a positive sign is used to indicate an upward flux. In the bulk parameterization, the moist enthalpy flux is related to standard meteorological observations via an empirical coefficient, such that
e3
where CK is an exchange coefficient for enthalpy, Um is the mean measured wind speed, and the subscript s denotes measurement at the surface of the water. The surface enthalpy is specified by using the saturation value of the humidity at the surface. The exchange coefficients are thus expected to depend on wind speed and the stability. To compare results of measurements at various levels and stability conditions, the 10-m neutral exchange coefficient was used:
e4
where U10N and k10N are the equivalent neutral wind speed and moist enthalpy at 10 m. The values of CK10N can thus be estimated from measurements of mean quantities once the turbulent fluxes are determined.

3. Calorimetric method for obtaining bulk enthalpy flux

The integral conservation method (referred to as the calorimetric method) was used to determine the moist enthalpy flux through the interface on the basis of a heat content budget applied to a control volume of water (Fig. 1a). The technique is based on the principle of measuring the amount of heat lost by the water body to the air as cooler air is blown over the surface. This is the total moist enthalpy flux, such that
e5
where is the specific heat capacity of liquid water (4.181 J kg−1 K−1 at 25°C), ρl is the density of liquid water (997 kg m−3 at 25°C), ∂TW/∂t is the rate of change of the bulk water temperature obtained by polynomial fit to a time series of bulk water temperature, VW is the total volume of water, and A is the surface area of the air–water interface exposed to the wind.
Fig. 1.
Fig. 1.

(a) Cartoon of test section of ASIST. Control volume for the calorimetric method denoted by the dashed box. Shaded gray sections denote water piping through which conductive heat transfer may occur through the walls. Arrows show transfers of heat through water surface, sidewalls, and bottom. (b) Scaled diagram of the ASIST wind-wave flume, showing air inlets and piping detail.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

If thermal gradients exist at the walls of the tank and water pipes, the source of the resulting total heat loss from the water, as expressed by the right-hand side of (5), can consist of four components. These are the interfacial enthalpy flux, spray-mediated fluxes, conductive losses through sidewalls and piping, and infrared radiative heat transfer (Fig. 1a). The only spray-mediated flux that contributes to the observed enthalpy flux using water volume calorimetry is that due to reentrant spray (i.e., droplets that lose heat to the air through evaporation, conduction, and convection and cool the water body on reentering it). If the heat loss induced by conduction and radiation is known and subtracted from the total heat loss, the total moist enthalpy flux per unit surface area (W m−2) due to both interfacial fluxes and reentrant spray can be inferred by
e6
where represents the conduction- and radiation-induced cooling rate of the water through the piping and sidewalls of the tank.

The advantages of using the calorimetric method over the direct eddy correlation method in a wind-water tunnel at high wind speeds are as follows: 1) The vertical component of the wind, which is difficult to measure directly, is not required. 2) The observations are averaged over the entire water surface of the wind-wave tank and over several minutes, thereby eliminating the statistical uncertainty of point sampling (Donelan 1990). 3) The bulk averaged heat flux estimate is directly comparable to the bulk flux parameterizations, simplifying estimation of the transfer coefficient. 4) The measurements can be made in a greatly expanded range of wind speeds.

4. The experiments

a. Experimental setup of the wind-wave tank

The ASIST wind-wave tank (Fig. 1b) has a working section of 15 × 1 × 1 m3 that is constructed with transparent acrylic panels to allow flow visualization and optical measurements. During the enthalpy flux experiments, the tank was filled with freshwater to a 0.42-m depth, leaving 0.58 m for airflow. The use of freshwater, as opposed to saltwater, has a pronounced effect on the bubbles produced in breaking waves and thereby the smallest droplet scales (diameters < 25 μm). However, the larger droplets that will contribute most significantly to the reentrant spray are robustly produced and have been observed to scale similarly with wind as in field observations (Toffoli et al. 2011).

The air side of the tank was operated in open (ventilating) mode to allow steady-state fluxes to be obtained. In this mode the air flume flaps were kept open so that air (at the ambient external temperature and humidity) entered the flume from the outside and, after one circuit, exited to the open air. Airflow was generated by a fan that could provide maximum centerline wind speeds up to 19 m s−1 in the ventilating mode. At the air inlet, a honeycomb screen provided nearly uniform horizontal airflow and an adjustable floor was hinged to bring the airstream smoothly onto the water surface.

At the downwind end of the tank, a beach (uniformly spaced sloping acrylic rods) was installed to absorb the wave energy and minimize wave reflections. The initial air–water temperature difference was adjusted by changing the water temperature with a heat exchanger (in the range of 1.3°–9.2°C warmer than air). The recirculating water tunnel is driven by a pump and a continuous current of 0.08 m s−1 was generated to circulate and mix the water throughout the experimental runs. The total water volume in the tank and return pipe was 9.7 m3 and the area of the still water surface was 15 m2.

b. Instrumentation and measurement techniques

During each experiment all of the quantities were measured that were required to use the calorimetric method to calculate the moist enthaply flux. Figure 2 shows the locations of the instruments during the experiment. Mean temperatures of air and water were obtained using thermistor probes (Thermometrics, AS125), whose sampling control block (1560 Black Stack System, Hart Scientific) allowed measuring the air and water temperature alternately with the same analyzer, thereby avoiding cross calibration errors. The sampling control block switched between air and water temperature measurements every 2.5 s. These measurements were made at two fetches of 0.38 and 11.78 m in the airstream and water tank with instrument accuracy of 0.002°C. For the overall enthalpy transfer measurements, the temperatures at the two fetches in both the air and water were averaged.

Fig. 2.
Fig. 2.

Arrangement of temperature, humidity, and airspeed sensors in the working section of the recirculating water and ventilating air flume.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

In early phases of the experiment, it was observed that in high winds, spray droplets were deposited directly on the downwind (fetch of 11.78 m) thermistor probe located 29 cm above the mean water surface. The droplets would then evaporate and affect the measurements. This spray contamination of the temperature sensor was avoided by the use of an aspirated protective housing. The air temperature was measured as air from the flume was continuously pumped out through a ceiling port into the protective housing. The protective unit is a 30-cm-long tube, 3 cm in diameter and built of acrylic so that visual inspections for accumulation of water droplets could be made.

The performance of the protective housing was tested by comparing measurements from identical sensors inside and outside of the device of measurements by identical sensors inside and outside the device (Fig. 3). The device was effective at protecting the sensor from contamination by impacting spray droplets, and the flow through the tube was slow enough that no thermodynamic heating effect was noticeable. This rather slow flow rate was found to be adequate for measurements of mean temperature. It did, however, limit our ability to extract the high-resolution temperature differences between the two air temperature sensors necessary to determine the unmeasured spray terms as discussed in section 5b(3). Consequently, the unshielded measurements were used for this purpose in the wind speed range where there was no spray directly impacting the air temperature sensor 29 cm above the water surface at 11.78-m fetch.

Fig. 3.
Fig. 3.

Air temperature at a fetch of 11.78 m during a run in which wind speed was increased from 0 to its maximum (39 m s−1 referred to 10-m height) and decreased again to 0 (gray line). The black solid line is the measurements of air temperature by the shielded thermistor sensor, and the black dash-dotted line is the measurements by the unshielded thermistor sensor. The contamination of temperature sensor by spray is reflected in the sudden drop in the temperature from the unshielded sensor.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

Surface skin temperature was obtained by an infrared camera (ThermaCAM SC 3000, FLIR Systems), which, because of the absorption properties of water in the infrared region of the electromagnetic spectrum, measures temperature in only the top few micrometers of water. The camera viewed the water surface at normal incidence through a window built into the tunnel ceiling at a fetch of 5.9 m. The field of view was about 41 × 31 cm2 in area and temperature changes on the order of 0.03°C could be resolved. When the IR observed skin temperature was used in the calculations of the flux in (5) it made a negligible difference in the enthalpy transfer coefficient in (4) and (2) in low to moderate winds. This does not imply that a cool skin was not present; rather, it was not important to the overall bulk flux estimate. Because of the difficulty in observing the surface skin temperature in high winds, the bulk temperature from the thermistors was used for all runs.

Mean specific humidity was measured with an LI-6262 gas analyzer (LI-COR), a closed-path, nondispersive, infrared (NDIR) gas analyzer, at fetches of 2.93 and 15 m. In this instrument the water vapor concentration measurements are based on the difference in absorption of infrared radiation passing through the sample and reference cells. Measurements were made in air from the flume that was continuously pumped out through a ceiling port (0.58 m above the still water surface) into the flow meter (Cole Parmer). The moist air from the flume was diluted by 20% with nitrogen to prevent condensation in the optical path of the gas analyzer. The gas analyzer was calibrated using an LI-610 dewpoint generator (LI-COR) before and after the experiment. Since each enthalpy flux measurement applies to the entire water surface, the mean value of the specific humidity obtained at the two fetches was used.

Wind measurements were made with a standard Pitot-static tube at 6-m fetch and at a fixed height of 0.2 m above the mean water surface. The differential pressure transducer of the Pitot tube was calibrated using a Chattock gauge. The analog signals of humidity and wind speed were digitized and recorded at a sampling rate of 25 Hz.

Given measurements of Um, T, and q at 0.20, 0.58, and 0.58 m above the mean water surface, respectively (Table 1), the neutrally stable 10-m values along with the Monin–Obukhov length and drag coefficient were obtained by assuming a log profile. The calculation was performed iteratively with the stability correction ignored for the first iteration. Subsequently the corrections of Dyer (1974) were employed. Previously measured drag coefficients from Donelan et al. (2004) were used to obtain at each wind speed . These measurements were made in the same conditions in the ASIST wind-wave facility. A polynomial was fit to the Donelan et al. (2004) drag coefficient versus wind speed relationship to allow iterative solutions at intermediate U10N values.

Table 1.

Summary of enthalpy flux experiments, June 2006–March 2007. Shown are total duration of run t, water temperature TW, mean air temperature T, specific humidity q, wind speed Um at 0.2 m above the surface, enthalpy flux HK as calculated from Eq. (6), moist enthalpy transfer coefficient CK obtained from measurements 0.58 m above the mean water surface, and wind friction velocity u* from Donelan et al. (2004).

Table 1.

Values for the sensible HT and latent HE heat fluxes were then obtained on the assumption that the Dalton and Stanton numbers are equal to the (measured) enthalpy exchange coefficients (Table 1). The u* values were then used in conjunction with the HT and HE heat fluxes to calculate T* and q* by (7) and (8):
e7
e8
The stability parameter may then be obtained by
e9
These values were then used in the similarity flux-profile relationships of Paulson (1970) with Dyer’s (1974) nondimensional gradients, to calculate the 10-m reference U10N, q10N, and T10N. Water–air temperature differences were always positive (unstable boundary layer) so that convergence was rapid, requiring at most seven iterations. The 10-m enthalpy value k10N was then obtained using q10N and T10N in (2).

c. Procedure for moist enthalpy transfer measurements

The experimental approach was to determine an overall heat transfer rate for the whole tank by monitoring the temperature decrease of the water. The total moist enthalpy flux is that portion of the heat content in the recirculating water volume transferred to the overlying airflow during an experimental run at a steady wind speed. This integral calorimetric measurement was employed because it avoids the sampling error inherent in point measurements (Donelan 1990). Furthermore, eddy correlation measurements in the laboratory require instrumentation with frequency response beyond 100 Hz, well out of reach of available humidity sensors.

The water volume temperature decrease includes sensible and latent heat losses through the air–water interface, conductive and radiative heat losses through the walls and piping to the surroundings of the tank, and the sensible heat transferred by reentrant spray. To quantify the losses through the walls and piping separate runs were conducted at various temperature differences across the tank walls with an insulating cover installed over the water surface (hence no turbulent fluxes). The term was then obtained from a polynomial fit to the water temperature measured during a covered run with the same air–sea temperature difference and wind speed as in the total heat loss measurement. Covering the surface also eliminated the radiative transfers through the air–water interface. The difference between the surface and air temperature were used to estimate the radiative transfers following Çengel and Turner (2001). The radiative transfers were found to be less than 1% of the turbulent fluxes even at the lowest wind speeds and were subsequently neglected in the calculations.

The bulk water temperature during a flux run decreased at a slower rate when an insulating cover was installed over the water surface (Fig. 4). The heat lost by the water is manifested by the temperature drop. Separate regression lines (the second-order polynomial fits) to these yield estimates of the total heat loss [the first term on the right-hand side of (6)] and the conductive heat loss through the piping and walls of the test section and the infrared radiative heat losses of the system [the second term on the right-hand side of (6)] as two time series, respectively. This allows us to obtain a time series of the interfacial enthalpy flux in accordance with (6).

Fig. 4.
Fig. 4.

Temperature decrease with time during a steady wind speed run. The dotted line is the measured bulk water temperature during a flux run for a reference wind speed of about 16 m s−1, and the solid line is the water temperature during a duplicate run with an insulating cover installed over the water surface.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

Note that estimates of the moist enthalpy flux by the calorimetric method given in (5) and (6) rely on the assumption that TW and TWC must represent layer-averaged mean bulk water temperatures. Thus, the water was continuously circulated at a slow speed (0.08 m s−1) for bulk water temperature measurements in all the runs presented here to assure that the water column was well mixed.

At the start of each constant wind speed run, the water was heated using the heat exchanger while the inline circulation pump was operated at a rather high speed (0.4 m s−1) to mix the entire water mass rapidly. The wind was maintained at low speed to keep the temperature and the concentration of water vapor in the air at the ambient outside air level as the initial condition. When the specified water temperature was reached, the heat exchanger was shut off, the water pump slowed down to 0.08 m s−1 and, once the water velocity stabilized, the wind was set to a specified speed to begin the data gathering. The length of the experimental runs varied between 10 and 40 min, depending on wind speed. This was long enough to obtain an accurate estimate of the rate of heat loss by the water mass. In total, 103 enthalpy flux runs were made with constant wind speeds ranging from 0 to 17 m s−1 at 0.2-m height and water–air temperature differences ranging from 1.3° to 9.2°C.

5. Results and discussions

a. The transfer coefficient of enthalpy

A dataset of 69 runs was used for estimation of bulk enthalpy transfer coefficients (Table 1) before correction to the 10-m neutrally stable reference value. Other data were measured but were omitted from analysis because of unreliable mean air temperature measurements by an unshielded thermistor at high winds or malfunction of a thermistor. After applying the log-profile corrections as discussed in section 4b, each run produced a time series of 1-min averaged qs, q10N, Ts, and T10N from which to compute ks and k10N from (2). Corresponding 1-min averages of HK were obtained from the TW and TWC time series using (6), and finally a 1-min averaged estimate of CK10N was determined using (4). An overall mean of these 1-min averages yielded an averaged CK10N for each run.

The value of CK10N varied between 0.000 97 and 0.0021 for U10N ranging from 0.6 to 39 m s−1 (Fig. 5). A minimum CK10N was observed at wind speeds between 2 and 5 m s−1 over which the flow conditions changed from aerodynamically smooth to rough. Increasing CK10N toward lower wind speeds corresponds to the flow over a smooth surface (Donelan 1990; Liu et al. 1979; Ocampo-Torres et al. 1994; Wu 1992). For wind speeds greater than 3 m s−1, the turbulent diffusivity increases with the surface roughness due to the presence of waves. This enhances the turbulent mixing of the air-side resistant quantities, sensible heat and water vapor, and thereby the exchange coefficient of enthalpy. This increase in CK10N (about 20% in the range of wind speeds 5–15 m s−1) was caused by the roughening of a surface exposed to a turbulent stream of fluid. It is less than the corresponding increase in the 10-m neutral drag coefficient CD10N, which increases by up to 100% over the same range of wind speeds (Donelan et al. 2004; DeCosmo et al. 1996; Large and Pond 1981). Thus the CK10N/CD10N ratio decreases over this wind regime as discussed in Haus et al. (2010). This weaker dependence of CK10N on wind speed can be explained by the exchange mechanism of water vapor and heat. The water vapor and heat transports are brought about primarily by molecular processes in the wind speed range considered (5–15 m s−1), while momentum transport is also caused by the form drag of pressure acting on the slopes of waves (e.g., Savelyev et al. 2011).

Fig. 5.
Fig. 5.

Exchange coefficient for the moist enthalpy transfer coefficient vs the reference wind speed. The values were obtained from water volume calorimetry, which includes a contribution from reentrant spray and were corrected for stability effects.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

b. The effects of spray

At high wind speeds, air–sea sensible and latent heat exchanges are known to result from two processes: 1) interfacial fluxes controlled by molecular processes right at the interface and 2) spray fluxes from the surface of spray droplets (Andreas et al. 2008). It has been suggested that for wind speeds above about 12 m s−1 the contribution of spray to the exchange of water vapor and heat becomes important, thereby increasing the moist enthalpy exchange coefficient (Andreas et al. 2008; Andreas and DeCosmo 1999, 2002; Emanuel 2003; Wu 1979). Model studies have suggested that the spray sensible and latent heat fluxes become comparable to the corresponding interfacial fluxes once the wind speed exceeds about 20 m s−1 (Andreas 1992) to 28 m s−1 (Fairall et al. 1994).

1) Spray observations

The total moist enthalpy transfer coefficient was observed to decrease slightly with increasing wind speed above 20 m s−1 (Fig. 5). However, significant amounts of spray were observed in those runs having wind speeds above 20 m s−1, as previously reported in Toffoli et al. (2011) and shown in Fig. 6. It should be noted that this imaging technique is limited to larger spray droplets that cause significant scattering of incident light.

Fig. 6.
Fig. 6.

Laterally stacked series of images (captured at 250 Hz) from a high-speed line-scan camera at wind speed of U10N = 40 m s−1. A laser beam was directed downward through the top of the test section at a fetch of 9 m. The transition from dark to light represents the wave surface, and bright spots above this surface indicate large numbers of spray droplets throughout the boundary layer.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

Measurements of the freshwater droplet distribution in the ASIST tank were made using a Cloud Droplet Imaging Probe (CDIP) as used in Fairall et al. (2009) (Fig. 7). The probe was mounted on a shaft that could be raised and lowered. It was positioned such that the sampling windows were above a level where the amount of spray in the air was so high that the instrument windows were occluded [greater than significant wave height Hs]. When this occurred the recorded data were clearly degraded as the sample area decreased significantly. The wind speed dependence of the droplet volume spectrum at a fixed level of 0.22 m above the mean surface is shown in Fig. 7. These laboratory-observed freshwater droplet concentrations were within the range of available oceanic observations as shown in Fig. 2 of Andreas et al. (2010). For example, at the highest wind speeds reported in Andreas et al. (2010) of about 20 m s−1, which is approximately equivalent to U10N = 40 m s−1 in our experiments, the spray concentrations converted to a volume concentration were 0.25 cm3 cm−3 μm−1. This is close to the value of 0.30 cm3 cm−3 μm−1 recorded in ASIST by the CDIP instrument at the equivalent wind speed (Fig. 7).

Fig. 7.
Fig. 7.

Freshwater droplet volume spectrum as observed by a Cloud Droplet Imaging Probe (CDIP) mounted horizontally looking upwind at 9.7-m fetch. The vertical level above the mean surface was 0.22 m, and the wind speed was set to a range of values from 30 to 50 m s−1. The wind speed was observed at the centerline of the tank and converted to a reference 10-m neutral wind speed U10N given above.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

Note that the calorimetric method measures the loss of heat from the water to extract the total moist enthalpy transfer coefficient. No discrimination between latent and sensible heat transfer is available from this measurement alone. The measurement includes the contributions of both the heat diffusion process for the interfacial fluxes (e.g., Ling and Kao 1976) and reentrant spray in the higher wind conditions as discussed in the next section.

2) Can the effects of reentrant spray be observed in this experiment?

As pointed out by Andreas and Emanuel (2001), the only mechanism by which spray can cool the water volume is by being ejected from the warmer water, cooling in the air, and then returning to the water. The question that must be addressed then is whether the contribution of reentrant spray to the water volume heat budget can be accurately captured in these laboratory experiments through the entire range of observed wind speed conditions.

There are three key time constants (following Andreas 1992, 2005, 2010) that must be considered when looking at this question in the open ocean: the duration of suspension of the spray droplet in the airflow tf, the temperature evolution time or e-folding scale for droplet cooling tτ, and the droplet radius evolution time scale tr. In the laboratory we have a fourth time scale imposed, that being the time before the droplet is carried outside of the test section tL.

The tL scale is relatively straightforward to estimate based on the wind speed (0–19 m s−1 at 29 cm above the water surface) and length of the tank (15 m). From visual observation spray generation begins almost immediately upon the wind entering the tank. Therefore the maximum value of tL in the strongest winds approaches 0.78 s and will be longer in lighter winds.

The tτ and tr scales have been estimated by Andreas (2005) for a range of salinities. These estimates were adapted by E. L Andreas (2011, personal communication) for freshwater, resulting in the ranges given in Table 2. The e-folding scales for freshwater are strongly dependent on droplet radius and range in order from about 10−5 to 2.0 s and 10−2 to 103 s for temperature and radius respectively, for droplets ranging from 1 to 500 μm.

Table 2.

Relevant droplet evolution time scale estimates for ASIST wind-wave tank at three wind speeds as observed at a level of one-half the wavelength of the dominant wave. The term tL is the time required for a droplet to exit the tank, tf is the time required for a spray particle to reenter the water, tτ is the temperature evolution time scale, and tr is the droplet radius evolution time scale.

Table 2.

An estimate of the duration of suspension is much more elusive than the other three scales. The simple approach used in Andreas (2010), in which spray is generated at the elevation of Hs and then falls back to a fixed level, does not apply in this case of strongly forced waves. Hs is a reasonable choice for the suspension height, although considerable lofting above this level can certainly occur due to nonzero vertical droplet velocities at the crest (e.g., Fairall et al. 2009). However, the distance over which the droplet must fall before reentering the water may not be related directly to the wave height. Andreas (2010) used a scaling of ½Hs for the vertical length scale over which the droplet needed to fall, but in strongly forced conditions the droplet most likely will impinge upon a wave farther downwind and does not have to fall to a lower elevation than the suspension height.

The variable suspension height of droplets is illustrated by the time series of surface elevation in Fig. 6 where many spray particles are observed both above and below the local wave height. Droplets ejected from the second wave from the right are traveling behind three larger waves in the group, which are likely to be the location of reentry of the droplet. In the wind wave tank this effect is even more pronounced than in less strongly forced conditions as the waves grow in height substantially in the downwind direction. The relevant time scale is then related to the relative speed of the droplet to the wave phase speed and the wavelength:
e10
where Cp is the wave phase velocity and is the horizontal component of the droplet velocity defined as , with being the wind speed at a vertical reference level of one-half the dominant wavelength λ and the droplet slip velocity, which is size dependent (Fairall et al. 2009).

Given typical values in the wind-wave tank of λ = 0.5 m, and invoking the linear dispersion relation to calculate the wave phase velocity, calculating Uλ/2 = 10 m s−1 from the log profile discussed in section 4b and assuming a distribution of slip velocities from 0% to 75% (Us = 0–7.5 m s−1) gives a tf scale ranging from 0.05 to 0.4 s. The suspension duration from (10) is inversely proportional to wind speed, which is counter to the trend from Andreas (2010). However, because in this experiment there are very young waves (Uλ/2Cp) and large droplet sizes (>10 μm), this is reasonable. The applicability of this scaling to open ocean conditions requires further evaluation.

Given the time scales as defined above, there are three requirements that must be met for this set of experiments to include the contribution from reentrant spray. The first requirement is that spray droplets reenter the water before exiting the tank (tf < tL). This condition is met for most of the droplets generated in the tank, except for those at the downwind end (Table 2). The second requirement is that the droplets have not evaporated entirely before returning to the surface (tr > tf). This condition is met for most of the droplets except for those approximately smaller than 10 μm, based on the Andreas (2005) scaling. The third requirement is that the droplets have changed temperature before reentering the water (tτ < tf). This condition is met for the smaller droplet sizes but may limit the ability of this method to observe the spray effect for droplets larger than approximately 200 μm.

In summary, the calorimetric method implemented here should capture the reentrant spray contribution to the moist enthalpy flux for droplet sizes in the range of about 10–200 μm. The range of 10–200 μm encompasses the bulk of the droplet distribution for the range of wind speeds considered here (Fig. 7). Droplet sizes less than about 25 μm are dominated by bubble bursting, which would be quite different in saltwater as opposed to the freshwater used in this study. However, Jones and Andreas (2012) summarized many oceanic spray observations and found that for U10N > 16 m s−1 spume droplets greater than 50 μm are generated, while there was little bubble production found at particle sizes larger than 25 μm (Lewis and Schwartz 2004). The large spume droplets are likely limited in size because they are torn into smaller droplets in the strong wind speeds as shown by Mueller and Veron (2009).

These estimates suggest that the calorimetric method as implemented in this study captures a significant fraction of the reentrant spray contribution to the total moist enthalpy flux. The exception is at the highest wind speed where large spume particles (300–600 μm) directly torn from the wave crests (Anguelova et al. 1999) or the destabilized interface (e.g., Marmottant and Villermaux 2004; Soloviev and Lukas 2010) are clearly evident.

3) Air volume moist enthalpy budget study to estimate missing spray-mediated transfers

As discussed in the previous section, in the open ocean reentrant spray is the only spray-related contributor to the net total moist enthalpy flux (Andreas and Emanuel 2001). In the wind-wave tank there may be additional contributions due to the incomplete evaporation of spray particles that exit the tank. The calorimetric method applied to the water volume is not capable of observing the portion of the spray sensible heat flux that is due to droplets that do not completely evaporate and are not reentrant.

For the purpose of estimating the contribution of spray that does not evaporate or reenter the tank, a moist enthalpy budget was applied to a control volume of air above the mean water level (Fig. 8). The control volume was chosen as having dimensions covering the full air cross section in the test section (mean water level to tank ceiling and walls) and extending for 11.7 m in the along-tank direction between the temperature and humidity measuring stations. The temperature was observed at the locations of the two thermistors (fetches of 0.38 and 11.78 m) and the humidity measurements were made at fetches of 2.9 and 14.9 m.

Fig. 8.
Fig. 8.

Schematic of the heat budget of the control volume above the mean water level. Total length of the control volume is 11.7 m; dy = 1.0 m and dz = 0.58 m.

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

The moist enthalpy balance (in watts) of the control volume assuming steady, one-dimensional airflow with constant free stream velocity is given by (11):
e11
where KIN is the measured moist enthalpy entering the test section, KINT is the moist enthalpy transferred by turbulent and diffusive processes across the air–sea interface, KSPRAY,RE-ENT is the enthalpy transferred to the water by reentrant spray, KSPRAY,IN is the enthalpy carried by spray drops upward across the air–sea interface, and KWALL is the enthalpy transferred to the surroundings through the top and sidewalls by conduction and radiation. This wall transfer term necessarily consists of only a sensible heat component. Also, KOUT is the measured moist enthalpy leaving the test section, and KSPRAY,OUT is the enthalpy transferred out of the test section by spray droplets that do not completely evaporate in the control volume. These incompletely evaporated droplets carry an amount of sensible heat that depends on their source location and their size-dependent temperature and evaporation scales.
The total moist enthalpy of the air volume at the inlet and outlet boundaries in watts can be calculated from
e12
e13
where qIN and qOUT are the inlet and outlet specific humidity, TIN and TOUT (K) are the mean entrance and exit air temperatures, respectively, the volume flux is dydzUm, and ρmix is the average density of the moist air. Values of the heat capacity (cp = 1.003 × 103 J kg−1 K−1, cpυ = 1.84 × 103 J kg−1 K−1) were used for dry air and water vapor, respectively, and Lυ = 2.5 × 106 J kg−1.
The sum of KINT, KSPRAY,IN, and KSPRAY,RE-ENT can be calculated from the measured HK in (6) multiplied by the water surface area between the input and outlet measuring stations AW as expressed in (14). This balance is required because it is the relative enthalpy difference (in watts) between the spray that leaves the surface and that which returns to the surface that constitutes the spray enthalpy flux:
e14
The enthalpy transferred through the wall separating two media KWall (W) under steady conditions and surface temperatures can be determined by the introduction of thermal resistance concepts (Çengel and Turner 2001). It can be separated into the conductive KC,Wall and radiative KR,Wall transfer rates:
e15
and
e16
where TR is the bulk temperature (K) of the surrounding room air (outside the tank), σ is the Stefan–Boltzmann constant (5.670 373 × 10−8 W m−2 K−4), T2 is the outer surface temperature of the wall, the area of the wall surface is AWall, and κ is the thermal conductivity of acrylic (0.19 W m−1 K−1). The dimensionless thermal emissivity ε of clear acrylic is estimated to be 0.94; thus, Rtotal, which is the total thermal resistance between the air in and outside the wall of thickness L and is in units of kelvins per watt, can be determined as
e17
where h∞1 and h∞2 are the convection heat transfer coefficients (W K−1 m−2). The term 1/(h∞1AWall) represents the thermal resistance of the air against heat convection into the wall, and L/(AWall) is the conduction resistance of the wall. The last term represents the combined thermal resistance of the outer wall surface against heat convection and radiation. In this approach, the air and material properties and the heat transfer coefficients (Nusselt correlations) were taken from Çengel and Turner (2001) while the other required parameter values are measured. Considering the losses through the walls of the control volume the heat loss (W) is
e18
Rearranging the enthalpy balance equation (11), we are left with the unknown spray term on the left and the measured terms on the right:
e19
While we cannot discriminate between the three components of the enthalpy transfer to the air volume from the water surface (−KINTKSPRAY,IN + KSPRAY,RE-ENT) on the right-hand side of (19), their sum is known from the water volume calorimetry in (14). Equation (19) then defines the loss of enthalpy due to nonevaporated spray that is blown out of the tank. This term can then be used to calculate the maximum potential magnitude of the unmeasured spray-mediated transfer terms in the water volume calorimetric method by assuming that this enthalpy would be returned to the tank if it were not bounded in the downwind direction. This is a conservative estimate because in an unbounded tank a proportion of the spray droplets would be evaporated before reentering and would not transfer enthalpy.

In this analysis, a dataset of nine runs from the present flux data with the unshielded thermistor was chosen for the estimation of the unmeasured spray contributions to the water–air enthalpy transfer. Because calculation (19) required that the precise entrance and exit enthalpies be known and they are measured by independent instruments, the balance of KIN and KOUT as expressed in (19), considering only interfacial fluxes and wall losses, was computed at the lowest observed wind speeds of U10N = 3.8 m s−1. This value was chosen because it was below the threshold for which any spray contribution to the fluxes could be expected. A correction was then made to the humidity measurement (qOUT) to force the resulting KSPRAY,OUT to zero. This bias (0.001 401 kg kg−1, or about 16% of qOUT) was then applied to the other terms. Furthermore, in order to obtain a valid enthalpy balance, the dataset was limited to winds less than 30 m s−1 where spray droplets began to impinge directly on the thermistor that was mounted at a level of 0.29 m above the mean water surface.

Using adjusted values of HK that accounted for the unmeasured terms in the bulk formulation for total enthalpy transfer, estimates for the total enthalpy transfer coefficients varied by up to 23% (Fig. 9). This difference did not increase with wind speed, once the winds were strong enough to generate spray. It is important to note that this unmeasured quantity is an upper limit of the possible spray contribution to the laboratory observed fluxes. Some fraction of the spray that exits the tank would be reentrant and thereby contribute to the moist enthalpy flux and some would be evaporated completely and not contribute. The enthalpy exchange coefficient including spray is about 6% larger at U10N = 8 m s−1 and about 38% larger at U10N = 13 m s−1 and higher. It does not show the strong dependence on spray predicted by Andreas (2011).

Fig. 9.
Fig. 9.

Enthalpy transfer coefficients calculated from the water volume only (squares) and the total potential contribution of the unmeasured spray terms as estimated from the air volume enthalpy budget (circles).

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

The measurements of HK, including as they do some of the reentrant spray, are an upper limit on the purely interfacial enthalpy transfer coefficient due to turbulence in the air boundary layer. Insofar as the outgoing spray contribution to the enthalpy flux is an upper limit to the missing reentrant spray (Fig. 9), the adjusted CK10N values are an upper limit to the effective enthalpy transfer coefficients including spray-mediated transfers. The calorimetric measurements include some spray-mediated transfers and so the purely interfacial enthalpy transfer coefficient at winds above 20 m s−1 is clearly somewhat smaller than the observed CK10N (Fig. 5). Thus, the spray-mediated fluxes are seen to have at most a 38% effect on the enthalpy transfer coefficient and the effect does not increase appreciably with wind speed; in other words, the spray-mediated enthalpy flux scales nearly linearly with wind speed.

c. Comparison of CK10N with field measurements

The values of enthalpy exchange coefficients for neutral conditions based on the reference wind speed were compared with data from oceanic eddy-correlation measurements of DeCosmo et al. (1996) during the Humidity Exchange Over the Seas (HEXOS) experiments and Zhang et al. (2008) in the Coupled Boundary Layer and Air–Sea Transport (CBLAST) program (Fig. 10). Note that CK10N values of HEXOS are computed from sensible and latent heat flux data reported in the literature. Furthermore, in order to make a proper comparison, CK10N estimates from HEXOS are modified to account for three established correction factors of Fairall et al. (2003). The results from HEXOS and CBLAST are shown scattered about the laboratory CK10N values. HEXOS CK10N values are scattered between approximately 0.8 × 10−3 and 1.9 × 10−3 about an average of 1.2 × 10−3 for a range of wind speeds between 6 and 18 m s−1. CBLAST CK10N values show a considerable scatter between approximately 0.5 × 10−3 and 2.3 × 10−3 about an average of 1.16 × 10−3 in the wind speed range of 16–29 m s−1.

Fig. 10.
Fig. 10.

Comparison of laboratory observed enthalpy coefficient (open diamonds) with the results from field experiments. Bin averages (filled diamonds) with 95% confidence intervals are shown for the laboratory observations. All values adjusted to the 10-m reference height. Field data from the HEXOS experiment as reported in DeCosmo et al. (1996) are shown (gray circles) along with their bin averages (yellow circles) with 95% confidence intervals and the overall mean value (yellow line). CBLAST experiment data from Zhang et al. (2008) are shown (gray triangles) along with their bin averages (cyan triangles) with 95% confidence intervals and the overall mean value (cyan line).

Citation: Journal of the Atmospheric Sciences 69, 9; 10.1175/JAS-D-11-0260.1

It is apparent that the laboratory measurements are consistent with field estimates of CK10N. However, the scatter in the field data is such that the details of the variations of CK10N are obscured. To estimate reliable wind speed dependence of CK10N, the data are averaged in bins of 10-m neutral wind (Fig. 10). The bin width increases slightly at the higher wind speeds, where there were less dense data. Error bars indicate the statistical uncertainty (95% confidence interval) of the bin average based on the distribution within the wind speed bin. The between-runs reproducibility of our laboratory measurements is indicated by the small uncertainty.

In the range of wind speeds of 5–20 m s−1, our laboratory measurements agree particularly well with field estimates of CK10N. For wind speeds between 20 and 30 m s−1, CK10N from CBLAST shows a hint of decrease with increasing wind speed, while our CK10N remains practically constant. However, taking into account that this tendency in the CBLAST data is statistically insignificant because of the large standard error, we can consider that there is no disagreement between our results and the CBLAST measurements. For wind speeds beyond 30 m s−1, our results show a slight decrease of CK10N with increasing wind.

Interpreting this laboratory result in terms of spray evaporation in the field, we note that fresh relatively dry air enters the control volume at one end of the tank and is externally vented after a single pass over the water. Therefore, the humidity in the air never approaches saturation. Seawater also has a slightly lower vapor pressure (~2% difference) than freshwater and will therefore stop evaporating at relative humidity below 100%. This will tend to increase the latent heat transfer relative to the open ocean where the boundary layer becomes more humid as spray evaporates and provides a negative feedback to further evaporation (Andreas 2005).

Conversely, the spray that exits the tank without reentering the water or being significantly modified by evaporation will transfer sensible heat to the air volume. This will increase the sensible heat in the air volume relative to the open ocean; however, it will not directly affect the water volume in the laboratory because the spray is not reentrant (Andreas and Emanuel 2001). We have estimated this exiting spray quantity in the air volume enthalpy balance and have thereby established an upper limit on the spray-mediated transfer (Fig. 9). However, we cannot determine if the spray evaporation over the open ocean is less effective in increasing the net enthalpy flux than we have measured here because of the feedback effects mentioned above.

6. Conclusions

This study has provided high-precision laboratory observations using freshwater of the net interfacial and reentrant spray contributions to the transfer coefficient of moist enthalpy for 10-m neutral wind speeds up to 39 m s−1. The coefficient (referenced to a 10-m height) decreased with increasing wind speeds for smooth flows (U10N < 3 m s−1), increased with wind for rough flows (U10N > 5 m s−1), and was virtually independent of wind for fully rough flows with spray (13 < U10N < 30 m s−1). For winds above 30 m s−1, the enthalpy transfer coefficient reduces slightly and maintains that level to the highest wind speed measured of 39 m s−1. This reduced saturation level occurs at roughly the same wind speed at which the drag coefficient measured in the same tank by Donelan et al. (2004) flattens out. The laboratory measurements include the interfacial enthalpy fluxes as well as part of the spray-mediated fluxes and, as such, represent an upper bound on the purely turbulent (interfacial) enthalpy fluxes.

The laboratory CK10N was found to agree well with the HEXOS results of DeCosmo et al. (1996) in the range of 6–18 m s−1. For the wind range of 16–29 m s−1, the CBLAST results of Zhang et al. (2008) also do not contradict our observations. Our analysis using both water volume calorimetry and an air volume enthalpy budget demonstrates that the unmeasured spray-mediated fluxes may account for up to a 38% increase in the overall moist enthalpy transfer coefficient at high winds. This provides an upper limit for the total moist enthalpy transfer coefficient including spray-mediated transfers.

Acknowledgments

We thank Ivan Savelyev and Jun Zhang for helpful discussions and Michael Rebozo for invaluable assistance in setting up and conducting the experiment. Chris Fairall’s generous loan of the CDIP spray sampling system provided valuable droplet distributions. We also thank Ed Andreas, who provided estimates of the e-folding scales, and two other anonymous reviewers for their contributions through the review process. We gratefully acknowledge the support of the Office of Naval Research under Grant N00140610258 and the National Science Foundation under Grant AGS0933942.

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  • Anderson, R. J., 1993: A study of wind stress and heat flux over the open ocean by the inertial-dissipation method. J. Phys. Oceanogr., 23, 21532161.

    • Search Google Scholar
    • Export Citation
  • Anderson, R. J., and S. D. Smith, 1981: Evaporation coefficient for the sea surface from eddy flux measurements. J. Geophys. Res., 86, 449456.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 1992: Sea spray and the turbulent air–sea heat fluxes. J. Geophys. Res., 97, 11 42911 441.

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  • Andreas, E. L, 2010: Spray-mediated enthalpy flux to the atmosphere and salt flux to the ocean in high winds. J. Phys. Oceanogr., 40, 608619.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 2011: Fallacies of the enthalpy transfer coefficient over the ocean in high winds. J. Atmos. Sci., 68, 14351445.

  • Andreas, E. L, and J. DeCosmo, 1999: Sea spray production and influence on air–sea heat and moisture fluxes over the open ocean. Air–Sea Exchange: Physics, Chemistry, and Dynamics, G. L. Geernaert, Ed., Kluwer, 327–362.

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  • Andreas, E. L, and J. DeCosmo, 2002: The signature of sea spray in the HEXOS turbulent heat flux data. Bound.-Layer Meteor., 103, 303333.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, P. O. G. Persson, and J. E. Hare, 2008: A bulk turbulent air–sea flux algorithm for high-wind, spray conditions. J. Phys. Oceanogr., 38, 15811596.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, K. F. Jones, and C. W. Fairall, 2010: Production velocity of sea spray droplets. J. Geophys. Res., 115, C12065, doi:10.1029/2010JC006458.

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  • Fig. 1.

    (a) Cartoon of test section of ASIST. Control volume for the calorimetric method denoted by the dashed box. Shaded gray sections denote water piping through which conductive heat transfer may occur through the walls. Arrows show transfers of heat through water surface, sidewalls, and bottom. (b) Scaled diagram of the ASIST wind-wave flume, showing air inlets and piping detail.

  • Fig. 2.

    Arrangement of temperature, humidity, and airspeed sensors in the working section of the recirculating water and ventilating air flume.

  • Fig. 3.

    Air temperature at a fetch of 11.78 m during a run in which wind speed was increased from 0 to its maximum (39 m s−1 referred to 10-m height) and decreased again to 0 (gray line). The black solid line is the measurements of air temperature by the shielded thermistor sensor, and the black dash-dotted line is the measurements by the unshielded thermistor sensor. The contamination of temperature sensor by spray is reflected in the sudden drop in the temperature from the unshielded sensor.

  • Fig. 4.

    Temperature decrease with time during a steady wind speed run. The dotted line is the measured bulk water temperature during a flux run for a reference wind speed of about 16 m s−1, and the solid line is the water temperature during a duplicate run with an insulating cover installed over the water surface.

  • Fig. 5.

    Exchange coefficient for the moist enthalpy transfer coefficient vs the reference wind speed. The values were obtained from water volume calorimetry, which includes a contribution from reentrant spray and were corrected for stability effects.

  • Fig. 6.

    Laterally stacked series of images (captured at 250 Hz) from a high-speed line-scan camera at wind speed of U10N = 40 m s−1. A laser beam was directed downward through the top of the test section at a fetch of 9 m. The transition from dark to light represents the wave surface, and bright spots above this surface indicate large numbers of spray droplets throughout the boundary layer.

  • Fig. 7.

    Freshwater droplet volume spectrum as observed by a Cloud Droplet Imaging Probe (CDIP) mounted horizontally looking upwind at 9.7-m fetch. The vertical level above the mean surface was 0.22 m, and the wind speed was set to a range of values from 30 to 50 m s−1. The wind speed was observed at the centerline of the tank and converted to a reference 10-m neutral wind speed U10N given above.

  • Fig. 8.

    Schematic of the heat budget of the control volume above the mean water level. Total length of the control volume is 11.7 m; dy = 1.0 m and dz = 0.58 m.

  • Fig. 9.

    Enthalpy transfer coefficients calculated from the water volume only (squares) and the total potential contribution of the unmeasured spray terms as estimated from the air volume enthalpy budget (circles).

  • Fig. 10.

    Comparison of laboratory observed enthalpy coefficient (open diamonds) with the results from field experiments. Bin averages (filled diamonds) with 95% confidence intervals are shown for the laboratory observations. All values adjusted to the 10-m reference height. Field data from the HEXOS experiment as reported in DeCosmo et al. (1996) are shown (gray circles) along with their bin averages (yellow circles) with 95% confidence intervals and the overall mean value (yellow line). CBLAST experiment data from Zhang et al. (2008) are shown (gray triangles) along with their bin averages (cyan triangles) with 95% confidence intervals and the overall mean value (cyan line).

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