1. Introduction
a. Motivation
The balance between moist enthalpy input and wind energy dissipation at the air–sea interface is thought to be critical to tropical storm development (Emanuel 1986). Over the last several decades a respectable body of knowledge has been developed on the processes of mass, momentum, and energy fluxes at the ocean surface in light to moderate winds. However, our direct knowledge of these fluxes in high winds remains sparse. At wind speeds (10-m equivalent; U10) above 30 m s−1, there is generally a significant quantity of spray entrained in the atmospheric boundary layer (Fairall et al. 1994). This transition zone from the spray-free to a spray-laden boundary layer seems to correlate with the apparent saturation of the drag coefficient, which occurs in the wind speed range of 30–40 m s−1, as observed in both laboratory (Donelan et al. 2004) and field (e.g., Powell et al. 2003; Potter et al. 2015) studies. One potential explanation for this is that the presence of spray in the boundary layer alters the vertical wind profile (Pielke and Lee 1991; Barenblatt et al. 2005), which can be shown to change the theoretical logarithmic relationships used to derive the aerodynamic roughness (Lykossov 2001). Kepert et al. (1999) demonstrated that including spray effects in a coupled atmosphere–ocean model can have a dramatic effect on the air–sea fluxes during a simulated tropical cyclone. However, direct observations of this remain elusive. The impact that the development of this spray layer has on the exchange of heat and momentum remains relatively unknown (Haus et al. 2010; Jeong et al. 2012). Determining this relationship holds implications for a number of oceanographic and atmospheric processes, including the rate of intensification of tropical cyclones (Soloviev et al. 2014).
The effects of sea spray on the air–sea interface are highly size dependent since particles are generated over a wide distribution of radii (nominally from 1 μm to 1 mm). Droplets with radii less than about 25 μm are likely produced by bubble bursting (e.g., Monahan et al. 1986; Clarke et al. 2006) and have a minimal effect on momentum and heat fluxes. This generation mechanism is likely only a minor source for particles larger than 25 μm (Lewis and Schwartz 2004). These larger particles are referred to as spume and thought to be generated largely by the process of wave breaking. Jones and Andreas (2012) summarized many oceanic spray observations and found that for U10 > 16 m s−1 droplets with radius greater than 50 μm may be generated. In the case of even higher winds, it becomes evident that large spume particles (300–600 μm) can be directly torn from the wave crests (Anguelova et al. 1999) or the destabilized interface (e.g., Marmottant and Villermaux 2004; Soloviev et al. 2014).
b. Spray effects on air–sea momentum exchange
There are a number of alternative explanations for the potential role of spray in altering the air–sea momentum exchange: 1) The return of spray droplets to the water surface suppresses the short waves that carry much of the stress (Andreas 2004). 2) The existence of a turbulence-suppressing, spray-laden layer above the air–sea interface inhibits the direct physical interactions between the sea surface and the atmosphere (Barenblatt et al. 2005; Bye and Jenkins 2006). 3) The onset of Kelvin–Helmholz instabilities leads to the production of spray and spume and the stabilization of the surface roughness as the crests of steep waves are blown off (Soloviev et al. 2014).
Early research suggested that the primary effect of spray would be to enhance air–sea momentum exchange because of the momentum required to accelerate spray droplets to the wind speed, which would then be transferred to the water upon reentry (Munk 1955; Pielke and Lee 1991). Subsequent studies based primarily on the low to moderate wind regime found this effect to be insignificant (Wu 1972). Fairall et al. (1994) calculated that the spray stress (wind to water) would have only a small influence (10% of the total stress) for winds up to
Andreas (2004) suggested that spray’s main role is to redistribute the wind’s momentum in the near-surface layer, with the spray acting to slow the near-surface wind speed by roughly 10% (for winds ~30 m s−1). As a result, although the total surface stress may be the same as in the absence of spray, the spray contribution to that stress increases with wind speed while the interfacial contribution decreases. The author recalculated the spray contribution by separating the stress into an interfacial and a spray contribution and found that spray could have a much stronger role than estimated by the earlier works. Furthermore, he speculates that the spray droplets returning to the sea surface would suppress short waves and thereby lead to a reduction in the surface roughness. The existence of a droplet evaporation layer (Andreas et al. 1995) close to the surface would further suppress turbulence close to the interface (Andreas et al. 2008) and lead to a reduction in interfacial transfers.
Alternatively, a theoretical model developed by Lighthill (1999), and expanded upon by Barenblatt et al. (2005), suggests a mechanism that would produce a sharp reduction in the atmospheric drag coefficient as a result of spray loading. This so-called sandwich model postulates that once the spray droplet size and concentration in the boundary layer reaches a threshold concentration the dynamics will evolve into a stably stratified multiphase flow, where the effective density of each layer is determined by the spray concentration (akin to thermodynamic stratification with spray instead of temperature). This model results in a significant decrease in the stress that is supported across the ocean–atmosphere interface—now the ocean–spray–atmosphere interface. Their spray layer thickness and the boundary layer velocity profile were found to be strongly dependent upon the spray droplet size, with the larger particles being the most significant to the stress reduction.
Bye and Jenkins (2006) and Bye and Wolff (2008) presented a unified boundary layer model that incorporated some of the basic elements of the Lighthill (1999) approach. The model is unified in the sense that it combines a wave model, a spray generation function based on breaking waves, and a boundary layer turbulence model. The unified model predicts a leveling off of
c. Spray effects on the enthalpy flux
Latent and sensible heat fluxes both contribute to the total moist enthalpy flux. At winds high enough to generate spray, these fluxes are generated through two distinct mechanisms: 1) molecular-scale interfacial fluxes that occur at the air–sea interface and 2) spray fluxes produced by droplets ejected from the water surface into the air (Andreas et al. 2008). Many authors have suggested that the spray contribution becomes important at wind speeds above ~12 m s−1, thereby increasing the overall moist enthalpy exchange coefficient (Wu 1979; Andreas and Decosmo 1999, 2002; Andreas et al. 2008; Emanuel 2003). Models have shown that, for wind speeds greater than approximately 20 m s−1, the spray sensible and latent heat fluxes are as large as the interfacial fluxes (Andreas 1992). Dropsonde data confirm this (Richter and Stern (2014)) for winds up to 70 m s−1. In the laboratory, Jeong et al. (2012) found that the total moist enthalpy transfer was essentially constant with increasing wind speed up to 40 m s−1. However, Andreas and Mahrt (2015) argued that Jeong et al. (2012) only captured the interfacial transfers, pointing to the need for additional spray-mediated enthalpy flux observations.
It has been shown by Andreas and Emanuel (2001) that spray can only cool the water volume by being ejected from the warmer water, cooling in the air, and then returning to the water. To quantify this cooling mechanism, there are three key time constants (following Andreas 1992, 2005, 2010) that must be considered: the duration of suspension of the spray droplet in the airflow
The
d. Spray production
The evolution, development, and ultimate impact of entrained spray and spume in the atmospheric boundary layer all depend on the rate at which spray is produced and the size-dependent vertical distribution of these particles above the ocean surface. This foundational knowledge has yet to be fully described in the literature for the full spectrum of particle sizes, particularly at wind speeds when spray is expected to be most significant for heat and momentum exchange across the air–sea interface. Spray generation source functions derived from limited field observations exhibit a very wide range of values, and none of these studies have achieved reliable measurements in hurricane conditions. The extreme conditions necessary to produce the spray volumes of interest make meaningful field observations an arduous, if not impossible, task (Melville 1996). Although the laboratory is a much simpler environment in which to make spray observations than in the field, it is still a complicated undertaking; consequently, there have been only limited observations of the spray distributions above breaking waves for either fresh or saltwater in the laboratory. Veron et al. (2012) made observations in high wind speeds that show orders of magnitude divergence from the Fairall et al. (2009) production rate (e.g., Fairall et al. 2009). More observational work is necessary to understand these results and to fully characterize the distribution of spume droplets above the wavy surface.
The present study addresses some of the gaps in the literature through laboratory observations in saltwater. Direct measurements of spume concentration profiles were made in hurricane-force winds above actively breaking waves. Experiments were done using filtered seawater and were conducted in 10-m equivalent wind speeds ranging from 36 to 54 m s−1. An unobtrusive optical technique was used that minimized the flow distortion and particle disruption. From these observed profiles, a bulk parameterization was used to estimate the corresponding source functions; these were compared to previous observations and typical source function models. Imaged particles ranged in radius from 80 to just over 1400 μm, which lie in the spume regime of the production spectrum. While laboratory experiments in these conditions are challenging, having controllable, repeatable experimental conditions makes this approach an attractive alternative to similarly aimed field campaigns.
2. Theoretical background: Quantifying spray generation
A comprehensive review of sea spray literature to date can be found in Veron (2015); the reader is directed to this article for further details regarding the theoretical and empirical background for spray generation mechanisms. The following is a condensed treatment of the material relevant to this study.
3. Laboratory observations
a. The facility
The experiments were carried out in the University of Miami Air–Sea Interaction Saltwater Tank (ASIST), which has a 15 m × 1 m × 1 m acrylic test section (Fig. 1). This facility is capable of generating both wind waves with a single turbine fan and one-dimensional mechanical waves. Spray images were collected 11.05 m downwind from the wind inlet, and the maximum sustained winds in the tank reached 54 m s−1 U10. This was observed via sonic anemometer 2.35 m upwind of the imaged volume, and the sampling volume of the anemometer was 20 cm above the still water line. The winds were referenced to 10 m following previous work done in ASIST (Donelan et al. 2004; Haus et al. 2010). All of the experiments presented here were done with an initial water depth of 0.42 m and using 10-μm filtered seawater pumped in from a local tidal inlet (Bear Cut). There are no nearby freshwater sources, and before being filtered the seawater was settled in a large basin to remove large suspended particulates. For all of the experiments, the salinity of the seawater was ~33 psu.
The drag parameter used in the present study comes from work done in ASIST by Donelan et al. (2004), where three independent methods were used to estimate this parameter as a function of wind speed. This laboratory study compared the results of the eddy correlation technique (e.g., Edson et al. 2013) with those from a profiling and momentum budget method, the latter being a technique that uses mass conservation in the flume and the pressure–slope relation. This provides a robust estimation of the aerodynamic drag as a function of wind speed for this facility. The observed
Multiple regression results for the generation function S0(r). The estimated mean, integrated spray flux in thousands of particles per unit water surface area per second (m−2 s−1) is given by
b. Data collection and processing
A Dantec Dynamics particle image velocimetry (PIV) data acquisition system was used to collect the spray imagery used in the analysis of the concentration function. The PIV system was modified for spray observations by rerouting the laser sheet through a liquid light guide to a strobe (Dantec ShadowStrobe). The strobe produced a collimated beam that helped minimize size distortion based on the distance from the light source. The beam illuminated a small section of a diffuser screen mounted on the outside of the ASIST wall and a camera (JAI CV-MSCL, 1.9 MP, 30 fps) was oriented directly opposite in order to capture images of this region. Spray droplets being advected through the volume between the camera and screen were imaged as a shadow projection (see Fig. 2). The camera–strobe system was mounted outside the acrylic tank and enabled undisturbed observations of vertical spray concentration profiles.
Sampling was done at two reference levels centered at 95 mm (lower) and 145 mm (upper) above the MWL in order to reconstruct
Image processing was done in two steps using the Dantec Dynamics shadow imaging software package. Each raw image was balanced initially to correct for irregularities in the image light sheet by taking the mean intensity of the set of 250 images. The raw frames were then normalized by this mean image, which resulted in higher contrast and easier particle detection. Droplet characterization was then carried out using an automatic shadow sizing routine. The detection algorithm was trained first by selecting a particle in one image in order to get a baseline for gray-level contrast and edge gradients. The steepness of the edge gradient determines how in and out of focus detected particles are: only gradients above a threshold steepness are considered in the plane of focus and counted. After the detection parameters were determined based on this “training,” the detection algorithm was automatically applied to every set of shadow images (>17 500 individual frames). The end result provided droplet centroid location and surface area, and the radius reported in this study was calculated assuming circular droplet projections.
This clearly begins to stop being valid for particles with radii exceeding 500 μm (see Fig. 3). This is an issue for the radius-dependent spray generation function, which relies on direct measurement of the particle radius at formation
Applying the identification criteria universally does not maximize detections for a particular set of 250 images, but it is a standardized means of spray detection and sizing, enabling direct comparison between respective data collections. This method is not only more expeditious than employing visual identification criteria, but it also minimizes the experimenter biases. It is expected that these biases would have been significant given the difficulty of consistently analyzing thousands of images. The success rate of the automatic processing algorithm was tested against visual inspections of a portion of the image sets. The results of the user-observed particle detection and the automatic processor were compared for every twenty-fifth frame of the 250 image sets. In general, the algorithm successfully detected 75%–90% of the droplets. The lowest-wind-speed trial tended to be underdetected by the algorithm, with a success rate just above 60%. Each set of 250 images was collected independently, and it is possible that this may be a result of low image contrast in this particular trial, which was observed when the images were inspected and compared to other trials. For all of the experiments, a radius dependence was observed in the algorithm’s success rate, in that smaller particles (10 pixels or less in diameter) were more likely to be missed than larger particles.
The camera used to acquire the droplet images was a medium telephoto lens with a 23.3° field of view. This is a nontelecentric lens, and thus the image magnification exhibits a dependence on an object’s location within the depth of field; however, experimentally this source of error in the reported particle sizes is small. The focal plane of the camera was calibrated 0.59 m away from the lens (center of the air space in ASIST). This yields a depth of field of order 3 mm and results in a magnification error in the particle sizing around 1%. This is much less than the uncertainty associated with the automatic detection and sizing algorithm used to process the imagery. In the plane of the ASIST center line, the sampling volume represented by the camera frame was 55 mm × 75 mm (Fig. 2). The across-tank dimension was determined in postcalibration to be 70 mm. This was found to be the operational depth of field and was quantified using a target with standardized circles of known diameters (and separation) between 1 and 2.5 mm. The edge-detection algorithm was unable to discriminate between in- and out-of-focus droplets to the precision of the camera lens’ depth of field (i.e., ±1.5 mm). The pixel resolution of each frame was 42 μm, which was determined using the standardized calibration target.
4. Results
Spray concentrations were measured in ASIST for five wind conditions with 10-m equivalent wind speeds ranging from 36 to 54 m s−1 and at two vertical reference levels (upper and lower) above the MWL in the tank; all of the experiments were done using filtered seawater (Fig. 3). Tests were carried out independently for a given wind speed and reference height with several collections of 250-image sets acquired per test. From these images, spray droplets were identified, sized, and then segregated into 50-μm-radius classes.
a. Observed number concentrations
The mass concentration for each discrete radius class was observed to decrease with height above the MWL and increase with wind forcing (Fig. 4). The total mass concentration was calculated from the raw spray counts at each acquisition level and normalized over the entire imaged volume. For both acquisition levels, a discernible peak in the mass concentration spectra observed between 500 and 800 μm. The postpeak slope tends to be steeper than the prepeak slope, and this is most pronounced at the higher wind speeds. When integrated across all radii, about 150% more water mass per unit air volume is observed in the lower level versus the upper level, with this difference increasing slightly with increasing wind speed. The vertical difference was most pronounced for the larger particles. The mass concentration observed in the upper frame saturates between 49.5 and 54 m s−1
The validity of the assumptions used to build the spray generation parameterization presented in section 2 can be tested by transforming the profiles
A subset of the results is given in Fig. 7 alongside similar results from the Fairall et al. (2009) study and unpublished saltwater observations made in ASIST during the Jeong et al. (2012) study. The Fairall et al. (2009) study made observations in both fresh and saltwater (only the latter is used for comparison here), and both wind and mechanical waves were used to generate spray droplets. The work reported from ASIST was conducted using saltwater and only tested wind-generated waves. For a comparison of fresh and saltwater droplet production, see Ortiz-Suslow et al. (2016).
All of the concentration spectra given in Fig. 7 have been transformed down to the source level using Eq. (12). Like these previous studies, the
The Fairall et al. (2009) observations in Fig. 7 come from the same wind forcing but different measurement heights and show within one order of magnitude collapse onto an effective dvdr value at the source level. The convergence tends to get better with increasing particle radius; however, it is unclear if this is a physical phenomenon or a result of the instrument bias noted in that previous study. In comparison, the ASIST-SIS data exhibit between half and one order of magnitude convergence, which remains fairly consistent across the entire size spectrum. In their analysis, Fairall et al. (2009) considered this level of collapse as satisfactory, but this conclusion may be questionable in the present study, given the ASIST-SIS spectra.
The differences in dvdr within the Fairall et al. (2009) and ASIST-SIS datasets seems to be most sensitive to the position of the original measurement relative to the source height. This may also explain the relative differences between all of the volume concentration spectra for the three datasets from Fairall et al. (2009), ASIST-SIS, and the ASIST-CIP. This is somewhat counterintuitive, since wind forcing (or some other physical variable) would be expected to be a stronger predictor of the volume concentration at the source height. This suggests that there is vertical variability in the profiles that cannot be removed by this transformation. This may explain why the collapse of dvdr onto a single value was limited for the ASIST-SIS observations.
b. Estimates of the generation function
The following analysis is done with regard to the ASIST-SIS dataset and reflects the observations of the present study. The observed
The
The ASIST-SIS
For comparable wind speeds, the estimates of S0(r) are about one-half order of magnitude less than the estimates of Veron et al. (2012). However, for both of these studies the radius dependences of the S0(r) spectra are remarkably similar (R2 > 0.98 for all wind speeds) and exhibit radius dependences between r−3 and r−5. Some of this similarity stems from these spectra being converted from concentration to source functions using the same parameterization. Even with less overall production observed, the ASIST-SIS results show several orders of magnitude more large particles (radii approaching 1 mm) than a production model with a size falloff closer to r−8 (Mueller and Veron 2009).
The directly observed concentration spectra from both Veron et al. (2012) and ASIST provides a more explicit comparison between these two observational studies (Fig. 9). The spectra from ASIST given in Fig. 9 are vertically averaged over the lowest six bins of the profile and are effectively from a
The ASIST observations show a slightly shallower radius falloff and thus significantly more circa 1-mm-radius particles, which is somewhat unexpected given the relative heights of the observations. The ASIST measurements were made at more than twice the fetch of those from Veron et al. (2012), so differences in the local wave development may be a reasonable explanation for this discrepancy. Regardless of these differences, in the context of the various model spectra given in Fig. 8a, there is relatively strong agreement across these two studies that the large particle production is significantly underpredicted by existing model functions (e.g., Mueller and Veron 2009).
c. Regression analysis
Up to this point, wave-state-dependent parameters have not been explicitly considered. However, the observed
5. Discussion
Regression coefficients to the empirical number concentration profile given in Eq. (28). MSE is the mean square error.
As an empirical solution to the number concentration profile, Eq. (28) could suggest that the
As an additional note, the recent review by Veron (2015) includes a slip factor parameterization
6. Conclusions
A laboratory investigation into sea spray generation in wind speeds ranging from 36 to 54 m s−1 U10 was conducted to fill gaps in the literature regarding the spume production rate. An extensive set of spume droplet shadow images has been collected showing the vertical distribution of particles above actively breaking waves. The range of observed particle radii was roughly 80–1400 μm, and the methods used enabled direct quantification of the mean size-dependent number concentration profiles necessary to estimate the vertical flux of sea spray at the water surface. Spume drops were imaged between 2 and 6 times the local Hs, and for the highest wind speeds droplets circa 1 mm in radius were observed in relatively high quantities at 3–4 times Hs. This may suggest that these large droplets have a longer-than-expected lifetime in the atmospheric boundary layer, which could affect the role these particles play in the fluxes across the air–sea interface. However, the particle transport information necessary to confirm this was not measured as part of the present study. This observation is limited to pure wind waves, and making similar observations, including droplet transport, with both wind and swell waves will be the focus of future efforts.
A bulk spume generation model (Fairall et al. 2009; Veron 2015) was used to infer the size-dependent generation function from the droplet concentration measurements. These estimated source functions affirm previous laboratory work in similarly high winds (Veron et al. 2012) that demonstrated that large spume droplets (in the vicinity of 1 mm) are produced at rates several orders of magnitude higher than would be predicted by a typical source model (Mueller and Veron 2009). Further statistical analysis showed that less additional spray flux was observed for each incremental increase in wind forcing. Also, the size dependence of the source function was found to exhibit a clear wind speed dependence, which does not agree with spume production theory (Fairall et al. 1994). A similar relationship was found in a recently published study (Veron et al. 2012), which had not been previously described. The results of converting the observed concentrations to size-dependent source functions, using the spume generation model, demonstrated that there was variance in the observational data that was not fully captured by the parameterization. To investigate this further, least-squares regression analysis was used to test the concentration profile implied by the model against the directly measured profile acquired from the shadow images. These tests demonstrate that the measured concentrations follow a logarithmic profile rather than the power-law profile prescribed by the model. This finding has significant implications for estimating the vertical flux of spume droplets, which is critical to understanding the role sea spray plays in the lower portion of the atmospheric boundary layer, particularly in tropical cyclones. It must be emphasized that these findings are purely empirical, but they do suggest that it is necessary to reevaluate the governing transport equations in order to better capture spume dynamics in these strongly forced conditions.
Acknowledgments
The laboratory experiments were supported by the NSF through Grant 0933943. Additional support was provided through ONR Grants N000141410643, N000141310144, and N000141210448. The authors appreciate the efforts of Mike Rebozo and Dr. Neil Williams for their help with the data collection. The constructive criticisms of three anonymous reviewers are greatly appreciated, as their careful efforts greatly improved this study. E. Lewis is thanked for his thoughtful comments that helped to strengthen this work, as is C. Fairall for the use of the CIP in ASIST. Also, M. Donelan is thanked for help acquiring and analyzing previously collected data in ASIST.
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