1. Introduction
The effects of sea spray on heat, moisture, and momentum exchange between the atmosphere and the ocean have been the subject of numerous studies since pioneering works by Bortkovskii (1973), Borisenkov (1974), Wu (1974), Ling and Kao (1976), and Andreas et al. (1995). Modern studies are particularly motivated by the need to resolve problems formulated in a theoretical paper by Emanuel (1995), which showed the crucial role of the ratio of the enthalpy transfer coefficient to the surface drag coefficient, which should exceed 0.75 for realistic hurricane intensities with the established parameters of the tropical atmosphere and ocean. The possibility of meeting this condition is indicated by meteorological (e.g., Powell et al. 2003; Holthuijsen et al. 2012; Takagaki et al. 2012, 2016) and oceanographic (Jarosz et al. 2007) observations, which demonstrate a nonmonotonous dependence of the drag coefficient on the wind speed, peaking at wind speeds of approximately 30–35 m s−1. There are also indications of an increase in the enthalpy exchange coefficient at hurricane winds (e.g., Richter et al. 2016; Bell et al. 2012). The influence of sea spray can be regarded as a plausible reason for both the reduction in the surface drag coefficient and the increase in the enthalpy transfer coefficient at hurricane winds. The corresponding reduction in turbulent stress is explained by Andreas (2004) and Kudryavtsev and Makin (2011) as the result of momentum exchange between droplets and airflow. Conversely, Makin (2005) and Kudryavtsev (2006) focused on the effect of the stable stratification of the marine atmospheric boundary layer by suspended spray droplets, in a similar way to work by Barenblatt and Golitsyn (1974). The efficiency of both mechanisms strongly increases with the size of the droplets and is proved to be most efficient for spume droplets (Kudryavtsev 2006; Andreas 2004; Kudryavtsev and Makin 2011). In accordance with the concept of reentrant spray proposed by Andreas and Emanuel (2001), these droplets also provide a large proportion of the spray-mediated enthalpy flux from the ocean to the atmosphere. The rate of production of sea spray is quantified by the spray generation function (SGF) 
In Troitskaya et al. (2018, hereafter Part I), we used high-speed video capture to show that, at wind speeds exceeding 20 m s−1, the dominant mechanism of spume droplet generation is “bag breakup” fragmentation. This process is similar to the fragmentation of liquid droplets and jets in gaseous flows (e.g., Gelfand 1996). Evidence of the presence of this spray-generating mechanism in a laboratory flume was first reported by Veron et al. (2012). The fragmentation starts with a small-scale elevation of the water surface, which then develops into a “microsail,” that inflates into a water film bordered by a thicker rim (thus forming the “bag”) that finally ruptures, producing hundreds of droplets. Recently (Troitskaya et al. 2017), we found that this phenomenon represents the dominant mechanism of spume droplet generation at high winds. Employing the general principals of statistical physics, in Part I we presented a statistical description of bag-breakup phenomena and used these statistics to derive the bag-breakup SGF, defined as the number of droplets of radius r produced per unit area of the water surface per unit time. High-speed video shows that bags generate spray in two ways: (i) by rupturing the film of the inflated bag, which produces film droplets with average radii of about 100 μm, and (ii) by fragmenting the rim of the bag, thus yielding rim droplets with average radii in the range of 500–1000 μm depending on the wind speed. Consequently, the SGF retrieved from our experiments was shown to be characterized by two peaks corresponding to the film and rim droplets, respectively. The rim-droplet peak located in the range 500–1000 μm is a distinctive feature of the bag-breakup spray generation mechanism.
The amount of spray depends not only on wind but also on fetch, which drastically differs between laboratory and field conditions. We expressed the empirical dependence of SGFs on fetch via a dimensionless parameter called the windsea Reynolds number, 
In this paper, we estimate the contribution of the bag-breakup mechanism to both the enthalpy and momentum fluxes in the atmospheric boundary layer over the ocean, which are known to be of importance for the development and maintenance of hurricanes (cf. Emanuel 1995). In particular, we consider the contribution of giant droplets, which significantly modify spray-mediated air–sea fluxes at hurricane winds compared to existing estimates based on conventional SGFs (e.g., Zhao et al. 2006; Andreas 1998; Fairall et al. 1994).
First, we estimate the impact of spray and bag breakup on the aerodynamic resistance of the water surface. We take three contributions into account. The first is the “droplet stress” caused by the acceleration of droplets by the wind in the course of their production from a small elevation in the water surface. This stress is almost completely provided by droplets originating from the fragmentation of the rim because of the dominant contribution of these rim droplets to the total droplet mass flux. The second contribution is the “bag stress” provided by bags (objects that look like microsails with typical sizes of ~1 cm), which act as obstacles to the near-water airflow. We also take into account the contribution related to the stable stratification in the near-surface airflow created by suspended droplets, which may also affect turbulence in the marine atmospheric boundary layer.
When estimating the effect of bag-breakup droplets on the moist enthalpy transfer from the ocean to atmosphere, we applied the concept of reentrant spray introduced by Andreas and Emanuel (2001), which considers the conservation of enthalpy in an air–water column. Here, we derive the spray-mediated enthalpy flux from equations of droplet microphysics developed by Pruppacher and Klett (1978), which also confirms the integral approach of Andreas and Emanuel (2001). Reentrant spray droplets that have cooled below the ambient air temperature due to evaporation of a small fraction of their volume fall back into the water and are the main contributors to the net ocean–atmosphere enthalpy flux. We show that these droplets are actually the giant “rim” droplets originating from bag-breakup fragmentation. We provide estimates of the enthalpy and sensible and latent heat fluxes using the approximate formulas derived by Andreas (2005). Currently, it is problematic to develop a more complex model, for example, similar to the stochastic Lagrangian models developed by Edson and Fairall (1994), Mueller and Veron (2014a), and Troitskaya et al. (2016). The most significant uncertainty is the distribution of the initial velocities of droplets ejected from the water surface. This strongly affects the motion of spray, especially the largest droplets, and the spray-mediated fluxes [cf. discussion of the momentum flux in Druzhinin et al. (2017) and Troitskaya et al. (2016)].
Our estimates provide only upper limits on the spray-mediated enthalpy flux and exchange coefficient as they neglect the impact of the spray on the near-surface temperature and moisture profiles, thus reducing the feedback effect (see discussion by Bao et al. 2000, 2011; Bianco et al. 2011; Mueller and Veron 2014b).
The structure of the paper is as follows. Section 2 briefly describes the properties and statistics of droplets originating from the bag-breakup mechanism (discussed in detail in Part I) that are necessary for evaluating the spray-mediated fluxes. We estimate the contribution of the bag-breakup events to the aerodynamic resistance of the water surface in section 3 and discuss the effect of the stable stratification of the marine atmospheric boundary layer by suspended droplets in section 4. In section 5, we derive the spray-mediated fluxes using the heat balance equations for a single droplet formulated by Pruppacher and Klett (1978). Estimates of the contribution of the droplets to the air–sea enthalpy flux are provided in section 6. In all sections, the application of two models for the GFS fetch dependency is discussed. Section 7 presents a summary of the results.
2. The bag-breakup SGF
In this section, for convenience, we briefly summarize some properties of the statistics of bags that were revealed in Troitskaya et al. (2017) through postprocessing of high-speed video of the dynamics of the water surface under the action of high-speed airflow in a wind-wave flume.
(a) Parameter 〈τR〉 vs wind friction velocity u*. The error bars depict the mean-square error of the expected value, the solid curve is approximated by Eq. (6), and the dashed curves show the uncertainty of the approximation. (b) Displacement of the inflating canopy of the bag (top view) obtained by superimposition of a sequence of frames of high-speed video taken with an interval of 4.5 ms. (c) Displacement of the canopy of the bag from top to bottom along the line in panel (b) (open circles) and the canopy radius (closed circles) vs time.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
To estimate the effect of the bag-breakup spray production mechanism in the ocean, we have to take into account the dependence of the amount of spray not only on wind but also on fetch, which differs drastically between laboratory and field conditions. Using Eq. (2) for the specific number of bags provides the universal SFG, which can be used directly both in the laboratory and the field if the appropriate wave-age parameter Ω for field conditions is used.
The wave-age parameter is a good means of defining fetch in the rotating and displacing wind fields typical of hurricanes. Direct measurements under hurricane conditions by Wright et al. (2001) yielded Ω = 2.5–3.5. We use this parameter below to estimate fluxes and exchange coefficients under field conditions.
Note that Eqs. (2) and (8) were obtained on the basis of a limited dataset obtained in a laboratory experiment in a straight channel with a very short wind fetch. Currently, sufficient data are not available to allow confident extrapolation to field conditions, and so we cannot favor one of these expressions over the other. Below, we compare the estimates of fluxes and exchange coefficients obtained by using each of them.
3. Contribution of bag-breakup events to the aerodynamic resistance of the water surface at hurricane winds
Let us now estimate the contribution of bag-breakup events to the momentum flux in the marine atmospheric boundary layer. This contribution is determined by two components, both working to increase the surface drag coefficient. The first is the surface stress, or the bag stress FMb, provided by the canopies of bags with typical sizes of ~1 cm forming obstacles to the near-water wind flow. The second component is the spray-mediated momentum flux, or the droplet stress FMd, determined by the momentum acquired by droplets in the course of their production. Both components are estimated below.
a. The bag stress
To estimate the contribution of the canopies of the bags to the aerodynamic resistance of the water surface, we need to determine the drag force imposed by each canopy on the surrounding airflow. The analysis of individual frames of high-speed video allowed us to investigate the temporal evolution of bags as well as their characteristic geometric dimensions. In particular, it was revealed that both the canopy radius and the translation of the entire bag in the process of its evolution are linear functions of time (Figs. 1b,c). Since the velocity with which the bag advances under the drag of the airflow is constant, there is equilibrium between the air pressure difference on opposite sides of the canopy of the bag and the surface tension of the inflated film.
Contribution of bag breakup to air–sea momentum exchange: plots of calculations using (top) Eq. (8) and (bottom) Eq. (2) for the specific number of bags. (a),(c) Partial contributions of droplets produced by the bag-breakup mechanism to the momentum flux P. Values of the 10-m wind speed U10 are 40 m s−1 (marker 1), 50 m s−1 (marker 2), and 60 m s−1 (marker 3); the wave-age parameter Ω = 2.5. (b),(d) Contributions to the surface stress caused by bags FMb [Eq. (14)], droplets FMd [Eq. (16)], and direct turbulent transfer FMw [Eq. (17)] vs 10-m wind speed U10. The vertical bars depict variations in the wave-age parameter Ω from 2.5 to 3.5.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
b. The droplet stress
Strictly speaking, Eq. (15) gives an upper bound estimate of the contribution of droplets to the surface drag because we neglect the portion of the momentum flux that a droplet can give back to the atmosphere during gravitation settling as its velocity is adjusted to the decreasing local airflow velocity. However, we do not expect this to have a strong effect because of the high inertia of the giant droplets that contribute most to the momentum flux. With an increase in the size of the droplet, there will be a simultaneous increase in the time for droplet velocity adjustment to the velocity of the surrounding airflow and decrease in the time of residence of the droplet in the atmosphere due to the increase of the gravitational settling velocity. The quantitative estimates in the appendix show that the residence time is less than the adjustment time for droplets with radii above 150 μm for a wind speed of 20 m s−1, above 300 μm for a wind speed of 40 m s−1, and above 450 μm for a wind speed of 60 m s−1 (see Fig. A1a). This means that droplets with larger radii do not have time to transfer the momentum accumulated in the entire process of production back to the wind flow during the residence time and this effect can be neglected. Comparison with Fig. 2a allows us to conclude that our assumption is correct up to a wind speed of 40 m s−1, when the peak contribution to the momentum flux corresponds to droplets with a radius of approximately 500 μm, but that it may be broken at higher wind speeds.
As for FMb, the dependence of FMd on the wind speed is determined by two opposite tendencies: on the one hand, the increase in the number of droplets [cf. Eq. (7)], and on the other, the decrease in droplet size proportional to the average bag size, which decreases with increasing wind speed according to Eq. (4). As with FMb, using Eq. (2) for the specific number of bags in Eq. (7) for the SGF gives a faster increase in the number of droplets with wind speed than using Eq. (8), and accordingly, the latter indicates more rapid saturation of the surface stress with increasing wind speed. Besides, as with the bag stress, lower droplet stress at winds below 30 m s−1 is predicted with Eq. (8). The peculiarities described can be seen by comparing the corresponding curves in Figs. 2b and 2d.
Surface drag coefficient CD vs U10 under our stress model. Dashed curve shows CD from Foreman and Emeis (2010). Experimental data: squares, diamonds, triangles, and circles are from Powell et al. (2003), crosses are from Holthuijsen et al. (2012), asterisks are from Bell et al. (2012), closed circles are from Richter et al. (2016), gray dots are from Jarosz et al. (2007), half-closed circles are from Hawkins and Rubsam (1968), half-closed triangles are from Miller (1962), and half-closed squares are from Miller (1964). The dashed line floating bars mark CDN(U10N) in a neutrally stable atmosphere, and the solid line floating bars mark CD(U10) when the effect of the buoyancy of the droplets is taken into account. The vertical bars depict variations in the wave-age parameter Ω from 2.5 to 3.5. Calculations use (a) Eq. (8) and (b) Eq. (2) for the specific number of bags.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
4. The effect of stable stratification of the marine atmospheric boundary layer by suspended droplets
Figures 3a and 3b present the predictions for CD through Eq. (24) for the two models of the dependence of the SGF on the wind fetch. It can be seen that the effect of the stable stratification of the atmosphere due to the presence of droplets is not strong and results in only an approximately 7%–8% decrease in the surface drag coefficient. It also results in a decrease in CD at very high winds and a peaking dependence, CD(U10), for both models. Thus, we can conclude that the comprehensive model, which includes the triple effect of the form drag of bags, the spray inertia, and the density stratification of the airflow by suspended droplets can provide the peaking function CD(U10).
5. Heat and enthalpy fluxes from droplets to the atmosphere
According to Emanuel (1995), hurricane intensity is controlled by the net moist enthalpy transfer from the ocean to the atmosphere rather than by the separate contributions of the sensible and latent heat fluxes. The sea spray contribution to the net air–sea enthalpy flux is recognized by Andreas and Emanuel (2001) in the concept of reentrant spray. Assuming the conservation of the overall enthalpy in an air–water column, Andreas and Emanuel (2001) showed that droplets completely evaporated to the atmosphere do not contribute to the net enthalpy flux between the atmosphere and ocean. For these droplets, the latent heat of evaporation is exactly compensated for by the sensible heat extracted by the spray from the atmosphere. Thus, a contribution to the net enthalpy flux from the ocean to the atmosphere can be provided only by the fraction of spray droplets that fall back into the ocean. The sizes of the droplets that fall to the ocean can be estimated from the criterion that the velocity of their gravitational settling exceeds the wind friction velocity u*. The estimates in the appendix show that spray droplets with radii above 150 μm will fall down to the ocean even at hurricane winds. The integral relations derived by Andreas and Emanuel (2001) are not sufficient for evaluating the partial contributions of droplets of different sizes to the heat and enthalpy fluxes. To do this, we need to determine the fluxes released to the atmosphere from a single droplet.
a. The enthalpy flux
Here we derive an expression for the enthalpy flux and sensible and latent heat lost from the droplets to the atmosphere based on the droplet microphysics equations discussed by Pruppacher and Klett (1978). The equation for the evolution of the droplet temperature is derived from the condition that the total heat (or enthalpy) flux to the droplet (the integral of the heat flux density over the entire droplet surface) 
On the other hand, a change in the moist enthalpy (the total heat content of the atmosphere) occurs as the droplet exchanges heat with the atmosphere through two physical processes. The first is the thermal conductivity, which provides the diffusion heat flux from the droplet to the atmosphere. This is opposite to the diffusion flux from the atmosphere to the droplet: 
Figure 4 shows the dependence of droplet evolution time scales, τr, τf, and τT, on the radius r. The figure shows that τr ≫ τf for large droplets with radius r > 100 μm, that is, the size of these droplets essentially does not change before they fall back into the water. On the other hand, for these droplets τT is less or comparable to τf, which means that the droplets have enough time to cool to their equilibrium temperature with an insignificant change in their size.
Dependence of droplet evolution time scales vs radius r: evaporation time τr, (dashed curve), residence time in the air τf at U10 between 30 and 60 m s−1 in 2 m s−1 increments (gray strip), and temperature relaxation time τT (solid curve). Bulk parameters are U10 = 30–60 m s−1, Tw = 25°C, Ta = 27.5°C, and RH = 96%; wave-age parameter Ω = 2.5.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
b. The latent and sensible heat fluxes
Figures 5a and 5c show the partial contribution of droplets of different sizes to the enthalpy and latent and sensible heat fluxes from spray to atmosphere, namely, the integrand of the integral in Eq. (37), 
Contribution of the droplets originating from bag breakup to air–sea heat exchange: calculations use (top) Eq. (8) and (bottom) Eq. (2) for the specific number of bags. (a),(c) Partial contribution of droplets to the total enthalpy flux (solid curve) and to latent (dashed black curve) and sensible (dashed gray curve) heat fluxes. Values of U10 are 40 m s−1 (marker 1), 50 m s−1 (marker 2), and 60 m s−1 (marker 3); the wave-age parameter Ω = 2.5, Tw = 27.5°C, Ta = 25°C, and RH = 96%. (b),(d) Spray-mediated latent and sensible heat and the total enthalpy fluxes for the same thermodynamic parameters of the atmosphere as in (a) and (c); the vertical bars depict variations in the wave-age parameter Ω from 2.5 to 3.5.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
6. Contribution of bag breakup to the air–sea enthalpy flux at hurricane wind speeds
Let us now consider the contribution of spray to the exchange coefficient of moist enthalpy, which, along with the surface drag coefficient, is another key factor in the hurricane energy balance (Emanuel 1995).
(a) Partial contributions of droplets to the enthalpy flux E. Values of U10 are 40 m s−1 (marker 1), 50 m s−1 (marker 2), and 60 m s−1 (marker 3); the wave-age parameter Ω = 2.5, Tw = 27.5°C, Ta = 25°C, and RH = 96%. (b) Contributions to the enthalpy flux from droplets (floating bars) and from direct turbulent transfer (black solid curve). (c) Fractional contribution of spray from bag breakup to the enthalpy flux. The dashed line denotes 0.5. The gray lines correspond to calculations using Eq. (8), and the black lines correspond to those using Eq. (2) for the specific number of bags; the vertical bars in (b) and (c) depict variations in the wave-age parameter Ω from 2.5 to 3.5. The thermodynamic parameters of the atmosphere are the same as in (a).
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
The dependencies of the enthalpy transfer coefficient Ck on the wind speed are shown in Fig. 7a. Both models predict similar values of Ck within the uncertainty caused the by variation in wave-age parameter Ω. The growth of Ck with wind exceeding 35–40 m s−1 at U10 results from the increase in the spray-mediated flux at these wind speeds (cf. with Fig. 6b). The predicted values of Ck differ only at winds above 50 m s−1 and then by no more than 8%–10%. Consequently, the ratio of the exchange coefficients Ck/CD increases and, at 35–40 m s−1 wind, exceeds 0.75, the lower limit for realistic model prediction of the maximum wind speed a hurricane can attain at the observed parameters of the atmosphere and ocean as discussed by Emanuel (1995) (Fig. 7b).
(a) The enthalpy transfer coefficient Ck vs U10. Experimental data: open triangles are from Black et al. (2007), circles are from Richter et al. (2016), squares are from Bell et al. (2012), half-closed circles are from Hawkins and Rubsam (1968), and half-closed triangles are from Miller (1962). (b) The ratio of the enthalpy and drag coefficients vs U10. The dashed line denotes the level 0.75. Experimental data: open triangles are from Black et al. (2007), closed circles are from Richter et al. (2016), squares are from Bell et al. (2012), half-closed circles are from Hawkins and Rubsam (1968), and half-closed triangles are from Miller (1962). The vertical bars depict variations in Ω from 2.5 to 3.5, Tw = 27.5°C, Ta = 25°C, and RH = 96%. The gray lines show calculations using Eq. (8), and the black lines show calculations using Eq. (2) for the specific number of bags.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
It should be taken into account that the above estimates give only the upper limits of the enthalpy flux and exchange coefficient since they neglect the feedback effects of droplets on the temperature and moisture profiles of the marine atmospheric boundary layer. These feedback effects can substantially reduce the contribution of droplets, as discussed by Bao et al. (2000, 2011), Bianco et al. (2011), and Mueller and Veron (2014b). However, a number of uncertainties complicate precise estimates of the feedback effect of spray. The most significant is the uncertainty in the initial velocities of droplets ejected from the water surface, which strongly influence the spray-mediated momentum flux [see discussion in Troitskaya et al. (2016) and Druzhinin et al. (2017)].
7. Summary
In Part I of this study, we showed that the dominant generation mechanism of spume droplets (i.e., drops of spray torn from the crests of waves by the wind) is that of bag-breakup fragmentation. This new spray-production mechanism is characterized by the formation of specific short-living (a lifetime of circa 10 μs) objects, bags, which look like canopies with radii of ~1–2 cm supported by thicker liquid rims. This structure results in the production of two scales of droplets after bag bursting and a double-peaked size spectrum of droplets with maxima at ~100 μm (the “film” droplets) and 500–1000 μm (the giant “rim” droplets). The bags and the giant droplets, the distinctive feature of the bag-breakup mechanism, turn out to make a significant contribution to both the heat energy supply from the ocean and mechanical dissipation in the atmospheric boundary layer, that is, factors responsible for the development and maintenance of hurricanes (Emanuel 1995).
In particular, the effect of bags and giant droplets can explain the nonmonotonous dependence of the surface drag coefficient CD on wind speed seen in meteorological (Powell et al. 2003; Holthuijsen et al. 2012) and oceanographic (Jarosz et al. 2007) observations. Indeed, the contribution of bag breakup to the momentum flux consists of two parts:
- the droplet stress, equal to the amount of momentum acquired by droplets in the course of their production, and
- the bag stress, provided by bags acting as microsails with typical sizes of ~1 cm, which act as obstacles to the near-water airflow.
Bag stress as well as droplet stress levels off at high winds due to the competition between two counteracting effects of the increasing wind speed, namely, the increasing number of bags and droplets and the weakening individual contributions of bags and droplets to the momentum flux due to decreasing bag sizes and lifetimes. It should be emphasized that even though bags and spray increase the surface drag in comparison with the pure form drag of surface waves, the tendency to saturation of the spray-and-bag-mediated component of the surface stress has the potential to explain the nonmonotonous dependence of the surface drag coefficient on wind speed. We also estimated the effect of stable stratification of the near-surface airflow by suspended droplets, which is known to reduce the intensity of air turbulence in the marine atmospheric boundary layer (Kudryavtsev 2006; Bao et al. 2011). The effect is not strong, leading to a less than 8% reduction of the surface drag coefficient. However, a combination of the above three factors leads to a nonmonotonous dependence of the drag coefficient on the wind speed.
We adapted the concept of reentrant spray initially formulated by Andreas and Emanuel (2001), who considered a column of adjacent layers of the atmosphere and the ocean, assumed conservation of the total enthalpy, and employed microphysical equations describing the evolution of a single droplet derived by Pruppacher and Klett (1978). This concept indicates that the contribution from spray to the thermal energy supply from ocean to atmosphere (quantified by the vertical flux of moist enthalpy Hk) is provided by droplets large enough to cool down below the ambient air temperature (due to the evaporation of only a small fraction of their volume) and then reenter the water. Our estimates show that the dominant contribution to the spray-mediated enthalpy flux is from giant rim droplets, and especially so at winds exceeding 35 m s−1. The contribution of the giant reentrant droplets generated by bag breakup increases with an increase in the wind speed and finally exceeds the near-surface turbulent heat flux when the wind speed is above 45–50 m s−1. As a result, the enthalpy exchange coefficient increases with strengthening wind. Consequently, the ratio of the exchange coefficients Ck/CD increases and, at 35–40 m s−1 winds, exceeds 0.75, the threshold predicted by Emanuel (1995) to reproduce the realistic intensity of tropical cyclones.
The above results show the critical importance of taking into account the contribution of large droplets and bags to the heat and momentum atmosphere–ocean exchange at high winds. However, these estimates are rather crude and give only upper limits to the enthalpy flux and exchange coefficient. Obtaining realistic quantitative estimates requires consideration of the feedback effect of the spray-mediated fluxes, which induce perturbations of the temperature and moisture profiles and reduce the spray-mediated fluxes (Bao et al. 2011; Bianco et al. 2011; Mueller and Veron 2014b). At the moment, the principal obstacle to solving this problem in a consistent way is uncertainty regarding droplet velocities at injection from the ocean surface into the atmosphere during bag breakup. Recent direct numerical simulation results show that the variation of droplet velocities at injection strongly affects the spray-mediated momentum flux (Druzhinin et al. 2017).
One other problem for the realistic estimation of the effect of bag-breakup fragmentation on air–sea fluxes is how to model the fetch dependence of the number of bag-breakup events, which determines the SGFs. Here we have compared two empirical models based on laboratory tank data and parameterization in terms of the windsea Reynolds number introduced by Toba and Koga (1986). At the moment, the available data do not allow a definitive choice to be made between the discussed models, but Eq. (2) looks more promising as it predicts realistic essential spray production at winds of 10–15 m s−1 at fetches typical for open-ocean conditions.
This work has been supported by the Russian Science Foundation (Project 14-17-00667), the Seventh Framework Programme (Project PIRSES-GA-2013-612610), and the Russian Foundation for Basic Research (Projects 14-17-00667, 16-05-00839, 17-05-00703, 18-55-50005). Sergej Zilitinkevich additionally acknowledges support from the Academy of Finland Project ClimEco 314 798/799. The basic salary of the authors from IAP is financed by the government contract 0035-2014-0032. The experiments were performed at the Unique Scientific Facility “Complex of Large-Scale Geophysical Facilities” (http://www.ckp-rf.ru/usu/77738/) and were supported by the President Grant for Young Scientists MC-2041.2017.5 and Russian Science Foundation (Project 18-77-00074). The authors thank Ms. Rebecca Thompson for improving the use of English in and organization of the text.
APPENDIX
Estimates of Giant Droplet Parameters in Terms of Exchange Processes
(a) The ratio of the relaxation time for a sphere with τStokes and time of residence of the droplet in the atmosphere vs r for three values of wind speed; the dashed line marks 1. (b) The gravitational settling velocity of a droplet vs its radius; the dashed line corresponds to 2 m s−1.
Citation: Journal of Physical Oceanography 48, 9; 10.1175/JPO-D-17-0105.1
Second, we estimate the sizes of droplets that will fall back into the ocean at high winds, that is, will not be suspended due to the effect of turbulent velocity fluctuations. The sizes of these droplets are estimated on the basis of the criterion that the velocity of their gravitational settling Vf , determined by Eq. (A3), exceeds the wind friction velocity u*. For hurricane winds, u* is around 2 m s−1 according to Powell et al. (2003). Figure A1b shows that droplets with radii above 150 μm will fall.
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Note that SGFs are proportional to the value P in Figs. 2a and 2c.
