Updated approximation formulas for the radius and temperature of saline droplets&#160;
Authors: Kozlov Dmitry , Troitskaya Yuliya 
Published: March 2022

&lt;p&gt;The number of spume droplets increases rapidly with wind speed [1], [2], so that under hurricane conditions the spray-mediated heat and momentum fluxes can have a significant impact on the exchanging processes between the ocean and the atmosphere. The estimation of the additional enthalpy flux, as well as latent and sensible heat fluxes, is based on the solution of the microphysics equations for a single saline droplet, detailed in [3]. In theoretical studies [4]-[6] it was shown that the evolution of the radius and temperature of a droplet can be described accurate enough using the following formulas:&lt;/p&gt;&lt;p&gt;T(t)=T&lt;sub&gt;wb&lt;/sub&gt;+(T&lt;sub&gt;w&lt;/sub&gt;-T&lt;sub&gt;wb&lt;/sub&gt;)e&lt;sup&gt;-t/&lt;em&gt;&amp;#964;&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt;&lt;/sup&gt;,&lt;/p&gt;&lt;p&gt;r(t)=r&lt;sub&gt;eq&lt;/sub&gt;+(r&lt;sub&gt;0&lt;/sub&gt;-r&lt;sub&gt;eq&lt;/sub&gt;)e&lt;sup&gt;-t/&lt;em&gt;&amp;#964;&lt;/em&gt;r&lt;/sup&gt;,&lt;/p&gt;&lt;p&gt;where T&lt;sub&gt;wb&lt;/sub&gt; is the wet bulb temperature, r&lt;sub&gt;eq&lt;/sub&gt; is the equilibrium radius, &lt;em&gt;&amp;#964;&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt; and &lt;em&gt;&amp;#964;&lt;/em&gt;&lt;sub&gt;r&lt;/sub&gt; is the e-folding time to reach that temperature T&lt;sub&gt;wb&lt;/sub&gt; and radius r&lt;sub&gt;eq&lt;/sub&gt;, T(0)=T&lt;sub&gt;w&lt;/sub&gt; is the temperature of the water, r(0)=r&lt;sub&gt;0&lt;/sub&gt; is the initial radius of the drop. However, the numerical solution of the microphysical equations of the droplet&amp;#8217;s thermodynamics showed that for the characteristic conditions of a tropical cyclone at the initial stage evaporation occurs much more intensively than after reaching the wet bulb temperature, and the characteristic time of this change is the same as for a change in temperature. In the present study, we propose an updated parameterization of the evolution of the radius and temperature of a single saline droplet, which provides more accurate describing of the droplet&amp;#8217;s thermodynamics. On its basis we obtained estimations of enthalpy, latent and sensible heat fluxes caused by droplets generated by bag break-up instability (the main source of spume droplets at extreme wind speeds [7]).&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;[1]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; E. L. Andreas. A review of the sea spray generation function for the open ocean // &lt;em&gt;Atmos. Interact.&lt;/em&gt; - 2002. - V. 1. - P. 1&amp;#8211;46.&lt;/p&gt;&lt;p&gt;[2]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; D. H. Richter and F. Veron. Ocean spray: An outsized influence on weather and climate // &lt;em&gt;Phys. Today&lt;/em&gt; - 2016. - V. 69. - &amp;#8470;11. - P. 34&amp;#8211;39.&lt;/p&gt;&lt;p&gt;[3]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; H. R. Pruppacher and J. D. Klett. &lt;em&gt;Microphysics of clouds and precipitation&lt;/em&gt;, D. Reidel. Norwell: Mass., 2010.&lt;/p&gt;&lt;p&gt;[4]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; E. L. Andreas. Time constants for the evolution of sea spray droplets // &lt;em&gt;Tellus, Ser. B&lt;/em&gt; - 1990. - V. 42 B. - &amp;#8470;5. - P. 481&amp;#8211;497.&lt;/p&gt;&lt;p&gt;[5]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; E. L. Andreas. Sea spray and the turbulent air-sea heat fluxes // &lt;em&gt;J. Geophys. Res.&lt;/em&gt; - 1992. - V. 97. - &amp;#8470;C7. - P. 11429&amp;#8211;11441.&lt;/p&gt;&lt;p&gt;[6]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; E. L. Andreas. Approximation formulas for the microphysical properties of saline droplets // &lt;em&gt;Atmos. Res.&lt;/em&gt; - 2005. - V. 75. - &amp;#8470;4. - P. 323&amp;#8211;345.&lt;/p&gt;&lt;p&gt;[7]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; Y. Troitskaya, A. Kandaurov, O. Ermakova, D. Kozlov, D. Sergeev, and S. Zilitinkevich. The &amp;#8220;bag breakup&amp;#8221; spume droplet generation mechanism at high winds. Part I: Spray generation function // &lt;em&gt;J. Phys. Oceanogr.&lt;/em&gt; - 2018. - V. 48. - &amp;#8470;9. - P. 2168&amp;#8211;2188.&lt;/p&gt;