Non-equilibrium Multi-fluid Model of a Marine Boundary Layer Laden with Evaporating Ocean Spray under High-wind Conditions

Even though forecasting of the track of Tropical Cyclones (TCs) has been improving steadily, there has been almost no change in the accuracy of intensity forecasts in the past 20-30 years. Thе steady progress in the forecast of the TC track is explained by the fact that the track is primarily defined by the large-scale atmospheric flow that is relatively easy to model and simulate numerically. In contrast, predicting the hurricane intensity requires understanding of complicated small-scale physical processes and mechanisms that govern the motion of the hurricanes. It has been shown that ocean spray is one of the multi-scale physical phenomena that defines the hurricane dynamics since it plays an important role in the exchange of momentum, heat and moisture between the atmosphere and the ocean during a storm.

In this work we have developed a two-temperature non-equilibrium variable density (non-Bousinessq) model to describe a spray-stratified turbulent marine atmospheric boundary layer structure and dynamics under high-wind conditions of a hurricane. The model is formulated as a boundary value problem for a system of differential equations that describes the vertical transport of a multi-phase flow of three components - dry air and water vapor (gas phase), and ocean spray (liquid phase). We have used an Eulerian multi-fluid type approach that considers spray as a continuous phase interpenetrating and interacting with the gas phase. The governing equations include conservations equations for mass, momentum and thermal energies for both gaseous and liquid phases. We have explicitly considered the sensible heat flux in the liquid phase, consequently the total heat flux from ocean to the atmosphere is the superposition of the latent heat flux and sensible heat fluxes in the air and in the spray. The model utilizes higher-order E-epsilon turbulence closure that includes several additional contributing physical factors (turbulent energy and its dissipation transport in the vertical direction, dependence of the turbulent mixing length on the spray stratification, spray inertia) that are shown to play an important role in the spray-stratified turbulent boundary layer dynamics.

We have shown that evaporating spray significantly redistributes the total heat flux between latent and sensible heat fluxes. The sensible heat flux becomes comparable with the latent heat flux when a relatively moderate amount of spray is introduced into the atmosphere with no sensible heat flux i.e. the atmosphere with constant vertical distribution of the potential temperature. Besides redistributing the total heat flux, the ocean spray also alters its value. We have demonstrated that the heat exchange rate between the ocean and the atmosphere slightly decreases for lower spray concentrations and increases for higher spray concentrations. The obtained results confirm that the impact of the non-equilibrium effects is significant over the complete range of possible spray concentration values.

This work is supported by a National Science Foundation grant under Award No. HRD-1036563.