Investigation of Sea Spray Effect on the Vertical Momentum Transport Using an Eulerian Multifluid-Type Model

Abstract

The Eulerian multi-fluid mathematical model is developed to describe the marine atmospheric boundary layer laden with sea spray under high wind condition of a hurricane. The model considers spray and air as separate continuous interacting turbulent media and employs the multi-fluid E – ε closure. Each phase is described by its own set of coupled conservation equations and characterized by its own velocity. Such an approach enables us to accurately quantify the interaction between spray and air and pinpoint the effect of spray on the vertical momentum transport much more precisely than could be done with traditional mixture-type approaches. The model consistently quantifies the effect of spray inertia and the suppression of air turbulence due to two different mechanisms: the turbulence attenuation, which results from the inability of spray droplets to fully follow turbulent fluctuations, and the vertical transport of spray against the gravity by turbulent eddies. The results of numerical and asymptotic analyses show that the turbulence suppression by spray overpowers its inertia several meters above wave crests resulting in a noticeable wind acceleration and the corresponding reduction of the drag coefficient from the reference values for a spray-free atmosphere. This occurs at a much lower than predicted previously spray volume fraction values ~ 10⁻⁵. The falloff of the drag coefficient from its reference values is stronger pronounced at higher altitudes. The drag coefficient reaches its maximum at spray volume fraction values ~ 10⁻⁴ that is several times smaller than predicted by mixture-type models. The Eulerian multi-fluid mathematical model is developed to describe the marine atmospheric boundary layer laden with sea spray under high wind condition of a hurricane. The model considers spray and air as separate continuous interacting turbulent media and employs the multi-fluid E – ε closure. Each phase is described by its own set of coupled conservation equations and characterized by its own velocity. Such an approach enables us to accurately quantify the interaction between spray and air and pinpoint the effect of spray on the vertical momentum transport much more precisely than could be done with traditional mixture-type approaches. The model consistently quantifies the effect of spray inertia and the suppression of air turbulence due to two different mechanisms: the turbulence attenuation, which results from the inability of spray droplets to fully follow turbulent fluctuations, and the vertical transport of spray against the gravity by turbulent eddies. The results of numerical and asymptotic analyses show that the turbulence suppression by spray overpowers its inertia several meters above wave crests resulting in a noticeable wind acceleration and the corresponding reduction of the drag coefficient from the reference values for a spray-free atmosphere. This occurs at a much lower than predicted previously spray volume fraction values ~ 10⁻⁵. The falloff of the drag coefficient from its reference values is stronger pronounced at higher altitudes. The drag coefficient reaches its maximum at spray volume fraction values ~ 10⁻⁴ that is several times smaller than predicted by mixture-type models.