A kinetic model for particle–surface interaction applied to rain falling on water waves

Abstract

We present a model for estimating the momentum flux from water drops falling onto a moving free surface. The theory is based on a kinetic approach whereby individual drops are modelled as point particles with mass and velocity, and are described collectively by a distribution function f (t, x, v, r). We show that the resulting momentum flux can be readily incorporated into free-surface Navier-Stokes and Euler models. As an illustration of this approach we examine the interaction between rainfall and linear deep-water surface waves. This particular application is not fundamentally different from the study of Le Méhauté & Khangaonkar (J. our methodology is more general and is novel in its use of a kinetic approach with an all-purpose drop distribution function. The applicability of the model to linear surface waves is found to be valid for surface-wave wavelengths ranging from approximately 3 to 250 m. We further show that rainfall modifies the usual wave dispersion relationship and induces wave amplification, or damping, depending on the rain rate, the rain impact angle and the wavelength of the surface wave. We solve for the amplification and damping rates analytically and show, among other results, that rain falling vertically will always damp the surface waves.

The impact of entrained air on ocean waves

“…The consequences on the waves enter through Bernoulli's equation and affect the dispersion of the waves. These issues are presented in Veron and Meussiens (2016) and not repeated here.…”

“…Another effect that has been ignored here is a full consideration of the water-air interface stress conditions when rain is present. In Veron and Meussiens (2016), a model is presented for how the impact of rain affects the boundary conditions (see their Eqs. 2.11, 2.14, and, for waves, 3.4), i.e., the pressure at the free surface is composed of the atmospheric pressure plus a rain-induced pressure.…”

The Impact of Rain on Ocean Surface Waves and Currents

“…Despite the numerous laboratory and theoretical studies (Veron & Mieussens, ) in this area, the effect of rain on the ocean surface remains one of the least understood processes in air‐sea interaction (Katsafados et al, ). This is largely due to the absence of field measurements of rain impacting ocean surface waves and very near‐surface flows.…”

Rain Calms the Sea - The Impact of Entrained Air

“…In high wind conditions the authors suggest that these changes in the free boundary condition could lead to damping as well as to an amplification of high frequency wave components, leading to smoother or rougher sea states, respectively. A model for impinging rain as a distributed pressure was proposed and investigated in [4]. Within the irrotational framework they use, the rain pressure distribution modifies the wave dispersion relation, affecting primarily the high frequency wave components.…”