24AIRSEA Vertical Decay of Swell-induced Momentum Flux in the Wave Boundary Layer

The assumption that swell-induced drag decays exponentially with the vertical distance above the mean sea surface level [i.e., D(z)=D₀exp(-αk), where D₀ is the swell drag at the surface, k is the swell wave number, z is the vertical distance, and a is considered to be a constant] is widely used in wave boundary layer models and other applications. This assumption is supported by a number of field observations and large eddy simulation (LES) studies. However, the decay constant a obtained from observational or numerical studies in the literature ranges from 1 to 2.1. The science behind such variation remains largely unknown.

This issue is examined using idealized LES simulations of a balanced marine boundary layer (MBL) over monochromatic propagating swell. It has been demonstrated that while swell drag tends to decay exponentially in all the simulations, a (referred to as decay coefficient hereafter) varies between 0.9 and 2.1 from simulation to simulation, depending on the stratification and wind shear in the wave boundary layer. In general, the decay coefficient a is close to unity when the MBL is convective or neutrally stratified. Under weakly stable conditions, the decay coefficient is around unity over swell propagating against winds. The largest a is around 2.1, corresponding to a moderately stable MBL over wind-following swell.