Vertical Transfer of Momentum by Internal Waves in the Western Part of the Mediterranean Sea

Abstract

Purpose. The work is aimed at studying both the momentum vertical transfer by internal waves with the regard for the Earth rotation and the shear current in the western part of the Mediterranean Sea, and the influence of turbulent viscosity and diffusion upon the indicated wave fluxes and the Stokes drift. Methods and Results. To solve the initial system of the hydrodynamics nonlinear equations, a weakly nonlinear approach was used. In the first order of smallness in the wave amplitude, the boundary problem for the vertical velocity amplitude was solved; in the second order in the wave amplitude, the nonlinear effects, namely the Stokes drift and the vertical wave momentum fluxes, were investigated. The indicated boundary problem was solved in two ways: by the perturbation method applied earlier and by the numerical one by the implicit Adams scheme of the third order of accuracy. The perturbation method assumes expansion of the solution and the wave frequency in a series by a small parameter proportional to the horizontal turbulent viscosity. The results obtained by the perturbation and numerical methods were compared. Coincidence of the results of calculating the dispersion curves by both methods is shown. However, for the wave damping decrement, the perturbation method yields the overestimated values, at that for the second mode the values are higher than those for the first one. The vertical wave momentum fluxes are nonzero, and theperturbation method yields the overestimated values for the flux uw. The vertical wave momentum flux vw is practically independent of turbulent viscosity and diffusion, and both methods give the identical results for it. The velocity component of the Stokes drift along the wave propagation direction is also insensitive to turbulent viscosity and diffusion, whereas the transverse component equals zero in the absence of turbulent viscosity and diffusion. Conclusions. The perturbation method provides the overestimated values of the wave damping decrements, the wave momentum flux uw and the transverse component of the Stokes drift velocity. The horizontal turbulent viscosity and diffusion exert practically no effect upon the wave momentum flux vw and the longitudinal component of the Stokes drift velocity