Mass Transport Velocity in Free Barotropic Poincaré Waves

Abstract

The mass transport velocity induced by long surface waves in a shallow, rotating viscous ocean is studied theoretically by using a Lagrangian description of motion. The depth is constant, and the water is homogeneous. Such waves are referred to as Poincaré waves, or sometimes Sverdrup waves, where the latter name usually is reserved for cases in which the effect of friction is taken into account. In the linear case, the primary wave field is significantly affected by the earth's rotation, requiring wave frequencies that are larger than the inertial frequency. In the nonlinear case, the inviscid version of these waves does not induce any mean mass transport. This situation changes when the effect of viscosity is taken into account, and it is shown that for long waves there exists a mean Lagrangian flow confined to a suitably defined bottom friction layer. A solution for constant eddy viscosity and a no-slip bottom is obtained analytically. This result is compared with those obtained numerically for the case in which the eddy viscosity in the bottom layer varies in the vertical and for the case when sliding is allowed at the seabed. In a qualitative sense, the results for the wave drift are surprisingly similar. For waves of the semidiurnal type, it is found that mean drift near the seabed is directed opposite to the wave propagation direction. Possible consequences for the transport of suspended bottom sediments are pointed out.