Stocks drift and vortex instability of the potential surface wave

It is shown that in the case of potential surface wave an exact solution of the equations of the nonlinear Lagragian’s dynamics of the fluid particle has the drift velocity as an eigenvalue. The fluid particle trajectory is a circular rotation around a center point moving with a constant drift velocity. The rotation frequency differs from the wave frequency by the Doppler’s shift caused by the drift velocity. The constant drift velocity, for the surface wave of small amplitude, coincides with the classical expression for the Stokes drift velocity.

It is also shown that in the cases with absence of the Stokes drift and with presence of the Stokes drift the vortex instability of a potential surface wave has the same futures. But the vortex temporal variability in the case of the Stokes drift is affected by the Doppler’s shift caused by the Stokes drift velocity. Hence it allows a conclusion that the vortex instability of a potential surface wave initiates turbulent mixing and Lengmure circulation in the ocean upper layer.