Wave‐driven inertial oscillations

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Abstract
In a nonrotating system, the shear Reynolds stresses exerted by surface or internal gravity waves vanish on account of the exact quadrature between the horizontal and vertical orbital velocities. It is shown that a rotation of the system induces small in‐phase perturbations, resulting in a mean Reynolds stress which can generate low frequency currents. If both the wave field and the ocean are homogeneous with respect to the horizontal coordinates, the low‐frequency response is an undamped inertial oscillation. If either the wave field or the ocean are weakly inhomogeneous, the oscillation disperses in the vertical and horizontal directions due to phase‐mixing of modes with closely neighboring frequencies. Other effects which produce small frequency shifts also contribute to phase‐mixing, for example the horizontal component of the Coriolis vector and nonlinear interactions with geo‐strophic currents. The analysis is based on operator representations which avoid normal mode decomposition and yield simple integro‐differential operators for each phase‐mixing process. Numerical results are presented for a continuously stratified model typical for a shallow sea (Baltic). The orders of magnitude and qualitative features are in reasonable agreement with observations.

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