Influence of the Nontraditional Approximation on Momentum Transfer by Internal Waves in a Shear Flow

Free internal waves in a plane-parallel stratified flow are considered in the Boussinesq approximation with allowance for the Earth’s rotation. The model under consideration is analytically resolvable with a linear flow velocity profile and uniform stratification, when the wave propagates perpendicular to the flow. It is shown that taking into account the contribution of the horizontal component of the angular velocity of the Earth’s rotation to the Coriolis force (the nontraditional approximation) practically does not change the dispersion curves; however, the vertical wave momentum flux $$\overline {{v}w} $$ increases slightly. The effect intensifies when approaching the equator. In the nontraditional approximation, the vertical momentum flux $$\overline {{v}w} $$ is nonzero even in the absence of a flow, while in the traditional approximation it is equal to zero.