Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Rot, the ratio of the inertial and tidal periods. When Rot < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Rot. When Rot > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Rot < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (∼100 m), the boundary layer becomes unstable even if tidal flow is weak (∼5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Rot > 1.0. However, when Rot < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N2 ∼ 10−6 s−2). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm2/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.