The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

Abstract

To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby numberRot= |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameterf. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z<zm); the stratified layer where the initial stratification remains and the flow is laminar (z>zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm<z<zt). Turbulence is scaled by the frictional velocityuτand the mixed-layer thicknesszm(uτanduτ/NwhereNis the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. AsRotapproaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomesRotcloser to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% forRot= 0.5 to 3.5% forRot= 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ =uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.