The tidally induced bottom boundary layer in a rotating frame: similarity of turbulence

Abstract

To investigate turbulent properties of the tidally induced bottom boundary layer (TBBL) in a rotating frame, we performed three-dimensional numerical experiments under unstratified conditions, varying the temporal Rossby numberRo_t= |σ*/f*|, where σ* andf* are the tidal frequency and the Coriolis parameter, respectively. The vertical profiles of the time-averaged currents and stresses showed good similarity and coincided well with the turbulent Ekman layer, when they were normalized by the modified ‘outer’ scales, the frictional velocityu*_τ,T* = 1/|f* + σ*| and δ* =u*_τ/|f* + σ*| for the velocity, time and length scales (σ* is positive when the tidal ellipse rotates anticlockwise). This means that the similarity in turbulent statistics is universally applicable to the TBBL in the world's ocean except near the equator. Although strong inertial waves contaminated the perturbation field whenRo_t~ 1 and masked the similarity, the apparent diffusivity κ*_apestimated by tracer experiments again showed similarity, since the inertial waves did not affect the mixing process in the present experiments. Thus, κ*_apcan be represented in terms of the three external parameters: the latitude (f*), the tidal frequency (σ*) and the tidal amplitude (u*_τ). The obtained scaling ofu*_τδ* =u*_τ²/|f*+σ*| for κ*_apsuggests that effective mixing may occur whenRo_t~ 1, i.e. near the critical latitude.