Scalings of the tidally induced bottom boundary layer in a shallow sea under a surface heating

Abstract

We have investigated properties of the tidally-induced bottom boundary layer (TBBL) in a shallow sea under a surface heating, by scale argument and DNS (Direct Numerical Simulation) experiment. Applying the existing scalings of the boundary layer, it is found that the height of TBBL H tbbl and the efficiency of tidal mixing ϵ are scaled to (u 4 * H/|σ + f |Bs) 1/3 and H hom /H tbbl , respectively, where u * is the friction velocity, σ the tidal frequency, f the inertial frequency (the Coriolis parameter), Bs the surface buoyancy flux, H the water depth, and H hom = u * /|σ + f | the height of TBBL in a homogeneous ocean. Results of DNS experiment agree with these scalings for fairly wide ranges of u * (or tidal amplitude U tide), H, Bs, and |σ/f |. In exceptional cases with slower Earth's rotations, weaker tidal flows, and shallower water depths, turbulence occurs intermittently and the scaling underestimates H tbbl and ϵ. The efficiency of tidal mixing ϵ varies from less than 1% to 7% for the experimental range. This variation can partly explain the reason why the critical value of Simpson-Hunter parameter which is an index of the position of tidal mixing front is different from place to place around the world.