Bottom Boundary Layer in Tidal Flow: Theoritical Models

We start with estimating the thickness of the bottom boundary layer in a tidal flow. For this purpose, to describe the effect of small-scale turbulence we introduce the effective coefficient of vertical turbulent viscosity v _T; , constant with height, and, following Charney [72], assume that the turbulent boundary layer remains hydrodynamically stable up to the moment when its effective Reynolds number $$ {R^{{\delta _T}}}{\rm{ = }}{U_\infty }{\delta _T}/{v_T}{\rm{ }}exceeds R_{cr}^{\delta l}. $$ If we now define the thickness of the turbulent boundary layer as δ _T = (2v _T /σ)1/2 we obtain the estimate $$ {\delta _T} \ge {\rm{ }}\frac{{2{U_\infty }}}{{\sigma R_{cr}^{{\delta _l}}}}, $$ where U_∞ is the tidal velocity amplitude outside the boundary layer; σ is the oscillation frequency.