Numerical modeling of separation eddies in shallow water

Abstract

The modeling of free‐surface flows is usually made based on the time‐averaged form of the Navier‐Stokes equations (i.e., the Reynolds equations) to filter out the turbulent fluctuations. For coastal waters and estuaries, the time‐averaged hydrodynamic equations are often further simplified by averaging over depth. Assuming the hydrostatic pressure field, the depth‐averaged equation of conservation of mass is urn:x-wiley:00431397:media:wrcr4526:wrcr4526-math-0001 where H is the total water depth, u = ( u , v ) is the depth‐averaged horizontal velocity components, and div denotes the divergence in the horizontal directions. Neglecting the Earth's rotation effects and shear stress at the free surface, and assuming ∇H/H ≪ 1, the depth‐averaged equation of conservation of momentum can be expressed as urn:x-wiley:00431397:media:wrcr4526:wrcr4526-math-0002 where ξ is the departure of the water surface for a horizontal datum, v ; is the kinematic viscosity of the fluid, ρ is the fluiddensity, u ′ is the velocity deviation from u due to vertical velocity profile, u ″ ; u ″ is the time‐averaged value of a dyadic product of velocity fluctuation due to turbulence, τ b is shearstress at the bottom boundary.