Modeling time dependence in a tidal boundary layer

Although the rate of acceleration and deceleration in a depth-limited tidal flow can be quite large, it has been found that quasi-steady logarithmic models or steady eddy diffusivitics can explain the turbulent field quite well (Gross andNowell, 1983;Long, 1981). A simple, time-dependent model was devised based on kinetic energy closure (Bradshaw et al., 1967) to simulate a depth-limited tidal boundary layer without the assumption of a time-independent eddy diffusivity. Computer solutions revealed that the parameterS = u_s/δΩ (u_s is a turbulent velocity scale, δ is depth, Ω is tidal frequency) governs the phasing of the velocity to the forcing pressure gradient. However, for values ofS reasonable for depth-limited estuarine tidal flow the ratio of the turbulent energy production-dissipation balance to rate of change of turbulent energy is always quite large, indicating that the turbulent adjustment rate is fast enough for the flow to be modeled with quasi-steady techniques.