Hysteresis of turbulent kinetic energy in nonrotational tidal flows: A model study

Abstract

For horizontally homogeneous barotropic conditions, nonrotational tidal (M 2 ) cycles of hydrodynamic fields are computed by the standard k — ε turbulence model for large Reynolds numbers. The characteristic tidal time lag between current and turbulent kinetic energy at the flow reversal turned out to be close to measurements in shallow tidal rivers reported in the literature. Using a scale transformation of the model equations, the phase shift between the surface and the bottom flow is shown to be related to the dimensionless Strouhal number. In shallow waters this number is large and the phase shift is negligible. In deeper water the Strouhal number is much smaller, the shift becomes significant, and the lag between current and turbulence quantities is even one order of magnitude larger than the shift. The results indicate that the k — ε turbulence model can reproduce the essential physical details of tidal flows.