| Abstract: | The paper deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no-slip condition is used at the seabed with a flow-dependent eddy viscosity related to the depth-mean current or the bed frictional velocity. Calculations show that it is essential to accurately resolve the high-shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high-shear layers which occur in these regions. With a flow-independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow-dependent viscosity, in particular a viscosity computed from the frictional velocity, a non-linear numerical instability can occur. A method of maintaining numerical stability in this case is also described. The importance of near-bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations. The influence of stratification on the computed tidal profiles is shown in the latter part of the paper. |
