MODELLING THE FLOW IN CURVED TIDAL CHANNELS AND RIVERS

摘要

Flows in tidal channel bends and river bends are very shallow and mildly curved free surface flows. The shallowness and the curvature of the flow lead to a few flow features which are difficult to reproduce with numerical models. An example is the second counter-rotating secondary flow cell that is observed along steep outer banks in river bends. This second cell has important consequences for the undermining of the outer bank. Only in relatively deep flows RANS-models do succeed in reproducing this second cell. Understandably the shallowness of this kind of flows leads to a preference for 2-D horizontal models. However, it is well known that due to differential advection main flow momentum is advected from the region of low velocity at the inside bend to the region with high velocity near the outside bend. Thus a negative eddy viscosity is required in a 2-D model, which however leads to stability problems. In 3-D computations there is no problem as the secondary flow and its advection effects are included in the computation. In curved shallow free surface flow another negative eddy viscosity phenomenon was observed, however. If the shear stress component that transports main flow across the channel is expressed as a gradient type of momentum transport, then again a negative eddy viscosity appears. This means that 3-D computations with gradient type turbulence models (e.g. eddy viscosity or k-ε models) can never yield such a stress component with the correct sign. The negative eddy viscosity can be understood by looking at the mechanism that creates the shear stresses, in this case parcels of water that move upwards and downwards over the flow retaining a substantial part of their original momentum. If we describe the exchange of momentum with a kind of vertical mixing length model, the same mixing length leads to correct shear stresses for all three stress components. In contradistinction to gradient type turbulence models, large eddy simulation (LES) does yield correct shear stresses.