Recirculating steady flow in harbours

Abstract

In this report the water flow in harbours, that are situated on a river, are considered. Due to the flow velocity difference between the river and the harbour, a turbulent mixing layer develops at the harbour entrance. The shallowness of the water induces the coexistance of two disparate turbulent length scales in these regions. Besides the "ordinary" small-scale 3D turbulence, which is generated by bottom friction, large quasi 2D turbulent structures are generated by horizontal shear in the mixing layer. These large structures have a typical turbulent length scale that, in contrast with the 3D turbulence, is at least several times the water depth. The standard 3D k-? turbulence model, takes only one turbulent length scale into account and, as a consequence, the computed eddy viscosities and Reynolds stresses are too low, which results in an underprediction of the velocities in the gyre. Therefore, a new turbulence model, based on the standard k-? turbulence model, was developed that does take non-isotropic behaviour of the turbulence into account. This new model consists of two distinct turbulence models, that together model the 3D and quasi-2D turbulence: the vertical eddy viscosity that determines the vertical Reynolds stresses are computed with a 3D k-? turbulence model, in which the production of turbulent kinetic energy is determined by vertical shear only, i.e. bottom friction. The horizontal eddy viscosity that determines the horizontal Reynolds stresses is computed by a 2D depth averaged k-? model, in which the production of turbulent kinetic energy is dependent upon horizontal velocity gradients only. Direct interaction bet ween the two turbulence models, by means of energy transfer, is neglected. However, interaction via the mean-flow equations still exists. The standard 3D k-? turbulence model and the new two-length-scale model were tested for two different geometries. Besides earlier measurements in a 1xl m2 harbour, new measurements that were carried out in a more realistic geometry were used for model testing. The laser Doppler experiments carried out in the latter scale model, clearly revealed the existance of two disparate turbulent length scales by studying the autocorrelation functions and the turbulent power density spectra at positions in the mixing layer and the river. In both cases, results from computations with the two-length-scale model were in better agreement with measurements than the standard one-length-scale K-? model, supporting the necessity to account for the non-istrophy of the turbulence.