# Experimental measurement and numerical modelling of velocity, density and turbulence profiles of a gravity current

Thesis (PhD (Civil Engineering))--Stellenbosch University, 2008.

Thesis

The velocity, density and turbulence profiles of a horizontal, saline gravity current were measured experimentally. Stable stratfication damped the turbulence and prevented the gravity current from becoming self-similar. The velocity and density prfiles were measured simultaneously and non-intrusively with particle image velocimetry scalar (PIV-S) technology. The application of the PIV-S technology had to be extended in order to measure the continuously stratified gravity current. Measurement of the Reynolds fluxes and Reynolds stresses revealed the anisotropic turbulent transport of mass and momentum within the gravity current body. These measurements also allowed the interaction between turbulence and stratification to be studied. The measured profiles were used to evaluate the accuracy of a gravity current model which did not assume self-similarity. The gravity current model was based on a Reynolds-averaged Navier-Stokes (RANS) multispecies mixture model. The Reynolds flux and Reynolds stress profiles did not show self-similarity with increasing downstream distance. Comparison of the vertical and horizontal Reynolds fluxes showed that gravity strongly damped the vertical flux. At a downstream location, where the bulk Richardson number was supercritical, the shear production profile had a positive inner (near bed) peak and a positive outer peak, while the buoyancy production pro le had a negative outer peak. Further downstream, where the bulk Richardson number was near-critical, the outer shear and buoyancy production peaks disappeared, due to the continuous damping of the turbulence intensities by the stable stratification. However, near bed shearing allowed the inner shear production peak to remain. Sensitivity analyses of different turbulence models for the gravity current model showed that the standard k -e turbulence model, as well as the Renormalization Group theory (RNG) k -e turbulence model, generally underpredicted the mean streamwise velocity profile and overpredicted the excess density pro le. The flux-gradient hypothesis, used to provide closure for the Reynolds uxes, modelled the vertical Reynolds ux reasonably, but not the horizontal flux. This did not compromise the results, since the horizontal gravity current had the characteristics of a boundary-layer ow, where the horizontal flux does not contribute significantly to the flow structure. It was shown that the gravity current model, implementing the standard k -e turbulence model with a constant turbulent Schmidt number of ot = 1;3, produced profiles which were within 10% - 20% of the measured profiles.