Internal waves and turbulent mixing in closed stratified basins

We present results of numerical simulations of a stratified reservoir with a three-layer stratification, subject to an oscillating surface shear stress. The simulations are carried out at a laboratory scale, using Large Eddy Simulation. We solve the three-dimensional Navier-Stokes equations under the Boussinesq approximation using a second-order accurate finite volume solver. The model was validated by reproducing experimental results for the reservoir response to surface shear stress and resonant frequencies of internal waves. In the first part of our research, we investigate the effect of sloped end-walls on mixing and internal wave adjustment to forcing within the basin, for three different periods of forcing. We find interesting combinations of wave modes and mixing under variation of the forcing frequencies and of the inclination of the end-walls. When the frequency of the forcing is close to the fundamental mode wave frequency, a resonant internal seiche occurs and the response is characterized by the first vertical mode. For forcing periods twice and three times the fundamental period the dominant response is in terms of the second vertical mode. Adjustment to forcing via second vertical mode is accompanied by the cancellation of the fundamental wave and energy transfer towards the high-frequency waves. The study shows that the slope of the end-walls dramatically affects the location of mixing, which has feedback on the wave field promoting higher vertical modes. The second part of our research is devoted to the investigation of the influence of Earth's rotation on the wave field. In this case, the ratio of forcing to inertial period plays the important role in discerning whether Kelvin or Poincare type waves will be excited which has direct consequences on the wave modal structure and the turbulent quantities. Superinertial forcing frequency excites Poincare waves that are observed to increase the amount of turbulent dissipation rate in the system. In the two cases, where the forcing period was half and twice the fundamental one, we observed that superinertial forcing frequency pushed the dominant internal wave response from first to second vertical mode. The study shows that the increase of the importance of the rotation rate over forcing increases the turbulent dissipation rate in the interior while decreasing it in the near-surface and near-boundary regions.