Laboratory-scale investigation of a periodically forced stratified basin with inclined endwalls

Abstract

We present results of numerical simulations of a stratified reservoir with a three-layer stratification, subject to an oscillating surface shear stress. We investigate the effect of sloped endwalls on mixing and internal wave adjustment to forcing within the basin, for three different periods of forcing. 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 response of a reservoir to surface shear stress and resonant frequencies of internal waves. We find interesting combinations of wave modes and mixing under variation of the forcing frequencies and of the inclination of the endwalls. When the frequency of the forcing is close to the fundamental mode-one 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 the second vertical mode is accompanied by the cancellation of the fundamental wave and energy transfer to higher-frequency waves. The study shows that the slope of the endwalls dramatically affects the location of mixing, which has a feedback on the wave field by promoting the generation of higher vertical modes.