Internal wave radiation by a turbulent fountain in a stratified fluid

Abstract

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.