Direct Numerical Simulation of a Weakly Stratified Turbulent Wake

Abstract

Direct numerical simulation (DNS) is used to investigate a time-dependent turbulent wake evolving in a stably stratified background. A large initial Froude number is chosen to allow the wake to become fully turbulent and axisymmetric before stratification affects the spreading rate of the mean defect. The uncertainty introduced by the finite sample size associated with gathering statistics from a simulation of a time-dependent flow is reduced, compared to earlier simulations of this flow. The DNS reveals the buoyancy-induced changes to the turbulence structure, as well as to the mean-defect history and the terms in the mean-momentum and turbulence-kinetic-energy budgets, that characterize the various states of this flow - namely the three-dimensional (essentially unstratified), non-equilibrium (or 'wake-collapse') and quasi-two-dimensional (or 'two-component') regimes observed elsewhere for wakes embedded in both weakly and strongly stratified backgrounds. The wake-collapse regime is not accompanied by transfer (or 'reconversion') of the potential energy of the turbulence to the kinetic energy of the turbulence, implying that this is not an essential feature of stratified-wake dynamics. The dependence upon Reynolds number of the duration of the wake-collapse period is demonstrated, and the effect of the details of the initial/near-field conditions of the wake on its subsequent development is examined