Direct numerical simulation of buoyancy-driven turbulence in stably stratified fluid

Abstract

We investigate the role of buoyancy force on the generation and decay of random motion in a homogeneously stratified fluid by means of direct numerical simulations (DNS) of the dynamic and thermodynamic equations. The simulations start from a fluid which is at rest but has appreciable temperature fluctuations. Therefore the flow initially evolves by extracting energy from the potential energy field. Three free parameters, the Reynolds number Re , the Prandtl number Pr and the stratification number St , characterize the flow. Among these numbers the stratification number, St = ( l T 0 / T ′ 0 ) (d T R /dz), is the most crucial one for the investigated problem. Here T ′ 0 and l T 0 are the initial r.m.s. temperature and the initial integral temperature lengthscale, respectively, and d T R /dz is the background stratification. St is a measure of the strength of background-temperature gradient compared to the initial mean fluctuating temperature gradient in the fluid. A critical stratification number of order one is found to separate an oscillating, non-turbulent flow from flow states which exhibit features of turbulence. When St > 1, the statistics reveal a nearly linear and strongly anisotropic flow as typical for gravity waves but the flow-field variables behave randomly. When St < 1, i.e. when the initial gradient of fluctuating temperature exceeds the gradient of its background value, the available potential energy is sufficient to create nonlinear motions which resemble turbulence in many aspects. The properties of such a flow are a transient state of enhanced stirring and mixing, enhanced rates of dissipation of temperature fluctuations, and a quick return to isotropy. The stratification number is an easily measurable parameter in field experiments in the ocean as well as in the atmosphere. Therefore St may be a useful indicator of whether a flow regime contains sufficient potential energy to create turbulence.