Direct numerical simulations of free convection beneath an air–water interface at low Rayleigh numbers

Abstract

Direct numerical simulations of a cooling air–water interface were employed to determine the structure of the temperature, velocity, and vorticity fields in the thin thermal boundary layer formed at the free surface. The simulations were performed at low to moderate Rayleigh numbers. In this flow, the turbulence is initiated by the Rayleigh instability at the interface and is maintained by buoyant production. Visualizations of the flow reveal that the temperature field at the interface is composed of large warm patches surrounded by cooler dense fluid which accumulates in thin bands. The cool fluid associated with the bands initially falls in sheets, but rapidly forms descending tubes and plumes. The turbulence statistics were scaled both with outer and inner variables. The latter scaling is based on the so-called surface strain model which is essentially consistent with Townsend’s inner scaling. It is found that the temperature statistics collapse well using inner variables. On the other hand, the vertical velocity scales well with inner variables within the thermal boundary layer, but at greater depths it becomes more appropriate to use outer scaling. The anisotropic nature of the velocity statistics in the core of the flow is ascribed to the relatively low Rayleigh numbers used in the simulations. An explanation for this anisotropy is offered based on a detailed examination of the turbulence kinetic energy balances.