Turbulent natural convection along a vertical plate immersed in a stably stratified fluid

Abstract

The paper considers the moderately turbulent natural convection flow of a stably stratified fluid along an infinite vertical plate (wall). Attention is restricted to statistically stationary flow driven by constant surface forcing (heating), with Prandtl number of unity. The flow is controlled by the surface energy production rateFs, molecular viscosity/diffusivity ν and ambient stratification in terms of the Brunt–Väisälä (buoyancy) frequencyN. Following the transition from a laminar to a turbulent regime, the simulated flow enters a quasi-stationary oscillatory phase. In this phase, turbulent fluctuations gradually fade out with distance from the wall, while periodic laminar oscillations persist over much larger distances before they fade out. The scaled mean velocity, scaled mean buoyancy and scaled second-order turbulence statistics display a universal behaviour as functions of distance from the wall for given value of dimensionless combinationFs/(νN2) that may be interpreted as an integral Reynolds number. In the conducted numerical experiments, this number varied in the range from 2000 to 5000.