Evgeni Fedorovich
School of Meteorology, University of Oklahoma, USA

Zero-order model of penetrative convection in linearly stratified fluid reevaluated through LES

Convectively mixed layers separated from the stably stratified, turbulence-free fluid by relatively shallow interfacial sublayers are commonly observed in geophysical flows. When the mixed layer develops over a heated surface, the buoyant forcing generates plumes of warm air that penetrate in the stably stratified fluid and entrain it through the density interface down into the mixed flow region. The properties of convective entrainment crucially depend on stratification in the stably stratified fluid. In many instances, this stratification is approximately linear, which corresponds to a height-constant temperature/density lapse rate.

The most popular theoretical model of entrainment is the so-called zero-order jump model. According to this model, the entrainment layer is represented by a zero-order discontinuity of the temperature/density
profile, and fluid below the density interface is regarded as absolutely mixed. The zero-order model contains several empirical constants that need to be estimated from experimental data. In the equilibrium entrainment regime, which is typically taken as reference entrainment case, the
zero-order model equations incorporate only one empirical constant, the so-called entrainment ratio.

In the present study, the integral parameters of convective entrainment such as the mixed-layer growth rate, entrainment ratio, and relative entrainment layer depth have been investigated numerically, by
means of a high-resolution large eddy simulation (LES), in conjunction with analytical solution of the zero-order model equations for the equilibrium entrainment regime, and available experimental data. Despite the extensive experimental and model studies, a consensus has not yet been reached
regarding the forms of inter-dependencies between the aforementioned parameters, especially in relation to their zero-order model representations. Based on the LES data, it is shown that these dependencies can greatly vary under nonequilibrium conditions. Even in the equilibrium
entrainment regime, relations between particular entrainment parameters retrieved from LES have been found to be rather variable and strongly dependent on the simulation data interpretation in terms of the zero-order model.