Nonstationarity of convective boundary layer growth in a heterogeneously stratified, shear-free atmosphere

Development of convective boundary layer in a uniformly stratified, shear-free atmosphere has been extensively studied experimentally, by means of bulk models of different kinds, and, most prominently, by numerical large eddy simulations (LES). It has been established that at times long enough for the CBL structure to forget about initial conditions, the boundary layer growth happens in an equilibrium (quasi-stationary) manner, with the convective entrainment – which is the driving mechanism of the CBL development – being controlled by the balance between the buoyancy energy supply from the underlying surface and the energy dissipation in the bulk of the CBL. Such balance, which leads to the CBL depth increasing as a square-root function of time, can be vividly illustrated in terms of the so-called zero-order model (ZOM) of entrainment. The ZOM approximates the horizontally averaged profile of buoyancy in the CBL as a function of height with a zero-order discontinuity in place of the capping inversion layer. An important empirically-based hypothesis underlying the ZOM in this case is the instantaneous adjustment of the CBL turbulence structure to the integral parameters of the layer. It is assumed, for instance, that appropriately scaled profiles of turbulence kinetic energy (TKE) and its dissipation rate integrate to universal constants over the layer. Experimental and numerical data generally support these assumptions.

This study is concerned with the extent, to which these assumptions are valid when the growing CBL encounters a discontinuity (or heterogeneity) in the stratification of the free atmosphere (a situation much more realistic than the stratification uniformity). Does the CBL turbulence regime instantly adjusts to the stratification change? Can convective entrainment still be regarded as a quasi-stationary process? How does the CBL depth change with time after the layer proceeds into the new environment, and how long does it take for the CBL to adjust to the new outer stratification?

We address these issues by applying LES to the case of CBL growing initially in a relatively weakly stratified atmosphere, with subsequent change to a stronger stratification (WS case), and to the inverse situation, when the layer passes through an abrupt change from stronger to weaker stratification (SW case). Regimes of CBL evolution were simulated for different stratification ratios and elevations of stratification discontinuity. Time changes of integral TKE and dissipation rate in the vicinity of stratification discontinuity were analyzed in conjunction with CBL depth changes. A ZOM framework was used to estimate differences between regimes of CBL evolution in a homogeneously versus heterogeneously stratified environment. It was found that a quasi-stationary version of the ZOM (and related parameterizations of the entrainment ratio) can still be used in the cases of gradual adjustment of entrainment to new stratification (as in most of WS cases simulated, independent of the stratification ratio), especially for the times well beyond the transition point. The adjustment time scales, evaluated for particular stratification ratios, turned out to be rather large compared to characteristic internal CBL time scales (e.g., to the turnover scale).