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, both in the laboratory and in nature (see, e.g., Deardorff et al. 1980, Boers and Eloranta 1986, Nelson et al. 1989), by means of bulk models of differing complexity (see, e.g., Tennekes 1973, Zilitinkevich 1991, van Zanten et al. 1999, Fedorovich and Mironov 1995), and, most extensively, though numerical large eddy simulations (LES; see, e.g., Deardorff 1974, Lewellen and Lewellen 1998, Sullivan et al. 1998, Lock and MacVean 1999, Fedorovich et al. 2004). 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 a 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. This balance leads to the CBL depth increasing as a function of the square-root of time. This behavior can be vividly illustrated in terms of the socalled zero-order model (ZOM) of entrainment introduced by Lilly (1968) and reevaluated against LES data in Fedorovich et al. (2004). 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 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 obtained to date generally support these assumptions. The present study is concerned with the extent to which the above 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 adjust to the stratification change? Can convective entrainment still be regarded as a quasistationary 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 (i) the shear-free CBL that grows initially in a relatively weakly stratified atmosphere, with subsequent change to a stronger stratification, and (ii) to the inverse situation, when the CBL passes through an abrupt change from stronger to weaker stratification. We then apply the ZOM formalism to analyze and interpret the numerical simulation data.