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In this work, we study the characteristics of a stably stratified atmospheric boundary layer using large-eddy simulation (LES). In order to simulate the stable planetary boundary layer, we developed a modified version of the two-part subgrid-scale model of Sullivan et al. This improved version of the model is used to simulate a highly cooled yet fairly windy stable boundary layer with a surface heat flux of wθ o = −0.05 m K s −1 and a geostrophic wind speed of U g = 15 m s −1 . Flow visualization and evaluation of the turbulence statistics from this case reveal the development of a continuously turbulent boundary layer with small-scale structures. The stability of the boundary layer coupled with the presence of a strong capping inversion results in the development of a dominant gravity wave at the top of the stable boundary layer that appears to be related to the most unstable wave predicted by the Taylor-Goldstein equation. As a result of the decay of turbulence aloft, a strong-low level jet forms above the boundary layer. The time dependent behaviour of the jet is compared with Blackadar's inertial oscillation analysis.

A new method for large eddy simulations is described and evaluated. In the proposed method the primary modeled quantity is the unfiltered velocity field appearing in the definition of the subgrid-scale stress tensor. An estimate of the unfiltered velocity is obtained by expanding the resolved large-scale velocity field to subgrid-scales two times smaller than the grid scale. The estimation procedure consists of two steps. The first step utilizes properties of a filtering operation and the representation of quantities in terms of basis functions such as Fourier polynomials. In the second step, the phases associated with the newly computed smaller scales are adjusted in order to correspond to the small-scale phases generated by nonlinear interactions of the large-scale field. The estimated velocity field is expressed entirely in terms of the known, resolved velocity field without any adjustable constants. The modeling procedure is evaluated in a priori analyses using direct numerical simulation results of channel flow at low Reynolds number and in actual large eddy simulations of channel flow at two different Reynolds numbers. In all cases, the new model performs better than or comparable to classical eddy viscosity models for the majority of physical quantities. In particular, all components of the subgrid-scale stress tensor are predicted accurately and the procedure naturally accounts for backscatter without any adverse effects on the numerical stability.

This study involves a numerical simulation of spatially evolving secondary instability in plane channel flow. The computational algorithm integrates the time-dependent, three-dimensional, incompressible Navier–Stokes equations by a mixed finite-difference/spectral technique. In particular, we are interested in the differences between instabilities instigated by Klebanoff (K-) type and Herbert (H-) type inflow conditions, and in comparing the present spatial results with previous temporal models. It is found that for the present inflow conditions, H-type instability is biased towards one of the channel walls, while K-type instability evolves on both walls. For low initial perturbation amplitudes, H-type instability exhibits higher growth rates than K-type instability while higher initial amplitudes lead to comparable growth rates of both H-and K-type instability. In H-type instability, spectral analysis reveals the presence of the subharmonic two-dimensional mode which promotes the growth of the three-dimensional spanwise and fundamental modes through nonlinear interactions. An intermodal energy transfer study demonstrates that there is a net energy transfer from the three-dimensional modes to the two-dimensional mode. This analysis also indicates that the mean mode transfers net energy to the two-dimensional subharmonic mode and to the three-dimensional modes.

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