Modification of boundary layer roll dynamics by induced tropospheric gravity waves
Creators: name: Heuff, Darlene N.
Publisher: name: University of British Columbia
Year: 2009

description: This study investigates two-dimensional coupled interactions between the convectively driven planetary boundary layer and overlying stable layer as a possible mechanism for the formation of large aspect ratio horizontal roll convection (i.e. roll width to height ratio greater than ~4). A two-layer spectral model of the lower atmosphere is developed where the lower layer represents the convectively driven planetary boundary layer, and the upper layer represents the remainder of the troposphere. Each model domain is investigated separately but incorporates key dynamical influences from the other. In the lower domain, a modified Rayleigh-Benard convection model (which replaces the upper bounding plane with a corrugated, rigid lid of a specified wavelength and amplitude) is used to model the effects of induced gravity waves on convectively driven horizontal roll vortices. Two analytical techniques are used: a weakly nonlinear perturbation analysis; and a fully nonlinear analysis of a truncated set of equations. The resulting systems of equations are transformed to wavenumber space using a Fourier integral technique which allows interaction between all scales of motion. Linear analytical and nonlinear numerical results indicate that rolls are induced for all nonzero values of the Grashof number in response to warping of the inversion base. Results from the weakly nonlinear perturbation analysis are shown to be misleading when compared to results obtained using the fully nonlinear method; specifically with respect to the influence of the harmonics of the imposed wavenumber on roll dynamics. Although the model is able to produce rolls which are larger than those associated with the onset of convection, results from the fully nonlinear analysis indicate that the dominant scale of convection (X) is limited to a range given by (0.75λ[sub p] ≤ A, ≤ l.5 λ[sub p]), where λ[sub p] is the preferred scale associated with classical Rayleigh-Benard convection. These results are robust as the band of wavenumbers containing the dominant scale is independent of both the wavenumber and amplitude of the corrugated upper boundary over a wide range of the parameters. This suggests a maximum increase in the scale of convection of 50% and therefore the proposed mechanism (as modeled) is not able to account for observed roll aspect ratios greater than ~5. The resonant mode of the stable upper layer using a simple one-layer, linear perturbation model has been found for a single set of atmospheric conditions. The mode with maximum potential for warping (and thus influence) at the inversion is determined based on energy considerations. The wavelengths corresponding to the resonant mode and dominant mode are found to be in good agreement with numerical results of Clark et al. (1986) and observations of Kuettner et al. (1987). Results from the current study support the interpretation of multiple scaling involving large-scale cloud formations presented by Balaji et al., (1993): i.e. observed large wavelength (~25 km) cloud formations (reported by LeMone and Meitin, 1984) are the result of a combination of important gravity wave and roll scales, rather than a direct result of roll vortices with horizontal scales which are comparable to observed cloud band widths.