Three‐dimensional numerical experiments on convectively forced internal gravity waves

Abstract

AbstractResults are presented of thermally forced dry and moist convection and the associated gravity wave fields from three‐dimensional numerical simulations using a non‐hydrostatic anelastic model. This paper extends earlier two‐dimensional simulations to include effects of the third spatial dimension employing a very similar environmental speed‐shear case for the study. The present simulations produce scattered fair weather cumuli in agreement with observations. In many important respects, the physical response is quite similar to that obtained in the earlier two‐dimensional calculations. The near‐uniform surface sensible heat flux results in Rayleigh modes filling the convective boundary layer (CBL) to begin with, whereas later, after convective motions start interacting with the overlying stable layer, larger horizontal scale deep modes become evident and in some cases dominant. The eigenfunction structure of these dominant forced normal modes consists of boundary layer eddies in the lower levels and gravity waves above. They are important organizers of the cumulus convection. As in the earlier two‐dimensional simulations, the efficiency of gravity wave excitation was found to be very sensitive to the mean wind shear in the region spanning the CBL and the overlying stable layer. The dominant horizontal wavelength in the shear direction ranges between 10 and 15 km in the free atmosphere whereas it peaks at about 6 km in the CBL.The strong difference between the preferred directions of alignment for the eddies in the CBL (rolls aligned with the mean shear) and the overlying waves (aligned with lines of constant phase normal to the shear) results in overall broken conditions. The boundary layer motions are organized in broken ‘varicose‐like’ rolls aligned approximately with the mean shear. The overlying waves show a somewhat more scattered pattern. This scattered‐type dominant forced modal response combined with the nonlinear effect of the clouds themselves results in a cloud pattern revealing a high degree of randomness. This cloud field randomness occurs in spite of a near‐zero horizontal wavenumber structure to the surface sensible heat flux.Exchanges of momentum between convective and mean motions in the CBL result in strongly curved stress profiles and a mixing out of the initial boundary layer shear. Sensitivity tests were performed where the mixing of momentum was partially compensated by the addition of low‐level pressure gradient terms.