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Three-dimensional convection in a Boussinesq fluid confined between horizontal rigid boundaries is studied in a series of numerical experiments. Convection in air, whose Prandtl number Pr = 0·71, is systematically investigated, together with another model for Pr = 1. Convection with a steadily changing mean temperature is also considered. Two-dimensional rolls over the Rayleigh number range 4500 [les ] Ra [les ] 24000 and three-dimensional flow patterns over the range 26000 [les ] Ra ≤ 32000 are shown to be stable in air when the mean temperature of the layer is constant ($\partial \overline{T}/\partial t = \eta = 0$). Discrete changes in the slope of the heat-flux curve are shown to exist in the ranges \[ 7000\leqslant Ra\leqslant 8000,\quad 12000\leqslant Ra\leqslant 14000\quad{\rm and}\quad 24000\leqslant Ra\leqslant 26000 \] in air. Only the last discrete transition in the heat flux is asSociated with a significant transition in the flow pattern. Two-dimensional rolls with a horizontally asymmetric distribution of upward and downward motions over the range 4500 [les ] Ra [les ] 8000, and three-dimensional flow patterns over the range 10 000 [les ] Ra [les ] 20 000 are shown to be stable when the mean temperature varies with time. The circulation in a three-dimensional cell depends on the sign of the mean temperature change: downward motions occupy the centre of the cell when $\partial\overline{T}/\partial t > 0$, and upward motions when $\partial\overline{T}/\partial t < 0 $. Motions start to be time dependent for Ra > 20000. Transitions in the planform are asSociated with discrete changes in the slope of the heat-flux curve. Transitions in both the heat flux and flow pattern depend quantitatively on the Prandtl number.

The results are stated of estimation of short-range forecasting of heavy precipitation (P ³ ³ 10 mm/12 hours) and strong wind at the height of 10 m (V ³ 10 m/s) using three nonhydrostatic models from the WRF family: ARW, ARW Glob, and NMM. The forecasts on the basis of all three models were carried out using two grids. The horizontal resolution of external grids varied from 9 to 16.5 km and that of the nested grids, from 3 to 5.5 km. For the ARW and NMM models, the values at side boundaries of external nested grids were taken from the forecasts on the basis of the global GFS NCEP model and for the ARW Glob model, from the global forecasts based on this model. The convection parameterization was turned off at nested grids for all models. The forecasts of heavy precipitation and strong wind at nested grids over the European territory of Russia were estimated from the radar and station measurements in summer 2008. It is obtained that all three models reproduce well enough the mesoscale convective systems and associated areas of heavy precipitation and strong wind but they have common shortcomings: they overestimate the amount and area of heavy precipitation and underestimate the strong wind speed. To a lesser degree, these shortcomings are typical of the ARW model. The possible reasons for systematic errors in the forecasts are discussed.

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Results of numerical simulations using the WRF-ARW nonhydrostatic model are presented for eight episodes of intense convection over European Russia in the summer of 2007. The calculations were performed on four nested grids with horizontal grid meshes of 27, 9, 3, and 1 km. Convection was parametrized on the first two grids and explicitly resolved on the other two. It has been found that simulations on finer grids with explicit calculation of convective flows make it possible to reproduce heavy rainfalls and strong-wind zones in the areas of intense convection. A preliminary verification of the short-range predictions of convective systems shows that the maximum 12-h precipitation totals and the maximum winds at 10 m are close, in the order of magnitude, to the observed values. Prediction of convection centers is the weakest point. Difficulties in the model verification associated with the absence of data with high space-time resolution are discussed.