Results of a three-dimensional numerical model are analysed in a study of turbulence and entrainment within mixed layers containing stratocumulus with or without parameterized cloud-top radiative cooling. The model eliminates most of the assumptions invoked in theories of cloud-capped mixed layers, but suffers disadvantages which include poor resolution and large truncation errors in and above the capping inversion.For relatively thick mixed layers with relatively thick capping inversions, the cloud-top radiative cooling is found to be lodged mostly within the capping inversion when the cooling is confined locally to the upper 50 m or less of the cloud. It does not then contribute substantially towards increased buoyancy flux and turbulence within the well mixed layer just below.The optimal means of correlating the entrainment rate, or mixed-layer growth rate, for mixed layers of variable amounts of stratocumulus is found to be through functional dependence upon an overall jump Richardson number, utilizing as scaling velocity the standard deviation of vertical velocity existing at the top of the mixed layer (near the center of the capping inversion). This velocity is found to be a fraction of the generalized convective velocity for the mixed layer as a whole which is greater for cloud-capped mixed layers than for clear mixed layers.

An efficient time‐dependent equation for predicting ground surface temperature devised by Bhumralkar (1975) and Blackadar (1976) is tested against a 12‐layer soil model and compared with five other approximate methods in current use. It is found to be generally superior if diurnal forcing is present and very much superior to the use of the insulated surface assumption. An analogous method of predicting ground surface moisture content is presented which allows the surface to become moist quickly during rainfall or to become drier than the bulk soil while evaporation occurs. These improved methods are not of much relevance unless the main influences of a vegetation layer are included. An efficient one‐layer foliage parameterization is therefore developed that extends continuously from the case of no shielding of the ground by vegetation to complete shielding. It includes influences of both ground and foliage albedos and emissivities, net leaf area index, stomatal resistance, retained water on the foliage, and several other considerations. When it is tested against data for wheat measured by Penman and Long (1960), it appears quite adequate despite the many simplifying assumptions. The parameterization predicts that errors of up to a factor of 2 in evapotranspiration can be incurred by ignoring the presence of a vegetation layer.

The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with subgrid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

No abstract

No abstract