A dynamical study is made of properties of cumulus convection and its preferred mode in a conditionally unstable atmosphere based on numerical experiments. The preferred mode of cumulus convection is determined as the steady convection cell which consists of an ascending saturated region and a descending unsaturated one attained eventually after random temperature disturbances are imposed initially. It is shown that the preferred cell size and the area ratio of the ascending region to the descending one depend on the mean vertical velocity and the static stability of the atmospheric layer in which the connections are imbedded. Inspection of each term of energy equations indicates that the preferred convection is of the mode for which the potential energy of the layer is at the lowest. Since the potential energy represents the static stability of the layer, the minimum value of the mean temperature lapse-rate can be observed when the preferred convection is realized.
The oceanic heat budget is calculated by conventional methods from ship observations in the Tropical Atlantic and Eastern Pacific during 1911-70. Zonal asymmetries between the Eastern and Western part of the oceans are studied at the examples of the warm Gulf Stream and Brazil, and the cold Canary, Benguela, and Humboldt Current domains. For the same latitude belt, the Canary Current area has a smaller latent heat flux and performs an export of energy to other parts of the globe of 39W m-2 in the annual mean as compared to an import of 43W m-2 in the Gulf Stream region. Off the Pacific coasts of Peru and Chile and the coasts of Southwest Africa, net radiation is reduced by extensive cloudiness, and latent and sensible heat fluxes are also comparatively small. Residual heat export within the oceanic water body is of similar magnitude as in the Brazil Current region, annual mean values amounting to 42, 16, and 30W m-2, respectively.
The solar radiation reflected by an array of finite broken clouds corresponding to cumuli is examined. The importance of the distribution of cloud size is demonstrated by using the actual cloud pattern ove Florida. The accuracy of simplified cloud models (plane-parallel infinite cloud or an array of identical clouds) to approximate the array of clouds with size distribution is examined. The result shows the following: (1) The model of plane-parallel infinite cloud causes fairly large error in the reflection. (2) The model of the array of identical clouds is still insufficient to approximate the array of distributed clouds. (3) When the sun is high, the difference between the models of cloud array becomes most evident and an accurate model for broken clouds is required. (4) The result of (3) is maintained even if the reflection from the clouds-earth surface system is considered.
The turbulence quantities such as the RMS of the vertical speed δw, and temperature δT, the dissipation rate of kinetic energy to heat ε, and the vertical diffusion coefficient KM, in the free convective mixing layer have been considered. Taking velocity scale W* and temperature scale T* for the convection layer, which has been proposed by Deardorff (1970) and others, and the depth of the mixing layer hm as scale height, the relations describing these quantities in the free convective constant flux layer are extended to the free convective mixing layer. These turbulence quantities are written as follows: δw=CwW3*ξ1/4 δT=cTT*ξ-1/4 ε=Cε(W3*/hm)ξ KM=CKMW*hm where C is a universal constant, ξ=1-z/hm, and z is height. The vertical profile of ε is determined by using the energy balance equation for the and temperature scale T* for the free convection layer, which has been proposed by Deardorff free convective layer and assuming linearly decreasing vertical heat flux with height as shown by many observations. Also, according to observed results, KM is assumed to be invariant with height. Moreover, using dimensional relations among KM, δw, δT, and ε, the vertical profiles of δw and δT are determined. The agreements of the above relations to the observations are fairly good.
Stagnant flow which appears upstream of a ridge when the airflow is stably stratified is studied by observing wind data and also by wind tunnel experiment. Stagnant flow in the atmosphere is shown to have a strong relation to the nocturnal inversion and disappears together with it. Since in the wind tunnel, thermal conditions are kept unchanged, the stability condition is controlled by changing flow velocity. Then, the flow features are dependent on flow velocity. But when the stagnant characteristics are described with respect to the Froude number given by Fγ=U/(gHΔθ/θ)1/2 both the results in the wind tunnel and atmosphere show qualitative agreement. A stagnant flow layer where airflow is stagnant or slightly opposite to the ambient flow is found to appear when the Froude number is less than some critical value. The critical Froude number above which the stagnant flow disappears is estimated to be about 2.3.