SUMMARYNurnciical experiments with a two-level, quasi-geostrophic mtxlel, described by Davies arid Davies (1900), have been extended in several ways; the grid spacing of the previous model has been halved, greatly rcducing numerical errors, and the lateral East-West span of the flow domain is much increased.Using this model a preliminary study is made of some of the large-scale features of the dynamics o l Ixiroclinic wave blocking by the formation of cold anticyclonic cells in high latitudes. In order to facilitate the computational work and the interpretation of the numerical results, a simple, idealized distribution of the large-scale thermal characteristics of an ocean and a continental region is chosen. Two variants of thc model are compared : model (a) is based on a heating function (independent of longitude) describing the climatological annual average over ocean surfaces : in model (b) the flow domain is divided into two longitudinal (North-South) zones; heating functions, roughly characteristic of annual and winter averages over the Ocean surfxes, are used over one zone and heating functions, roughly characteristic of similar averages over land surfaces, are employed over the other zone. Time integrations for the models have becn carried out for periods of 110 days. Blocking does not take place in model (a) but in model (b) the computed flow charts and the K' (t) function (total model eddy kinetic energy) lead to the interesting result that ' blocking ' takes place in high latitudes of the ' land mass ' area at broad scale minima of K', strongly suggesting that the blocking phenomenon is associated with global scale parameters. In the model those minima of K' associated with a large-scale, longitudinal, land-sea temperature differential of about 2°C led to blocking, but the minima associated with temperature differentials appreciably less than this did not produce blocking. The results also indicate an approximately linear dependence of the time scale of blocking on the large-scale, longitudinal, land-sea heating function differential.The prediction that blocking is associated with broad scale minima of K' has been studied in an analysis ol Northern Hemisphere synoptic charts for the winter of 1956-57, which include a well-formed blocking sitiration. Estimates of eddy kinetic energy were made for both surface and 500 mb charts for the sections (a) between 50"W and GOOE, (b) between 1lO"W and l W E , and for (c) the whole Northern Hemisphere. In each of these cases K' dropped to a well marked minimum just before the incidence of a characteristic blocking situation over north-west Europe from 21 December to 2R December, the behaviour of K' ( t ) over this period bcing closely analogous to that found in the model blocking situations.Another objective of the study is to make a comparison of two formulations of sub-grid scale represcntation. In the first instance, this is taken in the often-used form AF2 u. where u is the appropriate velocity component and A is an invariant of space and time; in the second ca...

Equations are constructed to represent quasi-stationary mean flow of momentum and heat on a spherical earth, averaged over a long period of time such as a year and over latitude circles. The crucial shearing Reynolds stress associated with meridional transfer of zonal velocity is assumed to depend linearly on a product of the earth's angular velocity, Q, and the meridional gradient of mean temperature: the shearing stresses associated with vertical transfer of zonal velocity and of meridional velocity are assumed to depend linearly on the vertical gradients of zonal and of meridional mean velocities respectively, and the mean eddy transfer of heat along a meridian is assumed to depend linearly on the mean meridional temperature gradient.All proportionality coefficients are taken to be independent of latitude. Two forms are assumed for the non-adiabatic atmospheric heat source function, Q, used in the thermodynamic equation. In the first case Q is assumed known (from analyses of observations) as a function of height and latitude. In the second case, Q incorporates a heating term which is partly controlled by the model itself and represents some of the characteristics of sensible and latent heat transfer. A solution of the basic equations is obtained in both caws in the form of double expansions in powers of two parameters, one depending on Q and the other on AT, the mean annual temperature difference between equator and pole. The solution is evaluated using Fourier techniques.The series expansions are found to be reasonably convergent for realistic values of the various parameters involved, three terms only being required in the AT expansion and five terms at most in the Sa expansion, but extensive numerical evaluation by digital computer is involved : the region considered is bounded by the tropopause and lies between the equator and 70" latitude. The computed zonal velocity has the characteristic east-west variation with latitude and a broad band maximum of 19 m sec-' and the meridional velocity the characteristic tricellular structure. A poleward eddy angular momentum flux and polar inversion are predicted.The results, through verification of the postulates, add support to the Rossby view of the general circulation in which the cyclonic-scale eddies act to release potential energy of the atmosphere to supply their own kinetic energy and form the mean zonal kinetic energy. They further indicate the value of the reconstructed ' austausch ' approach for this problem.

No abstract

No abstract

No abstract