The general circulation in a steady rotating‐dishpan experiment

Abstract

AbstractThis is the continuation of a previous paper (Q.J., 83, 1957) in which the structure of the steady rotating‐dishpan experiment was described. The present article begins with a calculation of the heat balance and a determination of the mechanisms that transport heat from heat to cold source. Of particular interest is the question whether the heat transport is effected by quasi‐geostrophic horizontal or by non‐geostrophic vertical circulations. Calculations were performed in the conventional polar coordinate system and also in a curvilinear coordinate system following the jet‐stream axis. In polar coordinates the heat transport is accomplished largely by horizontal circulations, and in the curvilinear coordinate system by an ageostrophic vertical mass circulation. Thus the ‘mechanism’ of heat transfer that is found depends largely on the framework of reference in which calculations are made.When the vertical circulations are averaged with respect to longitude in the two coordinate systems, a three‐cell structure with direct equatorial and polar branches and an indirect middle‐latitude branch is found in polar coordinates. In contrast, the calculations yield a single direct cell for the curvilinear system.Computation of the transport of absolute angular momentum in the two coordinate systems produces corresponding results.Calculations of kinetic and potential energy balance were performed in curvilinear coordinates. Production of kinetic energy by the mass circulation far exceeds actual net generation of kinetic energy, so that ‘eddies’ with respect to the jet‐stream axis convert kinetic energy to work done across the boundaries of the volume considered. Similarly, the potential energy release is achieved by means of the mass circulation while the eddies store potential energy poleward of the jet‐stream axis.An attempt was made to determine whether the velocity distribution near the top surface, especially the jet‐stream core, could be derived using only the mass circulation and the theorem of conservation of potential vorticity. The result showed that the velocity profile on the anticyclonic side of the jet stream is well reproduced by the calculation, but that the computed jet‐stream axis is situated far poleward of the observed position and that the computed strength of the jet centre exceeds the actual strength by 50 per cent.In conclusion, the result of the computations shows that at least two, and possibly a much greater number of general circulation ‘mechanisms’ can be found, depending upon the reference frame chosen. Mathematically, these solutions are all equally correct and yield the same total transports. From the physical viewpoint, the general circulation is represented as a simple heat engine in the curvilinear coordinate system. Considering the energy balance, the solution indicates that the kinetic energy of the general circulation is produced and maintained by the largest cell, the single direct circulation extending from heat to cold source, and that this kinetic energy is then converted to kinetic energy of smaller circulations.