THE DISTRIBUTION OF KINETIC ENERGY IN CERTAIN STEADY BAROTROPIC CURRENTS

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Abstract
The spreading of an energy concentration superimposed on a uniform zonal current at a particular latitude, may be characterized by the complete disappearance of the perturbation at infinity. Under this condition the vorticity equation for a nondivergent barotropic atmosphere can be linearized exactly for steady-state motion and reduces to the well-known Helmholtz wave equation. Its solution then is quite general, and is not subjected to any restrictive condition of small perturbations. Two cases of “dispersion” were studied, the problem of the deflection of a zonal current and the problem of a zonal jet stream. In the first case the northward velocity component was prescribed as a boundary condition, in the second case the eastward velocity component. Due to the assumption of nondivergent flow, both components cannot be arbitrarily prescribed since they must satisfy the continuity requirement. Prescribing the distribution of either velocity component along a fixed meridian by a function with a pronounced maximum at a given latitude, the other component is given by a sinusoidal function with decreasing amplitude. The streamlines of the resulting flow are computed for both the deflection problem and the jet-stream problem. In the former case the streamlines show a fully developed wave motion at large distances downstream, with decreasing amplitude and with a wave length approaching the stationary wave length of Rossby's barotropic waves. In the second case, the jet stream splits into two branches which develop downstream into a wave motion again of the same characteristic as before. These two branches are separated by the central line of the original jet stream, which is undisturbed, and are 180 degrees out of phase. Computed isolines of kinetic energy of the total flow (basic current plus perturbation) show the strongest energy concentration along the initial meridian, with consecutive maxima downstream decreasing in intensity, located in the case of deflection on the northeast side of ridges and on the southeast side of troughs. In the jet-stream case the maxima appear in the region of confluence of the separated branches. The spreading of energy downstream is evident from the almost uniform energy distribution far from the given line of concentration. The location of energy concentration visible in the crowding of streamlines in individual troughs and ridges in the deflection problem is in agreement with observations, while the splitting of the original jet stream into two branches is frequently observed on charts of the upper troposphere.

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