Jet stream and long waves in a steady rotating‐dishpan experiment: Structure of the circulation

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Abstract
The three‐dimensional structure of the flow of water in a steady rotating three‐wave dishpan experiment is computed and compared with the atmosphere.At first the experiment and methods of comparison between dishpan and atmosphere are described. Then motion and vorticity at the top surface are shown; trajectories leading from equatorial to polar rim of the pan are found. Next the three‐dimensional temperature field is determined, and from this the geostrophic motion at all depths.The flow pattern resembles the basic features of the middle‐latitude atmosphere in a remarkable way. Mobile long waves in a jet stream near the top overlie cyclonic and anticyclonic vortices farther down. There is, however, neither the counterpart of tropopause nor stratosphere in the temperature field, indicating that these features are not necessary for development of the basic flow pattern. Further, the distribution of momentum sources and sinks differs from that of the atmosphere, as momentum is given off to the inner (and possibly to the outer) cylinder, while most of the bottom acts as source. This throws doubt on the importance of momentum balance considerations for explanation of the principal flow features.Vertical motions are calculated in the interior of the fluid with the adiabatic assumption. Values again compare well with those of the atmosphere as does the distribution of centres of ascent and descent relative to long waves and cyclones. A positive correlation between temperature and vertical motion exists along the jet axis, hence there is release of potential energy. If averaging is performed along the jet‐stream axis, one finds that the centre of ascent lies equatorward, and the centre of descent poleward of the axis. Ifzonalaveraging is performed, however, the centre of ascent appears north of the zonal wind maximum, and the centre of descent on its equatorward side. This calculation uncovers a weakness of zonal averaging as a tool in studying the general circulation.Absolute vorticity is calculated on constant temperature surfaces in the interior of the liquid. It is found that the theorem of conservation of absolute vorticity is nearly fulfilled in the jet‐stream layer with wave motion; in the lower layer with vortices, validity of the theorem of conservation of potential vorticity is indicated qualitatively. The regions of convergence and divergence, as inferred from the vorticity changes along the relative stream‐lines, agree qualitatively with the vertical motion distribution.