On the Closure of Certain Assemblages of Trigonometrical by Wiener N.

By Wiener N.

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4 Spiral Structures in Galaxies 27 Fig. 11. Spiral galaxies (top to bottom: M51, M81, MlOl) background of the slowly increasing gravitational potential which is due to the rest of the disk, the halo and the corona. The resulting gravitational potential is such that the equilibrium linear velocity as a function of radius (the so-called rotation curve) is represented by an N -shaped curve: the central core is rotating practically as a rigid body and next to it there is a relatively narrow region where 28 2.

86 23° Fig. 10. Trajectory of an intrathermoclinic anticyclonic lens in the Atlantic. 62) 2. When the value of e; reaches a few dozen, the lifetimes of cyclonic vortices increase within an order of magnitude but are still substantially restricted by vortex dispersion spreading. 3. In a similar situation (when e; is several dozen), the lifetimes of anticyclonic vortices exhibit a much greater increase; they are now restricted by viscosity rather than by dispersion, This radical difference between the lifetimes of Rossby vortices with opposite polarities is a manifestation of the cyclone-anticyclone asymmetry in the oceans, which is probably similar to the asymmetry observed in the atmospheres of the giant planets.

The derivatives of this function with respect to coordinates x and y are velocity projections onto the y and x axes, respectively. 11). 4). 6 b) for shallow water. 3), in this case we have for the drift velocity where V* = V*(O). 5) becomes (Lltp - tp)t + V*tpx + V*tptpx + J(tp, Lltp) - V* R-1tpxY =0 . 7) are virtually the same. 6), illustrates the remarkable analogy between Rossby waves in shallow water and drift waves in plasma. Keeping this analogy in mind, we shall henceforth assume the qualitative conclusions drawn from the equation for Rossby waves to be applicable also in the case of plasma drift waves.

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