The Analytical Dynamics of the Spectral Vorticity Equation

Resonant Rossby Wave Triads and the Swinging Spring

“…He showed that if a fraction of the energy flows into smaller scales, then a greater fraction must flow into larger scales. Platzman (1962) investigated the analytical dynamics of the spectral vorticity equation for nondivergent motions on the sphere. He showed that, with three components, concurrent energy changes in the components of smallest and largest scale are of the same sign, and opposite in sign to that of the component of intermediate scale.…”

“…Rossby had the intuitive genius to isolate the factors that were essential for the existence of these waves, and to elucidate their dynamics by studying them in a model of maximum simplicity. A fuller discussion of the development of Rossby wave theory is presented in Platzman's (1968) Symons Lecture, (loc. cit.…”

Optimizing computations in weather and climate prediction models

“…When the series is truncated to just three wave numbers, the minimum for nonlinear flows (see Platzman, 1962), the vorticity takes on the truncated form, 2 Ψ Acos ly F cos kx 2Gsin lysin kx and the prediction system is represented by the following set of three ordinary differential equations in time;…”

Nonlinear Transfer of Kinetic Energy in the Atmosphere Using One- and Two-Dimensional Spectral Representation.

“…In i~n exp (iIX) is the complex conjugate of Y9 (X,u); and Pn(u)=P, (u) (Platzman, 1962). For the spherical harmonics, n-I gives the number of zeroes between the poles.…”

“…The nonlinear terms in the two-dimensional formulation are evaluated by the transform method described by Machenhauer and Rasmussen (1972) tN which eliminates the requirement for large numbers of interaction coefficients (Platzman, 1960). Very briefly, the transform method involves a conversion from the spectral domain to the physical domain, where the multiplication is performed, followed by a conversion back to the spectral domain.…”