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KE spectra is useful for understanding and tuning the dissipation mechanisms in the model. For a global model, it can be computed via a vector spherical harmonic transform of the instantaneous velocity field (or spherical harmonic transforms of the instantaneous vorticity and divergence scalars) on a spherical surface. For all the data below, we interpolate to 250mb (I think because this is the most energetic part of the atmosphere - check this?). Spherical harmonics can be thought of as polynomials in Cartesian coordinates (x,y,z) restricted to the sphere. For each degree k there will be 2k+1 polynomials (spherical harmonics) of total degree k. To compute the KE spectra, E(k), we sum the power (coefficient squared) over all degree k spherical harmonics.
The atmosphere is close to geostrophic balance, resulting in a kinetic energy spectrum that scales like E(k) ~ k^-3 as k ranges from 3000km to 800km. But at 600km (wave number 134), the atmosphere transitions into a k^−5/3 scaling that holds down to a few km. The transition, or breakdown of the geostrophic balance, is still not fully explained. The −5/3 scaling suggests a transition to three-dimensional isotropic turbulence, but this explanation can be quickly ruled out. This transition was first observed seen by Nastrom and Gage , who from aircraft observations. They suggested a combination of the known enstrophy generation from baroclinic instability with an unknown small scale energy source. Later investigators have speculated on where this source could come from: there are pure dynamical explanations and explanations which require convection and moist physics (such as thunderstorms).
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