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There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.
There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.
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