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The <B>k</B>-spectrum for a potential φ<SUB><B>k</B></SUB> is given by ⟨|φ<SUB><B>k</B></SUB>|<SUP>2</SUP>⟩=(1+<I>k</I><SUP>2</SUP>)<SUP>−1</SUP>(α+β<I>k</I><SUP>2</SUP>)<SUP>−1</SUP>, where α and β are constants. The existence of the two constants, α and β, in the spectrum is the consequence of the two rugged constants of motion. The spectrum is obtained using three different methods, namely, the method of Gibbs distribution, of Hopf’s equation and of Wiener Hermite expansion. Because of the similarity of the equation, the obtained spectrum should also apply to the hydrodynamic turbulence of geostrophic vortices."}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1410282679166284034","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000401840799"},{"@type":"NRID","@value":"9000254553652"},{"@type":"NRID","@value":"9000003292360"}],"foaf:name":[{"@language":"en","@value":"Hasegawa Akira"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Bell Laboratories"}]},{"@id":"https://cir.nii.ac.jp/crid/1410282679166284032","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000401840800"},{"@type":"NRID","@value":"9000254553653"}],"foaf:name":[{"@language":"en","@value":"Imamura Tsutomu"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of Physics, Kwansei Gakuin 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