Solution to the Charney Problem of Viscous Symmetric Circulation

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Abstract
The classical problem of viscosity-driven, axially symmetric meridional circulation, partly solved only for the midlatitudes by Charney, is solved here analytically in the whole globe and for any value of viscosity coefficient ν. The solution satisfies Hide's theorem for any Ekman number when Ro < 80E2, where Ro is the Rossby number and E is the Ekman number. For Ro > 80E2, the linear solution ceases to be asymptotically valid. The nonlinear, nearly inviscid regime of Held and Hou presumably is a subset of the second regime (for E → 0+ and Ro fixed). Abstract The classical problem of viscosity-driven, axially symmetric meridional circulation, partly solved only for the midlatitudes by Charney, is solved here analytically in the whole globe and for any value of viscosity coefficient ν. The solution satisfies Hide's theorem for any Ekman number when Ro < 80E2, where Ro is the Rossby number and E is the Ekman number. For Ro > 80E2, the linear solution ceases to be asymptotically valid. The nonlinear, nearly inviscid regime of Held and Hou presumably is a subset of the second regime (for E → 0+ and Ro fixed).

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