Velocity determination for steady atmospheric and oceanic flows

A general problem of velocity determination is considered for steady three-dimensional adiabatic flows of baroclinic fluids. A mathematical analogy between this problem and Nambu's mechanics is discussed. A constructive formula is obtained to determine the wind velocity vector in the atmosphere from the known distribution of potential temperature on isobaric surfaces. This formula generalizes the well-known oceanographic Needler formula to the case of compressible fluids. For an incompressible ocean, simple ("canonical") examples of exact velocity vector determination from the known fields of density (potential density), potential temperature, and salinity are given. Based on these model examples, a problem of hydrologic specification of the no-motion level is briefly discussed.