Journal of the Meteorological Society of Japan. Ser. II
Online ISSN : 2186-9057
Print ISSN : 0026-1165
ISSN-L : 0026-1165
Nots and Correspondence
A Conserved Quantity Related to Vorticity Component in the Direction of ∇θ×u
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2004 Volume 82 Issue 1 Pages 249-254


In a stationary rotating system, such a quantity is constructed, that is related to the absolute vorticity component in the direction of ∇θ×u. Here, θ is the potential temperature, and u is the wind velocity. In a nondissipative and adiabatic case, this quantity is materially conserved along the streamline. By the conservation property, if the pressure increases (decreases) along the streamline, then the circulation on the {∇θ, u} plane decreases (increases) there. This quantity is the derivative of the Bernoulli function B in the direction of ∇θ. In a dissipative case, wherein the Bernoulli function is decreased along the streamline, the gradient of the Bernoulli function is generated. As a result, this quantity is increased or decreased by the dissipation, just in the same way as the potential vorticity generation due to dissipation.

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© 2004 by Meteorological Society of Japan
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