正压本文重定向自 正壓

数学推导

${\displaystyle p=p(\rho )}$
${\displaystyle \rho =\rho (p)}$

${\displaystyle \nabla p=0}$

${\displaystyle {\frac {\partial \rho }{\partial x}}={\frac {\partial \rho }{\partial p}}{\frac {\partial p}{\partial x}}}$

${\displaystyle {\frac {\partial \rho }{\partial y}}={\frac {\partial \rho }{\partial p}}{\frac {\partial p}{\partial y}}}$
${\displaystyle {\frac {\partial \rho }{\partial z}}={\frac {\partial \rho }{\partial p}}{\frac {\partial p}{\partial z}}}$

${\displaystyle \nabla \rho =({\frac {\partial \rho }{\partial p}})\nabla p}$

${\displaystyle \nabla \rho =0}$

理想气体

${\displaystyle T={\frac {p}{\rho (p)R}}}$

${\displaystyle \nabla T={\frac {\nabla p}{\rho R}}-{\frac {p\nabla \rho }{\rho ^{2}R}}}$

${\displaystyle \nabla T=0}$

参考文献

• James R Holton, An introduction to dynamic meteorology, ISBN 0-12-354355-X, 3rd edition, p77.
• Marcel Lesieur, "Turbulence in Fluids: Stochastic and Numerical Modeling", ISBN 0-7923-0645-7, 2e.
• D. J. Tritton, "Physical Fluid Dynamics", ISBN 0-19-854493-6.