Источник поля скоростей

Last modified by Alexey Popov on 2020/12/24 17:53

$\nabla \cdot \mathbf v = \frac{1}{\rho_q}\rho_v - \frac{1}{\rho_q}\frac{\partial \rho}{\partial t}$

$\nabla \cdot \boldsymbol \theta = 0$

$\nabla \times \mathbf v = \frac{\partial \boldsymbol \theta}{\partial t} + \boldsymbol \omega$

$- c^2 (\nabla \times \boldsymbol \theta) = \mathbf a + \frac{\partial \mathbf v}{\partial t} + c^2\frac{1}{\rho_q}\nabla \rho$

$\nabla \times \mathbf a =- c^2\nabla \times (\nabla \times \boldsymbol \theta) - \frac{\partial^2 \boldsymbol \theta}{\partial t^2} - \frac{\partial\boldsymbol \omega}{\partial t}$

$\frac{1}{\rho_q}\rho_{v} \boldsymbol \omega = - c^2\square \boldsymbol \theta$

$\frac{1}{\rho_q}\rho_{a} \mathbf v = - c^2\square \mathbf v$

$c^2 (\nabla (\nabla \cdot \mathbf v )) - c^2 (\nabla \times (\nabla \times \mathbf v ))+ c^2 (\nabla \times \boldsymbol \omega) = \frac{\partial \mathbf a}{\partial t} + \frac{\partial^2 \mathbf v}{\partial t^2}$

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Created by Alexey Popov on 2020/12/24 17:19