Enstrophy equation: Difference between revisions
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The enstrophy equation describes the production and destruction of enstrophy <math> \Omega = \frac{1}{2} |\vec{\omega}|^2</math> | The enstrophy equation describes the production and destruction of enstrophy <math> \Omega = \frac{1}{2} |\vec{\omega}|^2</math>. For a stratified, Boussinesq fluid it is | ||
<math> \frac{D \Omega}{Dt} = \underbrace{\omega_i \omega_j e_{ij}}_\text{vortex tilting/stretching} - \underbrace{\frac{g}{\rho_0} \vec{\omega} \cdot \left[ \nabla \times (\rho \hat{k})\right]}_\text{baroclinic} - \underbrace{\nu (\nabla\times \vec{\omega})^2}_\text{viscous destruction} + \underbrace{\nu \nabla\cdot\left[ \vec\omega\times(\nabla\times\vec\omega)\right]}_\text{boundary production} </math> | <math> \frac{D \Omega}{Dt} = \underbrace{\omega_i \omega_j e_{ij}}_\text{vortex tilting/stretching} - \underbrace{\frac{g}{\rho_0} \vec{\omega} \cdot \left[ \nabla \times (\rho \hat{k})\right]}_\text{baroclinic production} - \underbrace{\nu (\nabla\times \vec{\omega})^2}_\text{viscous destruction} + \underbrace{\nu \nabla\cdot\left[ \vec\omega\times(\nabla\times\vec\omega)\right]}_\text{boundary production} </math> | ||
Latest revision as of 16:59, 18 September 2020
The enstrophy equation describes the production and destruction of enstrophy . For a stratified, Boussinesq fluid it is
![{\displaystyle {\frac {D\Omega }{Dt}}=\underbrace {\omega _{i}\omega _{j}e_{ij}} _{\text{vortex tilting/stretching}}-\underbrace {{\frac {g}{\rho _{0}}}{\vec {\omega }}\cdot \left[\nabla \times (\rho {\hat {k}})\right]} _{\text{baroclinic production}}-\underbrace {\nu (\nabla \times {\vec {\omega }})^{2}} _{\text{viscous destruction}}+\underbrace {\nu \nabla \cdot \left[{\vec {\omega }}\times (\nabla \times {\vec {\omega }})\right]} _{\text{boundary production}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34a37abc9e6237c64082c4255fe0dee25de9572c)