[地球流体電脳倶楽部] [dcmodel | dcmodel-tools] [numexp] [spmodel]

# 球面1.5層浅水強制計算

ここでは，雷雲を想定した質量強制を与えた1.5層浅水計算の実験結果を示す．

## Showman (2007)

• 実験結果
• 方程式系
• \begin{align} & \frac{D \boldsymbol{u}}{D t} + g' \nabla_z h + f \boldsymbol{k} \times \boldsymbol{u} = - \boldsymbol{D}_u, \\ & \frac{D g'h}{D t} + g'h (\nabla_z \cdot \boldsymbol{u}) = \sum S_{storm} + S_{rad} - D_{g'h} . \\ \end{align}

• 強制項
• 質量強制項 \begin{align} S_{storm} = s \cdot \exp \left [- \frac{R^2}{R_{storm}^2} - \frac{(t^*-t_0)}{\tau_{storm}^2} \right ] \end{align}

$$s = 5, \alpha = 0.5$$
放射緩和項 \begin{align} S_{rad} = - \frac{\langle g'h \rangle - g'h_{eq}}{\tau_{mass}} - \frac{g'h - \langle g'h \rangle}{\tau_{APE}} \end{align}

• パラメータの説明

## Brueshaber et al. (2019)

• 実験結果
• 方程式系
• Showman (2007) の連続の式に質量調整項 : $$S_{mass}$$ が加わる． \begin{align} & \frac{D \boldsymbol{u}}{D t} + g' \nabla_z h + f \boldsymbol{k} \times \boldsymbol{u} = - \boldsymbol{D}_u, \\ & \frac{D g'h}{D t} + g'h (\nabla_z \cdot \boldsymbol{u}) = \sum S_{storm} + S_{mass} +S_{rad} - D_{g'h} . \\ \end{align} 質量調整項 \begin{align} S_{mass} = - \left \langle \Sigma S_{storm} \right \rangle \end{align}

## 参考文献

A. P. Showman: Numerical simulations of forced shallow-water turbulence: Effects of moist con-vection on the large-scale circulation of jupiter and saturn J. Atomos. Sci. 64(9):3132-3157, Sept. 2007
S. R. Brueshaber, K. M. Sayanagi, and T. E. Dowling: Dynamical regimes of giant planet polar vortices Icarus, 323:46-61, May 2019