fluidsim.solvers.ns3d.strat.output.spect_energy_budget

SEB (fluidsim.solvers.ns3d.strat.output.spect_energy_budget)

class fluidsim.solvers.ns3d.strat.output.spect_energy_budget.SpectralEnergyBudgetNS3DStrat(output)

Bases: SpectralEnergyBudgetNS3D

Spectral energy budget of ns3d.strat.

Notes

\[ \begin{align}\begin{aligned}d_t E_K(\textbf{k}) = T_K(\textbf{k}) - C_{K\rightarrow A}(\textbf{k}) - D_K(\textbf{k}),\\d_t E_A(\textbf{k}) = T_A(\textbf{k}) + C_{K\rightarrow A}(\textbf{k}) - D_A(\textbf{k}),\end{aligned}\end{align} \]

where \(E_K(\textbf{k}) = |\hat{\textbf{v}}|^2/2\) and \(E_A(\textbf{k}) = |\hat{b}|^2/(2N^2)\).

The transfer terms are

\[ \begin{align}\begin{aligned}T_K(\textbf{k}) = \Re \left(\hat{\textbf{v}}^* \cdot P_\perp\widehat{\textbf{v} \times \boldsymbol{\omega}} \right),\\T_A(\textbf{k}) = - \Re \left(\hat{b}^* \widehat{\textbf{v} \cdot \boldsymbol{\nabla} b} \right) / N^2.\end{aligned}\end{align} \]

By definition, we have to have \(\sum T_K(\textbf{k}) = \sum T_A(\textbf{k}) = 0\).

The conversion term is equal to \(C_{K\rightarrow A}(\textbf{k}) = -\Re(\hat{v_z}^* \hat{b})\) and the dissipative terms are

\[ \begin{align}\begin{aligned}D_K(\textbf{k}) = f_{dK}(\textbf{k}) E_K(\textbf{k}),\\D_A(\textbf{k}) = f_{dA}(\textbf{k}) E_A(\textbf{k}),\end{aligned}\end{align} \]

where \(f_{dK}(\textbf{k})\) and \(f_{dA}(\textbf{k})\) are the dissipation frequency depending of the wavenumber and the viscous coefficients.

Classes

SpectralEnergyBudgetNS3DStrat(output)

Spectral energy budget of ns3d.strat.