fluidsim.solvers.plate2d.output.spatial_means

Spatial means (fluidsim.solvers.plate2d.output.spatial_means)

Provides:

class fluidsim.solvers.plate2d.output.spatial_means.SpatialMeansPlate2D(output)[source]

Bases: fluidsim.base.output.spatial_means.SpatialMeansBase

Compute, save, load and plot spatial means.

If only \(W\) is forced and dissipated, the energy budget is quite simple and can be written as:

\[ \begin{align}\begin{aligned}\partial_t E_w = - C_{w\rightarrow z} - C_{w\rightarrow \chi} + P_w - D_w,\\\partial_t E_z = + C_{w\rightarrow z},\\\partial_t E_\chi = + C_{w\rightarrow \chi},\end{aligned}\end{align} \]

where

\[ \begin{align}\begin{aligned}C_{w\rightarrow z} = \sum_{\mathbf{k}} k^4\mathcal{R}(\hat w \hat z^*),\\C_{w\rightarrow \chi} = -\sum_{\mathbf{k}} \mathcal{R}( \widehat{\{ w, z\}} \hat \chi ^* ),\\P_w = \sum_{\mathbf{k}} \mathcal{R}( \hat f_w \hat w^* )\end{aligned}\end{align} \]

and

\[D_w = 2 \nu_\alpha \sum_{\mathbf{k}} k^{2\alpha} E_w(k).\]

Classes

SpatialMeansPlate2D(output)

Compute, save, load and plot spatial means.