mixsea.shearstrain.gm_shear_variance

mixsea.shearstrain.gm_shear_variance(m, iim, N)[source]

GM model shear variance

Parameters:

m (array-like) – Vertical wavenumber vector [rad/m]
iim (array-like) – Wavenumber integration range, indexer to m
N (float) – Local buoyancy frequency [s^-1]

Returns:

Sgm (float) – GM shear variance normalized by N^2 [1/m^2].
Pgm (array-like) – GM shear spectrum for wavenumber range m.

Notes

Returns GM shear variance normalized by buoyancy frequency by integrating Pgm over a wavenumber range of the GM shear spectrum as presented in Kunze et al. (2006) [8] eq. 6:

\[\frac{_{GM}\left< V_z^2\right>}{\overline{N}^2} = \frac{3 \pi E_0 b j_\ast}{2} \int_{m_\mathrm{min}}^{m_\mathrm{max}} \frac{m^2 dm}{(m + m_\ast)^2}\]

with \(j_\ast=3\), \(E_0=6.3\times10^{-5}\), \(N_0=5.2\times 10^{-3}\) rad/s, \(b=1300\) m, and

\[m_\ast = \frac{\overline{N}}{N_0}\frac{\pi j_\ast}{b}\]