diff --git a/TurTLE/DNS_statistics.py b/TurTLE/DNS_statistics.py index b0f3aeb3e27544c32f98feed64c4af09bd2016ad..d4a764f366cb5893589f4df7c5957a445312900b 100644 --- a/TurTLE/DNS_statistics.py +++ b/TurTLE/DNS_statistics.py @@ -34,12 +34,12 @@ def compute_statistics( strict_Parseval_check = True): """Run basic postprocessing on raw data. The energy spectrum :math:`E(t, k)` and the enstrophy spectrum - :math:`\\frac{1}{2}\omega^2(t, k)` are computed from the + :math:`\\frac{1}{2}\\omega^2(t, k)` are computed from the .. math:: \sum_{k \\leq \\|\\mathbf{k}\\| \\leq k+dk}\\hat{u_i} \\hat{u_j}^*, \\hskip .5cm - \sum_{k \\leq \\|\\mathbf{k}\\| \\leq k+dk}\\hat{\omega_i} \\hat{\\omega_j}^* + \sum_{k \\leq \\|\\mathbf{k}\\| \\leq k+dk}\\hat{\\omega_i} \\hat{\\omega_j}^* tensors, and the enstrophy spectrum is also used to compute the dissipation :math:`\\varepsilon(t)`. @@ -202,7 +202,7 @@ def compute_time_averages(self): .. math:: U_{\\textrm{int}}(t) = \\sqrt{\\frac{2E(t)}{3}}, \\hskip .5cm - L_{\\textrm{int}} = \\frac{\pi}{2U_{int}^2} \\int \\frac{dk}{k} E(k), \\hskip .5cm + L_{\\textrm{int}} = \\frac{\\pi}{2U_{int}^2} \\int \\frac{dk}{k} E(k), \\hskip .5cm T_{\\textrm{int}} = \\frac{L_{\\textrm{int}}}{U_{\\textrm{int}}} @@ -469,10 +469,10 @@ def plot_basic_stats( print('WARNING: CFL computation does not make sense for non-isotropic grids') a.plot(self.statistics['t'] / self.statistics['Tint'], sresolution, - label = '$(k_M \eta_K)^{-1}$ (spatial resolution)') + label = '$(k_M \\eta_K)^{-1}$ (spatial resolution)') a.plot(self.statistics['t'] / self.statistics['Tint'], tresolution, - label = '$\\frac{\\Delta t}{\\Delta x} \sqrt{3}\\| u \\|_\infty$ (CFL upper bound)') + label = '$\\frac{\\Delta t}{\\Delta x} \\sqrt{3}\\| u \\|_\infty$ (CFL upper bound)') a.set_ylim(top = 1.05*max(sresolution.max(), tresolution.max()), bottom = 0)