drag drag_with_derivative IceBasalResistancePseudoPlasticLaw m_q m_sliding_scale_factor_reduces_tauc m_u_threshold m_u_threshold_factor print_info ~IceBasalResistancePseudoPlasticLaw

drag_with_derivative() void pism::IceBasalResistancePseudoPlasticLaw::drag_with_derivative ( double  tauc, double  vx, double  vy, double *  beta, double *  dbeta  ) const virtual Compute the drag coefficient and its derivative with respect to $\alpha = \frac 1 2 (u_x^2 + u_y^2)$. $$\begin{align*} \beta &= \frac{\tau_{c}}{u_{\text{threshold}}^q}\cdot (|u|^{2})^{\frac{q-1}{2}} \\ \diff{\beta}{\frac12 |\mathbf{u}|^{2}} &= \frac{\tau_{c}}{u_{\text{threshold}}^q}\cdot \frac{q-1}{2}\cdot (|\mathbf{u}|^{2})^{\frac{q-1}{2} - 1}\cdot 2 \\ &= \frac{q-1}{|\mathbf{u}|^{2}}\cdot \beta(\mathbf{u}) \\ \end{align*}$$ Reimplemented from pism::IceBasalResistancePlasticLaw. Definition at line 174 of file basal_resistance.cc. References pism::IceBasalResistancePlasticLaw::m_plastic_regularize, m_q, m_sliding_scale_factor_reduces_tauc, m_u_threshold_factor, and pism::square().