EC effective_viscosity effective_viscosity exponent flow flow_impl flow_n flow_n_impl FlowLaw hardness hardness_impl hardness_n hardness_n_impl m_A_cold m_A_warm m_beta_CC_grad m_crit_temp m_EC m_hardness_power m_ideal_gas_constant m_melting_point_temp m_n m_name m_Q_cold m_Q_warm m_rho m_schoofReg m_standard_gravity m_viscosity_power name softness softness_impl softness_paterson_budd ~FlowLaw

effective_viscosity() [1/2] void pism::rheology::FlowLaw::effective_viscosity ( double  hardness, double  gamma, double *  nu, double *  dnu  ) const Computes the regularized effective viscosity and its derivative with respect to the second invariant \( \gamma \). \begin{align*} \nu &= \frac{1}{2} B \left( \epsilon + \gamma \right)^{(1-n)/(2n)},\\ \diff{\nu}{\gamma} &= \frac{1}{2} B \cdot \frac{1-n}{2n} \cdot \left(\epsilon + \gamma \right)^{(1-n)/(2n) - 1}, \\ &= \frac{1-n}{2n} \cdot \frac{1}{2} B \left( \epsilon + \gamma \right)^{(1-n)/(2n)} \cdot \frac{1}{\epsilon + \gamma}, \\ &= \frac{1-n}{2n} \cdot \frac{\nu}{\epsilon + \gamma}. \end{align*} Here \( \gamma \) is the second invariant \begin{align*} \gamma &= \frac{1}{2} D_{ij} D_{ij}\\ &= \frac{1}{2}\, ((u_x)^2 + (v_y)^2 + (u_x + v_y)^2 + \frac{1}{2}\, (u_y + v_x)^2) \\ \end{align*} and \[ D_{ij}(\mathbf{u}) = \frac{1}{2}\left(\diff{u_{i}}{x_{j}} + \diff{u_{j}}{x_{i}}\right). \] Either one of nu and dnu can be NULL if the corresponding output is not needed. Parameters [in] B ice hardness [in] gamma the second invariant [out] nu effective viscosity [out] dnu derivative of \( \nu \) with respect to \( \gamma \) Definition at line 162 of file FlowLaw.cc. References hardness(), and m_schoofReg. Referenced by pism::stressbalance::compute_2D_stresses(), and pism::diagnostics::IceViscosity::compute_impl().