PISM, A Parallel Ice Sheet Model  stable v2.0.4 committed by Constantine Khrulev on 2022-05-25 12:02:27 -0800

◆ secondInvariant_2D()

static double pism::secondInvariant_2D ( const Vector2 U_x,
const Vector2 U_y 
)
inlinestatic

This uses the definition of squared second invariant from Hutter and several others, namely the output is \( D^2 = \frac 1 2 D_{ij} D_{ij} \) where incompressibility is used to compute \( D_{zz}. \)

This is the approximation of the full second invariant corresponding to the shallow shelf approximation. In particular, we assume that \( u \) and \( v \) are depth-independent ( \( u_z = v_z = 0 \)) and neglect horizontal derivatives of the vertical velocity ( \( w_x = w_y = 0 \)).

Definition at line 44 of file FlowLaw.hh.

References pism::Vector2::u, and pism::Vector2::v.

Referenced by pism::inverse::IP_SSAHardavForwardProblem::apply_jacobian_design(), pism::inverse::IP_SSAHardavForwardProblem::apply_jacobian_design_transpose(), pism::stressbalance::compute_2D_stresses(), pism::stressbalance::SSAFD::compute_nuH_staggered(), pism::stressbalance::SSAFD::compute_nuH_staggered_cfbc(), and pism::stressbalance::SSAFEM::PointwiseNuHAndBeta().