AccessType Aglen albers_conical_equal_area_to_proj args_string average_water_column_pressure axis_type_from_string AxisType azimuthal_equidistant_to_proj backend_to_string bedrock_surface_temperature blatter_xy_exact blatter_xy_source blatter_xz_cfbc_base blatter_xz_cfbc_exact blatter_xz_cfbc_source blatter_xz_cfbc_surface blatter_xz_exact blatter_xz_halfar_exact blatter_xz_halfar_source blatter_xz_halfar_source_base blatter_xz_halfar_source_lateral blatter_xz_halfar_source_surface blatter_xz_source blatter_xz_source_bed blatter_xz_source_surface blatter_xz_vanderveen_beta blatter_xz_vanderveen_exact blatter_xz_vanderveen_source_lateral blatter_xz_vanderveen_source_surface blatter_xz_vanderveen_thickness Box c1 c2 calendar calendar_from_file cf_to_proj check_c_call check_consistency_epsg check_forcing_duration check_input check_petsc_call choose_backend clear_fftw_array clip combine common_flags compute_area compute_cell_areas compute_coordinates compute_corrective_velocity compute_grounded_cell_fraction compute_horizontal_grid_size compute_horizontal_spacing compute_interface_velocity compute_lat_bounds compute_latitude compute_lon_bounds compute_lon_lat compute_lon_lat_bounds compute_longitude compute_node_types compute_strain_heating_errors computeSurfaceVelocityErrors config_from_options ConfigSettingFlag contains_epsg context_from_options convert_vec convert_vec copy_fftw_array count_CFL_violations create_backend create_restriction criticalW diag_metadata DiagnosticList Direction dx_estimate dx_min dy_estimate dy_min effective_change end_time ends_with enthalpy_from_temperature_cold epsg_to_cf exactFG exactP exactP_list F F fftfreq filename_add_suffix find_json_value fletcher64 floating_ice_sheet_area_fraction_name funcP g generate_mound_topography generate_trough_topography get_ get_all_arrays get_all_values get_proj_parameters get_real_part get_shared_ get_time get_value getsb getW GlobalMax GlobalMax GlobalMax GlobalMin GlobalMin GlobalReduce GlobalReduce GlobalSum GlobalSum GlobalSum GlobalSum GlobalSum Grid_FromFile grid_name grid_subset grid_transpose grid_z grounded_area_fraction grounded_ice_sheet_area_fraction_name h0 handle_fatal_errors ice_area ice_area_floating ice_area_grounded ice_bottom_surface ice_flow_rate_across_grounding_line ice_volume ice_volume_not_displacing_seawater IceModelTerminationReason increment_date init_interpolation_indexes init_step initialconditionW InitializationType integration_weights integration_weights InterpolationType intersect_ab intersect_ac intersect_bc invalid is_increasing join join_impl k label_components_impl lambert_azimuthal_equal_area_to_proj lambert_conformal_conic_to_proj lambert_cylindrical_equal_area_to_proj land_ice_area_fraction_name lapse_rate_correction latitude_longitude_to_proj limit_advective_flux limit_diffusive_flux logger_from_options LoggerLevel LonLat m0 make_nonnegative_preserving MaskValue max_timestep_cfl_2d max_timestep_cfl_3d max_timestep_diffusivity member mercator_to_proj Metadata nc_type_to_pism_type netcdf_version NodeType operator* operator< operator== operator> orthographic_to_proj p3 p4 pack_json_array parse_date parse_epsg parse_integer parse_integer_list parse_number parse_number_list part_grid_threshold_thickness pism_is_valid_calendar_name pism_type_to_nc_type pism_yac_error_handler polar_stereographic_to_proj print_checksum print_config print_diagnostics print_diagnostics_json print_unused_parameters print_vector print_vector printf process_extra_shortcuts process_input_options process_ts_shortcuts psteady R1 reference_date reference_date_from_file remove_narrow_tongues replace_character report_range reportErrors reporting_max_timestep restrict_data rhoi rhow rotated_latitude_longitude_to_proj same sea_level_rise_potential secondInvariant_2D set_config_from_options set_flag_from_option set_integer_from_option set_join set_keyword_from_option set_no_model_strip set_no_model_yield_stress set_number_from_option set_parameter_from_options set_real_part set_split set_string_from_option set_value setInitStateF setup_level show_usage show_usage_check_req_opts SNESScalarProblem SNESVectorProblem special_parameter SperA split square start_time step step stereographic_to_proj string_is_false string_is_true string_strip string_to_backend subset_start_and_count TEMPORARY_STRING_LENGTH timestamp total_grounding_line_flux transverse_mercator_to_proj triangle_area ts_diag_metadata TSDiagnosticList UNOType unpack_json_array upwind username_prefix v0 validate_format_string vector_max vector_min version vertical_perspective_to_proj volume_flow_rate_from_land_to_water wall_clock_hours warn_about_missing weights_piecewise_constant weights_piecewise_linear Wr write write_mapping write_run_stats

secondInvariant_2D() static double pism::secondInvariant_2D ( const Vector2d &  U_x, const Vector2d &  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 45 of file FlowLaw.hh. References pism::Vector2d::u, and pism::Vector2d::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::SSAFDBase::compute_nuH_cfbc(), pism::stressbalance::SSAFDBase::compute_nuH_everywhere(), and pism::stressbalance::SSAFEM::PointwiseNuHAndBeta().