advective_velocity basal_frictional_heating compute_vertical_velocity compute_volumetric_strain_heating define_model_state_impl diagnostics_impl diffusive_flux init m_cfl_2d m_cfl_3d m_modifier m_shallow_stress_balance m_strain_heating m_w max_diffusivity max_timestep_cfl_2d max_timestep_cfl_3d modifier shallow stdout_report StressBalance ts_diagnostics_impl update velocity_u velocity_v velocity_w volumetric_strain_heating write_model_state_impl ~StressBalance

compute_vertical_velocity() void pism::stressbalance::StressBalance::compute_vertical_velocity ( const array::CellType1 &  mask, const array::Array3D &  u, const array::Array3D &  v, const array::Scalar *  basal_melt_rate, array::Array3D &  result  ) protectedvirtual Compute vertical velocity using incompressibility of the ice. The vertical velocity \(w(x,y,z,t)\) is the velocity relative to the location of the base of the ice column. That is, the vertical velocity computed here is identified as \(\tilde w(x,y,s,t)\) in the page []vertchange. Thus \(w<0\) here means that that that part of the ice is getting closer to the base of the ice, and so on. The slope of the bed (i.e. relative to the geoid) and/or the motion of the bed (i.e. from bed deformation) do not affect the vertical velocity. In fact the following statement is exactly true if the basal melt rate is zero: the vertical velocity at a point in the ice is positive (negative) if and only if the average horizontal divergence of the horizontal velocity, in the portion of the ice column below that point, is negative (positive). In particular, because \(z=0\) is the location of the base of the ice always, the only way to have \(w(x,y,0,t) \ne 0\) is to have a basal melt rate. Incompressibility itself says \[ \nabla\cdot\mathbf{U} + \frac{\partial w}{\partial z} = 0. \] This is immediately equivalent to the integral \[ w(x,y,z,t) = - \int_{b(x,y,t)}^{z} \nabla\cdot\mathbf{U}\,d\zeta + w_b(x,y,t). \] Here the value \(w_b(x,y,t)\) is either zero or the negative of the basal melt rate according to the value of the flag geometry.update.use_basal_melt_rate. The vertical integral is computed by the trapezoid rule. Definition at line 277 of file StressBalance.cc. References pism::array::Array::add(), pism::array::Array3D::get_column(), pism::array::CellType::ice_free(), pism::array::CellType::icy(), pism::k, pism::Component::m_config, and pism::Component::m_grid. Referenced by update().