From f7b9f7baf531732ce75ef10196fd1e372a66616a Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Wed, 27 Oct 2021 14:20:37 +0000 Subject: [PATCH 1/8] Implementation of plastic potential --- cicecore/cicedynB/dynamics/ice_dyn_shared.F90 | 34 ++++++++++--------- cicecore/cicedynB/dynamics/ice_dyn_vp.F90 | 2 +- cicecore/cicedynB/general/ice_init.F90 | 32 +++++++++-------- 3 files changed, 37 insertions(+), 31 deletions(-) diff --git a/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 b/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 index 5e14d9686..78d1ef83a 100755 --- a/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 +++ b/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 @@ -63,9 +63,12 @@ module ice_dyn_shared real (kind=dbl_kind), public :: & revp , & ! 0 for classic EVP, 1 for revised EVP - e_ratio , & ! e = EVP ellipse aspect ratio - ecci , & ! 1/e^2 - dtei , & ! 1/dte, where dte is subcycling timestep (1/s) + e_yieldcurve, & ! VP aspect ratio of elliptical yield curve + e_plasticpot, & ! VP aspect ratio of elliptical plastic potential + epp2i , & ! 1/(e_plasticpot)^2 + e_factor , & ! (e_yieldcurve)^2/(e_plasticpot)^4 + ecci , & ! temporary for 1d evp + dtei , & +! 1/dte, where dte is subcycling timestep (1/s) ! dte2T , & ! dte/2T denom1 ! constants for stress equation @@ -220,7 +223,6 @@ subroutine set_evp_parameters (dt) !real (kind=dbl_kind) :: & !dte , & ! subcycling timestep for EVP dynamics, s - !ecc , & ! (ratio of major to minor ellipse axes)^2 !tdamp2 ! 2*(wave damping time scale T) character(len=*), parameter :: subname = '(set_evp_parameters)' @@ -230,10 +232,10 @@ subroutine set_evp_parameters (dt) !dtei = c1/dte ! 1/s dtei = real(ndte,kind=dbl_kind)/dt - ! major/minor axis length ratio, squared - !ecc = e_ratio**2 - !ecci = c1/ecc ! 1/ecc - ecci = c1/e_ratio**2 ! 1/ecc + ! variables for elliptical yield curve and plastic potential + epp2i = c1/e_plasticpot**2 + e_factor = e_yieldcurve**2 / e_plasticpot**4 + ecci = c1/e_yieldcurve**2 ! temporary for 1d evp ! constants for stress equation !tdamp2 = c2*eyc*dt ! s @@ -1352,10 +1354,10 @@ subroutine strain_rates (nx_block, ny_block, & - cxp(i,j)*uvel(i ,j-1) + dxt(i,j)*uvel(i ,j ) ! Delta (in the denominator of zeta, eta) - Deltane = sqrt(divune**2 + ecci*(tensionne**2 + shearne**2)) - Deltanw = sqrt(divunw**2 + ecci*(tensionnw**2 + shearnw**2)) - Deltasw = sqrt(divusw**2 + ecci*(tensionsw**2 + shearsw**2)) - Deltase = sqrt(divuse**2 + ecci*(tensionse**2 + shearse**2)) + Deltane = sqrt(divune**2 + e_factor*(tensionne**2 + shearne**2)) + Deltanw = sqrt(divunw**2 + e_factor*(tensionnw**2 + shearnw**2)) + Deltasw = sqrt(divusw**2 + e_factor*(tensionsw**2 + shearsw**2)) + Deltase = sqrt(divuse**2 + e_factor*(tensionse**2 + shearse**2)) end subroutine strain_rates @@ -1419,19 +1421,19 @@ subroutine viscous_coeffs_and_rep_pressure (strength, tinyarea, & zetax2ne = (c1+Ktens)*tmpcalcne ! northeast rep_prsne = (c1-Ktens)*tmpcalcne*Deltane - etax2ne = ecci*zetax2ne ! CHANGE FOR e_plasticpot + etax2ne = epp2i*zetax2ne zetax2nw = (c1+Ktens)*tmpcalcnw ! northwest rep_prsnw = (c1-Ktens)*tmpcalcnw*Deltanw - etax2nw = ecci*zetax2nw ! CHANGE FOR e_plasticpot + etax2nw = epp2i*zetax2nw zetax2sw = (c1+Ktens)*tmpcalcsw ! southwest rep_prssw = (c1-Ktens)*tmpcalcsw*Deltasw - etax2sw = ecci*zetax2sw ! CHANGE FOR e_plasticpot + etax2sw = epp2i*zetax2sw zetax2se = (c1+Ktens)*tmpcalcse ! southeast rep_prsse = (c1-Ktens)*tmpcalcse*Deltase - etax2se = ecci*zetax2se ! CHANGE FOR e_plasticpot + etax2se = epp2i*zetax2se ! else diff --git a/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 b/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 index 1a6c68548..c5ef50f67 100644 --- a/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 +++ b/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 @@ -46,7 +46,7 @@ module ice_dyn_vp use ice_domain, only: nblocks, distrb_info use ice_domain_size, only: max_blocks use ice_dyn_shared, only: dyn_prep1, dyn_prep2, dyn_finish, & - ecci, cosw, sinw, fcor_blk, uvel_init, vvel_init, & + cosw, sinw, fcor_blk, uvel_init, vvel_init, & seabed_stress_factor_LKD, seabed_stress_factor_prob, seabed_stress_method, & seabed_stress, Ktens, stack_velocity_field, unstack_velocity_field use ice_fileunits, only: nu_diag diff --git a/cicecore/cicedynB/general/ice_init.F90 b/cicecore/cicedynB/general/ice_init.F90 index 2e67af51c..b299ef77f 100644 --- a/cicecore/cicedynB/general/ice_init.F90 +++ b/cicecore/cicedynB/general/ice_init.F90 @@ -105,9 +105,10 @@ subroutine input_data use ice_dyn_shared, only: ndte, kdyn, revised_evp, yield_curve, & evp_algorithm, & seabed_stress, seabed_stress_method, & - k1, k2, alphab, threshold_hw, & - Ktens, e_ratio, coriolis, ssh_stress, & - kridge, brlx, arlx + k1, k2, alphab, threshold_hw, Ktens, & + e_yieldcurve, e_plasticpot, coriolis, & + ssh_stress, kridge, brlx, arlx + use ice_dyn_vp, only: maxits_nonlin, precond, dim_fgmres, dim_pgmres, maxits_fgmres, & maxits_pgmres, monitor_nonlin, monitor_fgmres, & monitor_pgmres, reltol_nonlin, reltol_fgmres, reltol_pgmres, & @@ -208,20 +209,20 @@ subroutine input_data namelist /dynamics_nml/ & kdyn, ndte, revised_evp, yield_curve, & - evp_algorithm, & + evp_algorithm, & brlx, arlx, ssh_stress, & advection, coriolis, kridge, ktransport, & kstrength, krdg_partic, krdg_redist, mu_rdg, & - e_ratio, Ktens, Cf, seabed_stress, & - k1, maxits_nonlin, precond, dim_fgmres, & + e_yieldcurve, e_plasticpot, Ktens, & + maxits_nonlin, precond, dim_fgmres, & dim_pgmres, maxits_fgmres, maxits_pgmres, monitor_nonlin, & monitor_fgmres, monitor_pgmres, reltol_nonlin, reltol_fgmres, & reltol_pgmres, algo_nonlin, dim_andacc, reltol_andacc, & damping_andacc, start_andacc, fpfunc_andacc, use_mean_vrel, & - ortho_type, & - k2, alphab, threshold_hw, & - seabed_stress_method, Pstar, Cstar - + ortho_type, seabed_stress, seabed_stress_method, & + k1, k2, alphab, threshold_hw, & + Cf, Pstar, Cstar + namelist /shortwave_nml/ & shortwave, albedo_type, & albicev, albicei, albsnowv, albsnowi, & @@ -367,7 +368,8 @@ subroutine input_data alphab = 20.0_dbl_kind ! alphab=Cb factor in Lemieux et al 2015 threshold_hw = 30.0_dbl_kind ! max water depth for grounding Ktens = 0.0_dbl_kind ! T=Ktens*P (tensile strength: see Konig and Holland, 2010) - e_ratio = 2.0_dbl_kind ! VP ellipse aspect ratio + e_yieldcurve = 2.0_dbl_kind ! VP aspect ratio of elliptical yield curve + e_plasticpot = 2.0_dbl_kind ! VP aspect ratio of elliptical plastic potential maxits_nonlin = 4 ! max nb of iteration for nonlinear solver precond = 'pgmres' ! preconditioner for fgmres: 'ident' (identity), 'diag' (diagonal), 'pgmres' (Jacobi-preconditioned GMRES) dim_fgmres = 50 ! size of fgmres Krylov subspace @@ -729,7 +731,8 @@ subroutine input_data call broadcast_scalar(alphab, master_task) call broadcast_scalar(threshold_hw, master_task) call broadcast_scalar(Ktens, master_task) - call broadcast_scalar(e_ratio, master_task) + call broadcast_scalar(e_yieldcurve, master_task) + call broadcast_scalar(e_plasticpot, master_task) call broadcast_scalar(advection, master_task) call broadcast_scalar(conserv_check, master_task) call broadcast_scalar(shortwave, master_task) @@ -1440,9 +1443,10 @@ subroutine input_data if (kdyn == 1 .or. kdyn == 3) then write(nu_diag,1030) ' yield_curve = ', trim(yield_curve) if (trim(yield_curve) == 'ellipse') & - write(nu_diag,1002) ' e_ratio = ', e_ratio, ' : aspect ratio of ellipse' + write(nu_diag,1002) ' e_yieldcurve = ', e_yieldcurve, ' : aspect ratio of yield curve' + write(nu_diag,1002) ' e_plasticpot = ', e_plasticpot, ' : aspect ratio of plastic potential' endif - + if (trim(coriolis) == 'latitude') then tmpstr2 = ' : latitude-dependent Coriolis parameter' elseif (trim(coriolis) == 'contant') then From 46c0d7ca98aaffdeaa79e3c87a08a13745709a43 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Wed, 27 Oct 2021 14:22:47 +0000 Subject: [PATCH 2/8] Modified ice_in --- configuration/scripts/ice_in | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/configuration/scripts/ice_in b/configuration/scripts/ice_in index 443ff1cbb..bb44663eb 100644 --- a/configuration/scripts/ice_in +++ b/configuration/scripts/ice_in @@ -141,7 +141,8 @@ Cstar = 20 Cf = 17. Ktens = 0. - e_ratio = 2. + e_yieldcurve = 2. + e_plasticpot = 2. seabed_stress = .false. seabed_stress_method = 'LKD' k1 = 7.5 From 07d6989a422e2eec3e0dd80abf1bf7bc42fbe64a Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Wed, 27 Oct 2021 14:32:32 +0000 Subject: [PATCH 3/8] Corrected minor issue for variable declaration --- cicecore/cicedynB/dynamics/ice_dyn_shared.F90 | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 b/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 index 78d1ef83a..23251b2d1 100755 --- a/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 +++ b/cicecore/cicedynB/dynamics/ice_dyn_shared.F90 @@ -68,7 +68,7 @@ module ice_dyn_shared epp2i , & ! 1/(e_plasticpot)^2 e_factor , & ! (e_yieldcurve)^2/(e_plasticpot)^4 ecci , & ! temporary for 1d evp - dtei , & +! 1/dte, where dte is subcycling timestep (1/s) + dtei , & ! 1/dte, where dte is subcycling timestep (1/s) ! dte2T , & ! dte/2T denom1 ! constants for stress equation From 58ee4cd122d2f900663f389ad3c264dce5daec94 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Wed, 27 Oct 2021 23:20:30 +0000 Subject: [PATCH 4/8] Modifs to the doc for plastic potential --- configuration/scripts/options/set_nml.alt03 | 2 +- doc/source/master_list.bib | 11 +++++ doc/source/science_guide/sg_dynamics.rst | 54 ++++++++++++--------- 3 files changed, 42 insertions(+), 25 deletions(-) diff --git a/configuration/scripts/options/set_nml.alt03 b/configuration/scripts/options/set_nml.alt03 index 255d77261..98e794735 100644 --- a/configuration/scripts/options/set_nml.alt03 +++ b/configuration/scripts/options/set_nml.alt03 @@ -19,7 +19,7 @@ sw_dtemp = 0.02d0 tfrz_option = 'linear_salt' revised_evp = .false. Ktens = 0. -e_ratio = 2. +e_yieldcurve = 2. seabed_stress = .true. use_bathymetry = .true. l_mpond_fresh = .true. diff --git a/doc/source/master_list.bib b/doc/source/master_list.bib index 7c2a45a35..55d27a0fa 100644 --- a/doc/source/master_list.bib +++ b/doc/source/master_list.bib @@ -979,6 +979,17 @@ @article{Roach18 volume = {123}, year = {2018} } + +@Article{Ringeisen21 + author = "D. Ringeisen and L.B. Tremblay and M. Losch", + title = "{Non-normal flow rules affect fracture angles in sea ice viscous-plastic rheologies}", + journal = TC, + year = {2021}, + volume = {15}, + pages = {2873-2888}, + url = {https://doi.org/10.5194/tc-15-2873-2021} +} + @Article{Tsujino18, author = "H. Tsujino and S. Urakawa and R.J. Small and W.M. Kim and S.G. Yeager and et al.", title = "{JRA‐55 based surface dataset for driving ocean–sea‐ice models (JRA55‐do)}", diff --git a/doc/source/science_guide/sg_dynamics.rst b/doc/source/science_guide/sg_dynamics.rst index 6d7d32976..f2b846512 100644 --- a/doc/source/science_guide/sg_dynamics.rst +++ b/doc/source/science_guide/sg_dynamics.rst @@ -350,9 +350,9 @@ Following again the LKD method, the seabed stress coefficients are finally expre .. _internal-stress: -*************** -Internal stress -*************** +******************************** +Internal stress and strain rates +******************************** For convenience we formulate the stress tensor :math:`\bf \sigma` in terms of :math:`\sigma_1=\sigma_{11}+\sigma_{22}`, @@ -378,15 +378,6 @@ CICE can output the internal ice pressure which is an important field to support The internal ice pressure (``sigP``) is the average of the normal stresses multiplied by :math:`-1` and is therefore simply equal to :math:`-\sigma_1/2`. -Following the approach of :cite:`Konig10` (see also :cite:`Lemieux16`), the -elliptical yield curve can be modified such that the ice has isotropic tensile strength. -The tensile strength :math:`T_p` is expressed as a fraction of the ice strength :math:`P`, that is :math:`T_p=k_t P` -where :math:`k_t` should be set to a value between 0 and 1 (this can -be changed at runtime with the namelist parameter ``Ktens``). The ice -strength :math:`P` is a function of the ice thickness distribution as -described in the `Icepack -Documentation `_. - .. _stress-vp: Viscous-Plastic @@ -395,28 +386,43 @@ Viscous-Plastic The VP constitutive law is given by .. math:: - \sigma_{ij} = 2 \eta \dot{\epsilon}_{ij} + (\zeta - \eta) D_D - P_R(1 - k_t)\frac{\delta_{ij}}{2} + \sigma_{ij} = 2 \eta \dot{\epsilon}_{ij} + (\zeta - \eta) D_D - P_R\frac{\delta_{ij}}{2} :label: vp-const -where :math:`\eta` and :math:`\zeta` are the bulk and shear viscosities. +where :math:`\eta` and :math:`\zeta` are the bulk and shear viscosities and +:math:`P_R` is a “replacement pressure” (see :cite:`Geiger98`, for example), +which serves to prevent residual ice motion due to spatial +variations of the ice strength :math:`P` when the strain rates are exactly zero. + An elliptical yield curve is used, with the viscosities given by .. math:: \zeta = {P(1+k_t)\over 2\Delta}, .. math:: - \eta = e^{-2} \zeta, + \eta = e_g^{-2} \zeta, where .. math:: - \Delta = \left[D_D^2 + {1\over e^2}\left(D_T^2 + D_S^2\right)\right]^{1/2} + \Delta = \left[D_D^2 + {e_f^2\over e_g^4}\left(D_T^2 + D_S^2\right)\right]^{1/2} + +and :math:`P` is the ice strength. :math:`P` is a function of the ice thickness distribution as +described in the `Icepack Documentation `_. + +Two modifications to the standard VP rheology of :cite:`Hibler79` are available. +First, following the approach of :cite:`Konig10` (see also :cite:`Lemieux16`), the +elliptical yield curve can be modified such that the ice has isotropic tensile strength. +The tensile strength :math:`T_p` is expressed as a fraction of :math:`P`, that is :math:`T_p=k_t P` +where :math:`k_t` should be set to a value between 0 and 1 (this can +be changed at runtime with the namelist parameter ``Ktens``). -and :math:`P_R` is a “replacement pressure” (see :cite:`Geiger98`, for -example), which serves to prevent residual ice motion due to spatial -variations of :math:`P` when the rates of strain are exactly zero. +Second, while :math:`e_f` is the ratio of the major and minor axes of the elliptical yield curve, the parameter +:math:`e_g` characterizes the plastic potential, i.e. another ellipse that decouples the flow rule from the +yield curve (:cite:`Ringeisen21`). :math:`e_f` and :math:`e_g` are respectively called ``e_yieldcurve`` and ``e_plasticpot`` in the code and +can be set in the namelist. -The parameter :math:`e` is the ratio of the major and minor axes of the elliptical yield curve, also called the ellipse aspect ratio. It can be changed using the namelist parameter ``e_ratio``. +By default, the namelist parameters are set to :math:`e_f=e_g=2` and :math:`k_t=0` which correspond to the standard VP rheology. .. _stress-evp: @@ -428,7 +434,7 @@ regularized version of the VP constitutive law :eq:`vp-const`. The constitutive .. math:: {1\over E}{\partial\sigma_1\over\partial t} + {\sigma_1\over 2\zeta} - + {P_R(1-k_t)\over 2\zeta} = D_D, \\ + + {P_R\over 2\zeta} = D_D, \\ :label: sig1 .. math:: @@ -455,7 +461,7 @@ parameter less than one. Including the modification proposed by :cite:`Bouillon1 .. math:: \begin{aligned} {\partial\sigma_1\over\partial t} + {\sigma_1\over 2T} - + {P_R(1-k_t)\over 2T} &=& {\zeta \over T} D_D, \\ + + {P_R\over 2T} &=& {\zeta \over T} D_D, \\ {\partial\sigma_2\over\partial t} + {\sigma_2\over 2T} &=& {\eta \over T} D_T,\\ {\partial\sigma_{12}\over\partial t} + {\sigma_{12}\over 2T} &=& @@ -466,7 +472,7 @@ Once discretized in time, these last three equations are written as .. math:: \begin{aligned} {(\sigma_1^{k+1}-\sigma_1^{k})\over\Delta t_e} + {\sigma_1^{k+1}\over 2T} - + {P_R^k(1-k_t)\over 2T} &=& {\zeta^k\over T} D_D^k, \\ + + {P_R^k\over 2T} &=& {\zeta^k\over T} D_D^k, \\ {(\sigma_2^{k+1}-\sigma_2^{k})\over\Delta t_e} + {\sigma_2^{k+1}\over 2T} &=& {\eta^k \over T} D_T^k,\\ {(\sigma_{12}^{k+1}-\sigma_{12}^{k})\over\Delta t_e} + {\sigma_{12}^{k+1}\over 2T} &=& @@ -720,7 +726,7 @@ Introducing another numerical parameter :math:`\alpha=2T \Delta t_e ^{-1}` :cite .. math:: \begin{aligned} {\alpha (\sigma_1^{k+1}-\sigma_1^{k})} + {\sigma_1^{k}} - + {P_R^k(1-k_t)} &=& 2 \zeta^k D_D^k, \\ + + {P_R^k} &=& 2 \zeta^k D_D^k, \\ {\alpha (\sigma_2^{k+1}-\sigma_2^{k})} + {\sigma_2^{k}} &=& 2 \eta^k D_T^k,\\ {\alpha (\sigma_{12}^{k+1}-\sigma_{12}^{k})} + {\sigma_{12}^{k}} &=& \eta^k D_S^k,\end{aligned} From 8fcc93ef99667d32e8891e79c8beaa0e34bad100 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Wed, 27 Oct 2021 23:37:57 +0000 Subject: [PATCH 5/8] Minor modifs to the doc --- cicecore/cicedynB/dynamics/ice_dyn_vp.F90 | 3 +++ doc/source/cice_index.rst | 4 +++- doc/source/science_guide/sg_dynamics.rst | 4 ++-- 3 files changed, 8 insertions(+), 3 deletions(-) diff --git a/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 b/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 index c5ef50f67..2f1285084 100644 --- a/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 +++ b/cicecore/cicedynB/dynamics/ice_dyn_vp.F90 @@ -1320,6 +1320,9 @@ end subroutine calc_zeta_dPr ! Computes the VP stresses (as diagnostic) +! Lemieux, J.-F., and Dupont, F. (2020), On the calculation of normalized +! viscous-plastic sea ice stresses, Geosci. Model Dev., 13, 1763–1769, + subroutine stress_vp (nx_block , ny_block , & icellt , & indxti , indxtj , & diff --git a/doc/source/cice_index.rst b/doc/source/cice_index.rst index 12bc8d32e..85acbece3 100644 --- a/doc/source/cice_index.rst +++ b/doc/source/cice_index.rst @@ -205,7 +205,9 @@ either Celsius or Kelvin units). "etax2", "2 x eta (shear viscous coefficient)", "kg/s" "evap", "evaporative water flux", "kg/m\ :math:`^2`/s" "ew_boundary_type", "type of east-west boundary condition", "" - "eyc", "coefficient for calculating the parameter E, 0\ :math:`<` eyc :math:`<`\ 1", "0.36" + "eyc", "coefficient for calculating the parameter E, 0\ :math:`<` eyc :math:`<`\ 1", "0.36" + "e_yieldcurve", "yield curve minor/major axis ratio", "2" + "e_plasticpot", "plastic potential minor/major axis ratio", "2" "**F**", "", "" "faero_atm", "aerosol deposition rate", "kg/m\ :math:`^2`/s" "faero_ocn", "aerosol flux to the ocean", "kg/m\ :math:`^2`/s" diff --git a/doc/source/science_guide/sg_dynamics.rst b/doc/source/science_guide/sg_dynamics.rst index f2b846512..8d2e8e0bc 100644 --- a/doc/source/science_guide/sg_dynamics.rst +++ b/doc/source/science_guide/sg_dynamics.rst @@ -405,9 +405,9 @@ An elliptical yield curve is used, with the viscosities given by where .. math:: - \Delta = \left[D_D^2 + {e_f^2\over e_g^4}\left(D_T^2 + D_S^2\right)\right]^{1/2} + \Delta = \left[D_D^2 + {e_f^2\over e_g^4}\left(D_T^2 + D_S^2\right)\right]^{1/2}. -and :math:`P` is the ice strength. :math:`P` is a function of the ice thickness distribution as +The ice strength :math:`P` is a function of the ice thickness distribution as described in the `Icepack Documentation `_. Two modifications to the standard VP rheology of :cite:`Hibler79` are available. From 91643ae9c4cbfe7e5b6f84b754fd73a7fc3c0a88 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Thu, 28 Oct 2021 14:38:47 +0000 Subject: [PATCH 6/8] More details in doc about the plastic potential --- doc/source/science_guide/sg_dynamics.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/source/science_guide/sg_dynamics.rst b/doc/source/science_guide/sg_dynamics.rst index 8d2e8e0bc..13f9dc163 100644 --- a/doc/source/science_guide/sg_dynamics.rst +++ b/doc/source/science_guide/sg_dynamics.rst @@ -420,7 +420,7 @@ be changed at runtime with the namelist parameter ``Ktens``). Second, while :math:`e_f` is the ratio of the major and minor axes of the elliptical yield curve, the parameter :math:`e_g` characterizes the plastic potential, i.e. another ellipse that decouples the flow rule from the yield curve (:cite:`Ringeisen21`). :math:`e_f` and :math:`e_g` are respectively called ``e_yieldcurve`` and ``e_plasticpot`` in the code and -can be set in the namelist. +can be set in the namelist. The plastic potential can lead to more realistic fracture angles between linear kinematic features. :cite:`Ringeisen21` suggest to set :math:`e_f` to a value larger than 1 and to have :math:`e_g < e_f`. By default, the namelist parameters are set to :math:`e_f=e_g=2` and :math:`k_t=0` which correspond to the standard VP rheology. From c1b0297bf426139af872bf847ead51b7ae4dcef6 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Thu, 28 Oct 2021 16:10:27 +0000 Subject: [PATCH 7/8] Added journal TC=the cryosphere in master_list.bib --- doc/source/master_list.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/source/master_list.bib b/doc/source/master_list.bib index 55d27a0fa..e4afa0c46 100644 --- a/doc/source/master_list.bib +++ b/doc/source/master_list.bib @@ -60,7 +60,7 @@ @string{CRST @string{IJHPCA={Int. J High Perform. Comput. Appl}} @string{PTRSA={Philos. Trans. Royal Soc. A}} @string{SIAMJCP={SIAM J. Sci. Comput.}} - +@string{TC={The Cryosphere}} % ********************************************** From 6b2abeb8f628ae578ab45dacaddbb42879244519 Mon Sep 17 00:00:00 2001 From: Jean-Francois Lemieux Date: Sun, 31 Oct 2021 19:42:01 +0000 Subject: [PATCH 8/8] Modified the doc following comments from Elizabeth and Philippe --- doc/source/science_guide/sg_dynamics.rst | 152 +++++++++++------------ 1 file changed, 76 insertions(+), 76 deletions(-) diff --git a/doc/source/science_guide/sg_dynamics.rst b/doc/source/science_guide/sg_dynamics.rst index 13f9dc163..9c529b8ec 100644 --- a/doc/source/science_guide/sg_dynamics.rst +++ b/doc/source/science_guide/sg_dynamics.rst @@ -351,7 +351,7 @@ Following again the LKD method, the seabed stress coefficients are finally expre .. _internal-stress: ******************************** -Internal stress and strain rates +Internal stress ******************************** For convenience we formulate the stress tensor :math:`\bf \sigma` in @@ -413,7 +413,7 @@ described in the `Icepack Documentation