!!****f* HYCOM_2.1.03/EVP_MPI/evp_stress !! !! NAME !! stress !! !! SYNOPSIS !! !! !! !! DESCRIPTION !! Computes strain rates and internal stress components. !! Computes the rates of strain and internal stress components for !! each of the four corners on each T-grid cell !! !! !! AUTHOR !! Elizabeth C. Hunke, Fluid Dynamics Group, Los Alamos National Laboratory !! !! HISTORY !! Oct 2006 - Modified to use HYCOM tiling logic - Knut Liseter !! 12.03.2007 - Added OMP directives !! 28.07.2009 - Corrected a few bugs and cleaned the code - Dany Dumont !! !! INPUT !! ksub -- Subcycling time step !! SIDE EFFECTS !! Sets up the following variables for evp_stepu !! stressm_[1-4] !! stressp_[1-4] !! stress12_[1-4] !! Keeps the following variables for diagnostics and mechanical redist !! Divu !! Delta !! shear !! Because a grid difference is involved, the effective margin is !! reduced by one !! !! SOURCE !! subroutine evp_stress_miz(ksub) use mod_evp #if defined(ICE_DYN_DIAG) use mod_common_ice, only : MIZ_MASK,strainI,strainII #endif use mod_common_ice, only : MIZ_MASK implicit none integer, intent(in) :: ksub ! subcycling step integer :: i, j real :: & divune, divunw, divuse, divusw ! divergence &, tensionne, tensionnw, tensionse, tensionsw ! tension &, shearne, shearnw, shearse, shearsw ! shearing &, msq_tension,msq_shear,divu_mean ! mean square tension, shear; mean of divu &, Deltane, Deltanw, Deltase, Deltasw ! Delta &, c0ne, c0nw, c0se, c0sw ! useful combinations &, c1ne, c1nw, c1se, c1sw &, detne, detnw, detse, detsw &, K2ne, K2nw, K2se, K2sw &, K3ne, K3nw, K3se, K3sw &, vdne, vdnw, vdse, vdsw &, etane, etanw, etase, etasw &, zetane, zetanw, zetase, zetasw &, prssne, prssnw, prssse, prsssw %, Eyoung, fac1, fac2, fac, pi, gamp, sep, hfloe &, maxstressm, maxstressp,maxstress12 &, minstressm, minstressp,minstress12 &, minvpD, maxvpD, cice, minvp integer :: & ij ! loop index, combination of i and j loops logical, parameter :: diag=.true. c --- From the collisional rheology model of Shen et al. (1987) real, parameter :: e=0.1 ! restitution coefficient real, parameter :: diam=30. ! diameter of floes real, parameter :: C0=1.1 ! max compactness of hexagonal packing real, parameter :: K1=(1-e**2)*0.5 ! factor fo ert. velocity assumption real, parameter :: rhoi=930. ! density of sea ice real, parameter :: cs=0.89 ! cutoff concentration to turn on MIZ real, parameter :: hmin=1.0 ! minimum ice thickness for VP at c=1 real, parameter :: hmax=2.0 ! maximum MIZ thickness at any concentration c --- MIZ viscosity ++ real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: & mizzeta &, mizeta &, mizprss &, mizvd logical :: USE_EVP!!criteria for EVP/MIZ stresses pi = 4.d0*atan(1.d0) maxstressm = -1e14 maxstressp = -1e14 maxstress12 = -1e14 maxvpD = -1e14 minstressm = 1e14 minstressp = 1e14 minstress12 = 1e14 minvpD = 1e14 !$OMP PARALLEL DO PRIVATE(j,i, !$OMP& divune, divunw, divusw, divuse, !$OMP& tensionne, tensionnw,tensionsw,tensionse, !$OMP& shearne, shearnw, shearsw, shearse, !$OMP& Deltane, Deltanw, Deltasw, Deltase, !$OMP& c0ne, c0nw, c0sw, c0se, !$OMP& c1ne, c1nw, c1sw, c1se, !$OMP& detne, detnw, detsw, detse, !$OMP& K2ne, K2nw, K2sw, K2se, !$OMP& K3ne, K3nw, K3sw, K3se, !$OMP& vdne, vdnw, vdse, vdsw, !$OMP& etane, etanw, etase, etasw, !$OMP& zetane, zetanw, zetase, zetasw, !$OMP& prssne, prssnw, prssse, prsssw, !$OMP& fac , dfloe, Eyoung, fac1, fac2,cice) !$OMP& SCHEDULE(STATIC,jblk) MIZ_MASK = 0.0!!test variable stored in mod_common_ice.F msq_tension = 0.0 msq_shear = 0.0 divu_mean = 0.0 do j=1-imargin,jj+imargin do i=1-imargin,ii+imargin if (icetmask(i,j)) then !----------------------------------------------------------------- ! strain rates ! NOTE these are actually strain rates * area (m^2/s) !----------------------------------------------------------------- ! divergence = e_11 + e_22 divune = cyp(i,j)*uvel(i ,j ) - dyt(i,j)*uvel(i-1,j ) & + cxp(i,j)*vvel(i ,j ) - dxt(i,j)*vvel(i ,j-1) divunw = cym(i,j)*uvel(i-1,j ) + dyt(i,j)*uvel(i ,j ) & + cxp(i,j)*vvel(i-1,j ) - dxt(i,j)*vvel(i-1,j-1) divusw = cym(i,j)*uvel(i-1,j-1) + dyt(i,j)*uvel(i ,j-1) & + cxm(i,j)*vvel(i-1,j-1) + dxt(i,j)*vvel(i-1,j ) divuse = cyp(i,j)*uvel(i ,j-1) - dyt(i,j)*uvel(i-1,j-1) & + cxm(i,j)*vvel(i ,j-1) + dxt(i,j)*vvel(i ,j ) ! tension strain rate = e_11 - e_22 tensionne = -cym(i,j)*uvel(i ,j ) - dyt(i,j)*uvel(i-1,j ) & + cxm(i,j)*vvel(i ,j ) + dxt(i,j)*vvel(i ,j-1) tensionnw = -cyp(i,j)*uvel(i-1,j ) + dyt(i,j)*uvel(i ,j ) & + cxm(i,j)*vvel(i-1,j ) + dxt(i,j)*vvel(i-1,j-1) tensionsw = -cyp(i,j)*uvel(i-1,j-1) + dyt(i,j)*uvel(i ,j-1) & + cxp(i,j)*vvel(i-1,j-1) - dxt(i,j)*vvel(i-1,j ) tensionse = -cym(i,j)*uvel(i ,j-1) - dyt(i,j)*uvel(i-1,j-1) & + cxp(i,j)*vvel(i ,j-1) - dxt(i,j)*vvel(i ,j ) ! shearing strain rate = 2*e_12 shearne = -cym(i,j)*vvel(i ,j ) - dyt(i,j)*vvel(i-1,j ) & - cxm(i,j)*uvel(i ,j ) - dxt(i,j)*uvel(i ,j-1) shearnw = -cyp(i,j)*vvel(i-1,j ) + dyt(i,j)*vvel(i ,j ) & - cxm(i,j)*uvel(i-1,j ) - dxt(i,j)*uvel(i-1,j-1) shearsw = -cyp(i,j)*vvel(i-1,j-1) + dyt(i,j)*vvel(i ,j-1) & - cxp(i,j)*uvel(i-1,j-1) + dxt(i,j)*uvel(i-1,j ) shearse = -cym(i,j)*vvel(i ,j-1) - dyt(i,j)*vvel(i-1,j-1) & - cxp(i,j)*uvel(i ,j-1) + dxt(i,j)*uvel(i ,j ) ! Define and store strain rate invariants for diagnostics #if defined(ICE_DYN_DIAG) !!TW change: 20140307 !!averaging of corners was done weirdly if (ksub.eq.ndte) then !! strainI(i,j) = 0.5*0.25*tarear(i,j)*(divune + divunw !! & + divuse + divusw) !! strainII(i,j) = 0.5*0.25*tarear(i,j)*sqrt( !! & (tensionne + tensionnw + tensionse + tensionsw)**2 !! & + ( shearne + shearnw + shearse + shearsw)**2) divu_mean = .25*(divune + divunw & + divuse + divusw) msq_tension = .25*(tensionne**2+tensionnw**2 & +tensionse**2+tensionsw**2); msq_shear = .25*(shearne**2+shearnw**2 & +shearse**2+shearsw**2); !!principal strains are strainI +/- strainII !!NB tension=e11-e22, shear=2*e12 strainI(i,j) = 0.5*tarear(i,j)*divu_mean strainII(i,j) = 0.5*tarear(i,j)*sqrt(msq_tension+msq_shear) endif #endif ! Ice concentration cice = max(aice(i,j),0.01) ! always > 0.01 hfloe = max(vice(i,j)/cice,0.10) ! always > 0.10 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!Define when NOT to use MIZ rheology ! VERSION 0 : Unstable ! USE_EVP = (aice(i,j).gt.cs) ! VERSION 1 : Stable but not realistic enough ! USE_EVP = (cice.gt.cs .or. hfloe.gt.hmax) ! VERSION 2 : Based on a waves-in-ice model. To be tested. USE_EVP = (hfloe .gt. (-1*hmin+((1-cice)*(hmax-hmin)/(1-cs)))) USE_EVP = (USE_EVP.or.(hfloe .gt. hmax)) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!Normal EVP stress if (USE_EVP) then ! Viscous-plastic regime computed with the EVP scheme ! 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)) Deltase = sqrt(divuse**2 + ecci*(tensionse**2 + shearse**2)) Deltasw = sqrt(divusw**2 + ecci*(tensionsw**2 + shearsw**2)) if (evp_damping) then ! enforce damping criterion c0ne=min(prss(i,j)/max(Deltane,4.*tinyarea(i,j)),rcon_evp(i,j)) c0nw=min(prss(i,j)/max(Deltanw,4.*tinyarea(i,j)),rcon_evp(i,j)) c0se=min(prss(i,j)/max(Deltase,4.*tinyarea(i,j)),rcon_evp(i,j)) c0sw=min(prss(i,j)/max(Deltasw,4.*tinyarea(i,j)),rcon_evp(i,j)) prs_sig(i,j) = prss(i,j)*Deltane/max(Deltane,4.*tinyarea(i,j)) ! ne else ! original version c0ne = prss(i,j)/max(Deltane,tinyarea(i,j)) c0nw = prss(i,j)/max(Deltanw,tinyarea(i,j)) c0se = prss(i,j)/max(Deltase,tinyarea(i,j)) c0sw = prss(i,j)/max(Deltasw,tinyarea(i,j)) prs_sig(i,j) = c0ne*Deltane ! northeast endif c1ne = c0ne*dte2T c1nw = c0nw*dte2T c1sw = c0sw*dte2T c1se = c0se*dte2T !----------------------------------------------------------------- ! the stresses ! kg/s^2 ! (1) northeast, (2) northwest, (3) southwest, (4) southeast !----------------------------------------------------------------- stressp_1(i,j) = (stressp_1(i,j) + c1ne*(divune - Deltane))*denom stressp_2(i,j) = (stressp_2(i,j) + c1nw*(divunw - Deltanw))*denom stressp_3(i,j) = (stressp_3(i,j) + c1sw*(divusw - Deltasw))*denom stressp_4(i,j) = (stressp_4(i,j) + c1se*(divuse - Deltase))*denom ! modified EVP as in Bouillon et al. OM 2013. stressm_1(i,j) = (stressm_1(i,j) + c1ne*ecci*tensionne)*denom stressm_2(i,j) = (stressm_2(i,j) + c1nw*ecci*tensionnw)*denom stressm_3(i,j) = (stressm_3(i,j) + c1sw*ecci*tensionsw)*denom stressm_4(i,j) = (stressm_4(i,j) + c1se*ecci*tensionse)*denom stress12_1(i,j) = (stress12_1(i,j) + c1ne*ecci*shearne*.5)*denom stress12_2(i,j) = (stress12_2(i,j) + c1nw*ecci*shearnw*.5)*denom stress12_3(i,j) = (stress12_3(i,j) + c1sw*ecci*shearsw*.5)*denom stress12_4(i,j) = (stress12_4(i,j) + c1se*ecci*shearse*.5)*denom else !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Collisional regime computed following Shen et al. (1987) MIZ_MASK(i,j) = 1.0!!test variable stored in mod_common_ice.F ! Convert strain rates units from m^2/s to 1/s ! (breaks curvilinear factors, ok for uniform grids) divune = divune*uarear(i,j) divunw = divunw*uarear(i,j) divusw = divusw*uarear(i,j) divuse = divuse*uarear(i,j) tensionne = tensionne*uarear(i,j) tensionnw = tensionnw*uarear(i,j) tensionsw = tensionsw*uarear(i,j) tensionse = tensionse*uarear(i,j) shearne = shearne*uarear(i,j) shearnw = shearnw*uarear(i,j) shearsw = shearsw*uarear(i,j) shearse = shearse*uarear(i,j) ! Used in the collisional rheology ! 1/s^2 !!det=e_11*e_22-e_12^2, so these should be minus signs !![TW 20140317] !!detne = 0.25*(divune**2+tensionne**2+shearne**2) !!detnw = 0.25*(divunw**2+tensionnw**2+shearnw**2) !!detne = 0.25*(divusw**2+tensionsw**2+shearsw**2)!NB should also be sw on LHS !!detne = 0.25*(divuse**2+tensionse**2+shearse**2) detne = 0.25*(divune**2-tensionne**2-shearne**2) detnw = 0.25*(divunw**2-tensionnw**2-shearnw**2) detsw = 0.25*(divusw**2-tensionsw**2-shearsw**2) detne = 0.25*(divuse**2-tensionse**2-shearse**2) ! K1, K2 and K3 are needed when you run the model without advecting ! the perturbation velocity. To set up perturbation velocity, ! you need a source (e.g. a wave parameterization). ! K2 ! 1/s fac = 4*sqrt(2.d0)*(1+e)/(pi**2) - sqrt(2.d0)*(1-e**2)/pi K2ne = fac*divune K2nw = fac*divunw K2sw = fac*divusw K2se = fac*divuse ! K3 ! 1/s^2 fac = -4*(1+e)/(3*pi) K3ne = K1*(0.375*divune**2 - 0.5*detne) + fac*(divune**2 - detne) K3nw = K1*(0.375*divunw**2 - 0.5*detnw) + fac*(divunw**2 - detnw) K3sw = K1*(0.375*divusw**2 - 0.5*detsw) + fac*(divusw**2 - detsw) K3se = K1*(0.375*divuse**2 - 0.5*detse) + fac*(divuse**2 - detse) ! Diagnostic v'/D based on assumption of stationary field ! 1/s vdne = 0.5*(sqrt(K2ne**2 - 4*K1*K3ne) - K2ne)/K1 vdnw = 0.5*(sqrt(K2nw**2 - 4*K1*K3nw) - K2nw)/K1 vdsw = 0.5*(sqrt(K2sw**2 - 4*K1*K3sw) - K2sw)/K1 vdse = 0.5*(sqrt(K2se**2 - 4*K1*K3se) - K2se)/K1 minvpD=min(minvpD,vdne,vdnw,vdsw,vdse) maxvpD=max(maxvpD,vdne,vdnw,vdsw,vdse) ! Background values of vd minvp=1.e-8 vdne=max(vdne,minvp/diam) vdnw=max(vdnw,minvp/diam) vdse=max(vdse,minvp/diam) vdsw=max(vdsw,minvp/diam) ! Final viscosities --- ! TODO: aice, vice to triangles? ! Thickness of an ice floe cice = max(aice(i,j),0.01) ! always > 0.01 hfloe = max(vice(i,j)/cice,0.10) ! always > 0.1 ! Simplifying factor sep=cice**3.5/max(0.01,sqrt(C0)-sqrt(cice)) ! unitless gamp=rhoi*(diam**2)*hfloe*sqrt(2.0)*0.25*(1+e)*sep/(pi**2) ! kg ! Shear viscosity ! etane = pi*gamp*vdne/(3*sqrt(2.0)) ! kg/s ! etanw = pi*gamp*vdnw/(3*sqrt(2.0)) ! etasw = pi*gamp*vdsw/(3*sqrt(2.0)) ! etase = pi*gamp*vdse/(3*sqrt(2.0)) ! Bulk viscosity ! zetane = pi*gamp*vdne/sqrt(2.0) ! kg/s ! zetanw = pi*gamp*vdnw/sqrt(2.0) ! zetasw = pi*gamp*vdsw/sqrt(2.0) ! zetase = pi*gamp*vdse/sqrt(2.0) ! if (j0+j==100) print *,'prssne',prssne ! if (j0+j==100) print *,'etane' ,etane if (evp_damping) then ! DD -- enforce damping criterion c0ne = min(gamp*vdne,rcon_miz(i,j)) c0nw = min(gamp*vdnw,rcon_miz(i,j)) c0sw = min(gamp*vdsw,rcon_miz(i,j)) c0se = min(gamp*vdse,rcon_miz(i,j)) else ! DD -- regular damping ! kg/s c0ne = gamp*vdne c0nw = gamp*vdnw c0sw = gamp*vdsw c0se = gamp*vdse endif c1ne = c0ne*dte2T c1nw = c0nw*dte2T c1sw = c0sw*dte2T c1se = c0se*dte2T ! denom1 = 1.0/(1.0 + dte2T) is the same as in the evp model denom2 = 1.0/(1.0 + 3*dte2T) !----------------------------------------------------------------- ! the stresses ! kg/s^2 ! (1) northeast, (2) northwest, (3) southwest, (4) southeast !----------------------------------------------------------------- stressp_1(i,j) = (stressp_1(i,j) + & c1ne*(pi*sqrt(2.0)*divune-vdne))*denom stressp_2(i,j) = (stressp_2(i,j) + & c1nw*(pi*sqrt(2.0)*divunw-vdnw))*denom stressp_3(i,j) = (stressp_3(i,j) + & c1sw*(pi*sqrt(2.0)*divusw-vdsw))*denom stressp_4(i,j) = (stressp_4(i,j) + & c1se*(pi*sqrt(2.0)*divuse-vdse))*denom stressm_1(i,j) = (stressm_1(i,j) + & c1ne*pi*sqrt(2.0)*tensionne)*denom2 stressm_2(i,j) = (stressm_2(i,j) + & c1nw*pi*sqrt(2.0)*tensionnw)*denom2 stressm_3(i,j) = (stressm_3(i,j) + & c1sw*pi*sqrt(2.0)*tensionsw)*denom2 stressm_4(i,j) = (stressm_4(i,j) + & c1se*pi*sqrt(2.0)*tensionse)*denom2 stress12_1(i,j) = (stress12_1(i,j) + & c1ne*pi*sqrt(2.0)*shearne*.5)*denom2 stress12_2(i,j) = (stress12_2(i,j) + & c1nw*pi*sqrt(2.0)*shearnw*.5)*denom2 stress12_3(i,j) = (stress12_3(i,j) + & c1sw*pi*sqrt(2.0)*shearsw*.5)*denom2 stress12_4(i,j) = (stress12_4(i,j) + & c1se*pi*sqrt(2.0)*shearse*.5)*denom2 maxstressm=max(stressm_1(i,j),stressm_2(i,j),stressm_3(i,j), & stressm_4(i,j),maxstressm) maxstressp=max(stressp_1(i,j),stressp_2(i,j),stressp_3(i,j), & stressp_4(i,j),maxstressp) maxstress12=max(stress12_1(i,j),stress12_2(i,j), & stress12_3(i,j),stress12_4(i,j),maxstress12) minstressm=min(stressm_1(i,j),stressm_2(i,j),stressm_3(i,j), & stressm_4(i,j),minstressm) minstressp=min(stressp_1(i,j),stressp_2(i,j),stressp_3(i,j), & stressp_4(i,j),minstressp) minstress12=min(stress12_1(i,j),stress12_2(i,j), & stress12_3(i,j),stress12_4(i,j),minstress12) ! if (j0+j==100) print *,'stressp',stressp_1(i,j) ! if (j0+j==100) print *,'stressm',stressm_1(i,j) ! if (j0+j==100) print *,'stress12',stress12_1(i,j) ! if (j+j0==101.and.i+i0==253.and.ksub==2) print *, ! & 'stressm(i=253,j=101,:):',stressm_1(i,j) ! Keep viscosities for study mizzeta(i,j) = zetane mizeta(i,j) = etane mizprss(i,j) = gamp*vdne**2 mizvd(i,j) = vdne endif !!end of EVP/MIZ check !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! endif!!check for ice presence enddo!!i enddo!!j !$OMP END PARALLEL DO ! if (diag) then ! call xcmaxr(maxstressm) ! call xcminr(minstressm) ! if (mnproc==1) print *,'min/max stressm:',minstressm,maxstressm ! call xcmaxr(maxstressp) ! call xcminr(minstressp) ! if (mnproc==1) print *,'min/max stressp:',minstressp,maxstressp ! call xcmaxr(maxstress12) ! call xcminr(minstress12) ! if (mnproc==1) print *,'min/max stress12:',minstress12,maxstress12 ! call xcmaxr(maxvpD) ! call xcminr(minvpD) ! if (mnproc==1) print *,'min/max vpD:',minvpD,maxvpD ! end if ! !call xcstop('(evp_stress_miz)') end subroutine evp_stress_miz !!******