#include"cppdefs.h" !----------------------------------------------------------------------- !BOP ! ! !ROUTINE: The non-local, exact weak-equilibrium stability function \label{sec:cmueA} ! ! !INTERFACE: subroutine cmue_a(nlev) ! !DESCRIPTION: ! ! The solution of \eq{bijVertical} and \eq{giVertical} has the shape indicated ! by \eq{b13}. This subroutine is used to update the quantities ! $c_\mu$, $c'_\mu$ and $\Gamma$, defined in \eq{b13}, from which all turbulent ! fluxes can be computed. The non-linear terms ${\cal N}$ and ${\cal N}_b$ are updated ! by evaluating the right hand side of \eq{NandNb} at the old time step. ! ! The numerators and the denominator appearing in \eq{cm} ! are polynomials of the form ! \begin{equation} ! \label{vdng} ! \begin{array}{rcl} ! D &=& d_0 ! + d_1 \overline{N}^2 + d_2 \overline{S}^2 ! + d_3 \overline{N}^2 \overline{S}^2 ! + d_4 \overline{N}^4 + d_5 \overline{S}^4 \comma \\[3mm] ! N_n &=& n_0 ! + n_1 \overline{N}^2 + n_2 \overline{S}^2 ! + n_3 \overline{T} \comma \\[3mm] ! N_b &=& n_{b0} ! + n_{b1} \overline{N}^2 + n_{b2} \overline{S}^2 \comma \\[3mm] ! N_\Gamma &=& ( g_0 ! + g_1 \overline{N}^2 + g_2 \overline{S}^2 ) \overline{T} ! \point ! \end{array} ! \end{equation} ! ! The coefficients of $D$ are given by ! \begin{equation} ! \label{vdi} ! \begin{array}{rcl} ! d_0 &=& 36 {\cal N}^3 {\cal N}_b^2 \comma \\[3mm] ! d_1 &=& 84 a_5 a_{b3} {\cal N}^2 {\cal N}_b \comma \\[3mm] ! d_2 &=& 9 (a_{b2}^2 - a_{b1}^2) {\cal N}^3 ! + 12 ( 3 a_3^2 - a_2^2) {\cal N} {\cal N}_b^2 \comma \\[3mm] ! d_3 &=& 12 (a_2 a_{b1} - 3 a_3 a_{b2} ) a_5 a_{b3} {\cal N} ! + 12 ( a_3^2 - a_2^2) a_5 a_{b3} {\cal N}_b \comma \\[3mm] ! d_4 &=& 48 a_5^2 a_{b3}^2 {\cal N} \comma \\[3mm] ! d_5 &=& 3 ( 3 a_3^2 - a_2^2)(a_{b2}^2 - a_{b1}^2) {\cal N} ! \point ! \end{array} ! \end{equation} ! The coefficients of the numerators $N_n$ and $N_b$ can be expressed as ! \begin{equation} ! \label{vni} ! \begin{array}{rcl} ! n_0 &=& 36 a_1 {\cal N}^2 {\cal N}_b^2 \comma \\[3mm] ! n_1 &=&-12 a_5 a_{b3} (a_{b1}+a_{b2}) {\cal N}^2 ! - 8 a_5 a_{b3} (-6 a_1+a_2+3 a_3) {\cal N} {\cal N}_b \comma \\[3mm] ! n_2 &=& 9 a_1 (a_{b2}^2 - a_{b1}^2){\cal N}^2 \comma \\[3mm] ! n_3 &=& 36 a_5 a_{b4} (a_{b1}+a_{b2}) {\cal N}^2 ! + 24 a_5 a_{b4} (a_2+3 a_3) {\cal N} {\cal N}_b \comma ! \end{array} ! \end{equation} ! \begin{equation} ! \label{vnbi} ! \begin{array}{rcl} ! n_{b0} &=& 12 a_{b3} {\cal N}^3 {\cal N}_b \comma \\[3mm] ! n_{b1} &=& 12 a_5 a_{b3}^2 {\cal N}^2 \comma \\[3mm] ! n_{b2} &=& 9 a_1 a_{b3} (a_{b1}-a_{b2}) {\cal N}^2 ! + a_{b3} (6 a_1 (a_2-3 a_3) ! - 4 (a_2^2-3 a_3^2) ) {\cal N} {\cal N}_b \comma ! \end{array} ! \end{equation} ! and the numerator of the term $\Gamma$ is ! \begin{equation} ! \label{vgi} ! \begin{array}{rcl} ! g_0 &=& 36 a_{b4} {\cal N}^3 {\cal N}_b \comma \\[3mm] ! g_1 &=& 36 a_5 a_{b3} a_{b4} {\cal N}^2 \comma \\[3mm] ! g_2 &=& 12 a_{b4} ( 3 a_3^2 - a_2^2) {\cal N} {\cal N}_b \point ! \end{array} ! \end{equation} ! ! !USES: use turbulence, only: eps use turbulence, only: P,B,Pb,epsb use turbulence, only: an,as,at,r use turbulence, only: cmue1,cmue2,gam use turbulence, only: cm0 use turbulence, only: cc1 use turbulence, only: ct1,ctt use turbulence, only: a1,a2,a3,a4,a5 use turbulence, only: at1,at2,at3,at4,at5 IMPLICIT NONE ! ! !INPUT PARAMETERS: ! ! number of vertical layers integer, intent(in) :: nlev ! ! !BUGS: ! Test stage. Do not yet use. ! ! !REVISION HISTORY: ! Original author(s): Lars Umlauf ! ! $Log: cmue_a.F90,v $ ! Revision 20.0 2013/12/14 00:13:28 fms ! Merged revision 1.1.2.1 onto trunk ! ! Revision 1.1.2.1 2012/05/15 16:00:53 smg ! initial cvs ci for these modules to mom5. ! AUTHOR:Griffies ! REVIEWERS: ! TEST STATUS: ! CHANGES PUBLIC INTERFACES? ! CHANGES ANSWERS? ! ! Revision 1.1.2.1.390.1 2012/04/23 20:30:29 smg ! updated to the gotm-2012.03.09 CVS tag. ! AUTHOR:Martin Schmidt ! REVIEWERS:Griffies ! TEST STATUS: ! CHANGES PUBLIC INTERFACES? ! CHANGES ANSWERS? ! ! Revision 1.1 2005-06-27 10:54:33 kbk ! new files needed ! ! !EOP !-----------------------------------------------------------------------! ! !LOCAL VARIABLES: integer :: i REALTYPE :: N,Nt,Pe,Pbeb REALTYPE :: xd0,xd1,xd2,xd3,xd4,xd5,xd6,xd7 REALTYPE :: xn0,xn1,xn2,xn3,xn4,xn5 REALTYPE :: xt0,xt1,xt2,xt3 REALTYPE :: xg0,xg1,xg2 REALTYPE :: d0,d1,d2,d3,d4,d5 REALTYPE :: n0,n1,n2,n3,nt0,nt1,nt2 REALTYPE :: gam0,gam1,gam2 REALTYPE :: nGam,dCm,nCm,nCmp REALTYPE :: cm3_inv,r_i ! !----------------------------------------------------------------------- !BOC cm3_inv = 1./cm0**3. xd0 = 36. xd1 = 84.*a5*at3 xd2 = 9.*(at2**2.-at1**2.) xd3 = - 12.*(a2**2.-3.*a3**2.) xd4 = 12.*a5*at3*(a2*at1-3.*a3*at2) xd5 = 12.*a5*at3*(a3**2.-a2**2.) xd6 = 48.*a5**2.*at3**2. xd7 = 3.*(a2**2.-3.*a3**2.)*(at1**2.-at2**2.) xn0 = 36.*a1 xn1 = - 12.*a5*at3*(at1+at2) xn2 = 8.*a5*at3*(6.*a1-a2-3.*a3) xn3 = 9.*a1*(at2**2.-at1**2.) xn4 = 36.*a5*at4*(at1+at2) xn5 = 24.*a5*at4*(a2+3.*a3) xt0 = 12.*at3 xt1 = 12*a5*at3**2. xt2 = 9.*a1*at3*(at1-at2) xt3 = ( 6.*a1*(a2-3.*a3) - 4.*(a2**2.-3.*a3**2.) )*at3 xg0 = 36.*at4 xg1 = 36.*a5*at3*at4 xg2 = -12.*at4*(a2**2.-3.*a3**2.) do i=0,nlev Pe = ( P(i) + B(i) )/eps(i) Pbeb = Pb(i)/epsb(i) r_i = 1./r(i) N = Pe + 0.5*cc1 - 1. Nt = 0.5*(Pe-1.) + ct1 + 0.5*r_i*(Pbeb - 1.) ! general Nt = (Pe-1.) + ct1 ! weak equilibrium d0 = xd0 * N**3. * Nt**2. d1 = xd1 * N**2. * Nt d2 = xd2 * N**3. + xd3 * N * Nt**2. d3 = xd4 * N + xd5 * Nt d4 = xd6 * N d5 = xd7 * N n0 = xn0 * N**2. * Nt**2. n1 = xn1 * N**2. + xn2 * N * Nt n2 = xn3 * N**2. n3 = xn4 * N**2. + xn5 * N * Nt nt0 = xt0 * N**3. * Nt nt1 = xt1 * N**2. nt2 = xt2 * N**2. + xt3 * N * Nt gam0 = xg0 * N**3. * Nt gam1 = xg1 * N**2. gam2 = xg2 * N * Nt dCm = d0 + d1*an(i) + d2*as(i) + d3*an(i)*as(i) + d4*an(i)*an(i) + d5*as(i)*as(i) nCm = n0 + n1*an(i) + n2*as(i) + n3*at(i) nCmp = nt0 + nt1*an(i) + nt2*as(i) nGam = ( gam0 + gam1*an(i) + gam2*as(i) )*at(i) cmue1(i) = cm3_inv*nCm/dCm cmue2(i) = cm3_inv*nCmp/dCm gam(i) = nGam/dCm end do return end subroutine cmue_a !EOC !----------------------------------------------------------------------- ! Copyright by the GOTM-team under the GNU Public License - www.gnu.org !-----------------------------------------------------------------------