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inigiss.F90
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inigiss.F90
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subroutine inigiss
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 2.1
implicit none
!
! -----------------------------------------------
! --- initialize nasa-giss vertical mixing scheme
! -----------------------------------------------
!
integer i,j,k
!
real slq2b_00,smb_00,shb_00,ssb_00,c_y0,c_y00,deltanum, &
deltaden,delta,rrcrn,rrcrp,theta_rcrn_deg,theta_rcrp_deg, &
delra_r,theta_r_deg,theta_r,sm_r0,sh_r0,ss_r0,ra_r,ra_r1, &
rit,ric,ri_r,rid_r,sm_r,sh_r,ss_r,smosloq_r,rit1,ric1, &
ri_r1,rid_r1,slq2_r,smosloq_0r,ra_r0,rit0,ric0,ri_r0,rid_r0, &
slq2_r0,c_y001,sisa1
!
integer iridsign,iridstep,irid,iri,mt0s,mtm1s,idfs,idif,irisign, &
iristep,itheta_r,jtheta_r,isailback,idifs,ira_r,ibg, &
ipenra_r
!
real acosh1,xx
# include "stmt_fns.h"
acosh1(xx) = log(xx+sqrt((xx**2)-1.0))
!
! --- initialize viscosity and diffusivity arrays
do j=1,jdm
do i=1,idm
do k=1,kdm+1
vcty(i,j,k)=diwm(i,j)
dift(i,j,k)=diws(i,j)
difs(i,j,k)=diws(i,j)
! --- no nonlocal forcing
ghats(i,j,k)=0.0
enddo
enddo
enddo
!
! --- dimensions for the tables in mxgiss routine
! --- the file is needed in order to preserve in the
! --- arrays for the Ri-tables
!
pidbl=3.14159265358979312
ntbl=251
nextrtbl0=62
ifexpabstable=1
nextrtbl1=500
nextrtbl=nextrtbl0+ifexpabstable*nextrtbl1
nposapprox=51
mt0=ntbl-nposapprox
mt=mt0+nextrtbl ! table dimensions
mt_ra_r=nposapprox-1
n_theta_r_oct=(((pidbl/4.)*mt_ra_r)/15.)*15
deltheta_r=(pidbl/4.)/(n_theta_r_oct)
!
! --- set other parameters
!
ri0=- 4.0 !C parameter(ri0=-20.D0)
ebase=2.71828182845904509
ifback=5 !Temperature=Salt diffusivity model background
!model swith.
! K_H,K_S (S=N/sqrt(Ri)),Ri=backfrac*Ri_Cr)
ifsali=1 !Salinity model switch (Canuto's)
ifepson2=2 !Background (epsilon/N^2) dimensionalization
!of diffusivities switch.
! cnst blw highst lvl frgr dies
epson2_ref=.288 !reference value of dissipation/N**2
!Value of (epsilon/N^2)/(1 cm/sec^2) used.
!See Canuto et al. JPO 2002 Sections 8&9.
!040126 Actual (epsilon/N^2) can vary with z,N and f .
eps_bot0=2.e-5 !The value of epsilon at the bottom in cgs,
!St.Laurent et al. JPO2001 give epsilon = 3to9e-9 W/kg
!for slopes and 2to5e-9 W/kg for crests and canyons.
scale_bot=5.e-4 !The scale (in cm) of exponential decrease of mixing
!above the bottom with height. St. Laurent et al. give
!150+-50 m for slopes, 500+-100 m for crests and canyons.
eplatidepmin=7.E-2 !Gregg et al. admit their formula eq.(2) for the
!latitude dependent factor L which scales turbulence
!won't work at the equator where it predicts epsilon=0.
!Introduce eplatidepmin, a minimum on the factor L .
wave_30=(pi/43082.0)*acosh1(5.24e-3/(pi/43082.0))
!reference value at 30degN with N=5.24e-3
!from Garerett and Munk, as used by Gregg et. al.
ifrafgmax=1 !Switch for limiting BackGround ra_r
!to at most Foreground ra_r when Ri>0
!for R_r in the [R_r_crit_DoubleDiffusion,
!R_r_crit_SaltFingers] regime.
ifsalback=5 !Salinity background modification switch.
!int.wvS=N/(Ri_i^(1/2)),Ri_icnst,
! ra_r_i=cnst*ra_r_crit.(theta_r)
ifchengcon=0 !old ocean cnsts,near-surf prof assump
ifpolartablewrite=0 !Switch to write out polar 2D
!turbulence table .
ifbg_theta_interp=1 !Introduce flag for use of \theta_r
!arrays to interpolate background.
!Intrplt 2D array
!(slq2_r1=array for (Sl/q)^2)
!with (Ri,Ri_d)indices
back_ph_0=(6.e-5)*(1.e2/(2.e0*pidbl))
!for ifsalback=3 case.
!Gargett et. al. JPO Vol.11 p.1258-71 gives
!for "the deep record",
!\phi_0=6\times10^{-5}s^{-2}cpm^{-1}.
!"cpm" is 'cycles per meter'.
!\phi_0=6\times10^{-5}s^{-2}(2 pidbl/100)^{-1}cm
adjust_gargett=1.0 !Gargett et. al. favor the value,
!k_0 = 0.1 cpm. But k_0=0.05-0.2 cpm
!might be viable, see section 5 of their
!paper. Take k_0 = 0.1 cpm * adjust_gargett,
!where adjust_gargett is adjustable.
!Convert to radians per cm:
!k_0 = 0.1 (2pi/100cm) * adjust_gargett.
!used for ifsalback=4 case also, but set
!adjust_gargett=1 for ifsalback=4
back_k_0=(0.1)*(2.0)*pidbl*(1.e-2)*adjust_gargett
!Introduce the lengthscale
!\Delta_0 \equiv pi/k_0 .
!The units of \Delta_0 are centimeters,
!with k_0 in radians per cm.
!`min turb' wvnmbr (cm^-1)
back_del_0=pidbl/back_k_0
back_s2=1.e-14 !back_s2 should be smaller than any normal Shear^2
back_sm2=1.0/back_s2 !1/back_s2 (sec^2)
ri_internal=1.0 !Parameter for ifsalback=4 case.
backfrac = 85.e-2 !Parameter for ifback or ifsalback=5 case.
!ifback=5: =cnst frac{Ri_cr};
!ifsalback=5:=cnst frac{ra_r_crit.(\theta_r)}
backfact = ebase**(-1) !Parameter for ifsalback=6 case.
ako = 1.6 ! Kolmogorov's constant
!
tpvot0 = 0.4 ! \tau_pv = {2 \over 5} \tau (B.1)
! "tpv/tau" = 2/5
! From the printed notes Canuto
! gave Armando on 980601 have:
sgmt=0.72 !Make "sgmt" a parameter.
!Standard value was 0.72.
tptot0=(1.0/5.0)*(1.0/(1.0+(1.0/sgmt)))
! \tau_p\theta over \tau
tpcot0=tptot0 !tau_pc over \tau
ttot0=sgmt !tau_\theta over \tau
tcot0=ttot0 !tau_c over \tau
tctot0=1.0/3.0 ! tau_c\theta } over \tau
tpvot = tpvot0
tptot = tptot0
tpcot = tpcot0
ttot = ttot0
tcot = tcot0
tctot = tctot0
!
if (mnproc.eq.1) then
write(lp,900)
900 format('nasa-giss mixed layer model selected'/ &
'turbulence calculated by 040128 hycom version'/ &
'stripped down from 030803 turb_2gi1a ncar')
endif !1st proc
!
! --- START OF SALINITY MODEL BACKGROUND LENGTHSCALE CALCULATION SECTION.
! --- ifsali.eq. 1 therefore:
! --- Calculate constant lengthscale for
! --- the background for ifsalback=3,4,5
! --- \Delta_0 ={B_1 pi \over (3 Ko)^{3/2}} l_0
! --- l_0 = {(3 Ko)^{3/2} \over B_1 pi} \Delta_0
! --- "back_l_0" is the constant background
! --- l_0 in centimeters.
!
! --- pass back B_1 from oursal2.
call oursal2_1a(0.,0.,slq2b_00,smb_00,shb_00,ssb_00, &
c_y0,c_y00,0,0)
!
back_l_0 = (((3.*ako)**(3./2.))/(b1*pi))*back_del_0
!
if (mnproc.eq.1) then
write(lp,*) "Dubovikov Internal wave constants for background."
write(lp,*) "Ratio of Background to Critical ra_r"// &
" [\\equiv ({Ri_T}^2 + {Ri_C}^2)^(1/2)]",backfrac
write(lp,*) "Lengthscale, del_0/(cm) =",back_del_0
write(lp,*) "Lengthscale, l_0/(cm) =",back_l_0
call flush(lp)
endif !1st proc
!
! --- Set step-size for *both* dimensions of 2D table here.
! --- ifsali.eq. 1
dri = -ri0/real(mt0)
!
! --- BUILD SALINITY MODEL TABLES VS. "Ri = Ri_T + Ri_C" AND "Ri_d = Ri_T - Ri_C".
! --- Use separate loops for calculation of independent table variables.
!
do iridsign=0,1
iridstep=(-1)**iridsign
do irid= 0,mt*iridstep,iridstep
! --- Set Ri_d table values. (See NBP59,63=p#A27,30.)
if(abs(irid).le.mt0) then
ridb(irid) = real(irid)*dri
else
mt0s = mt0*iridstep
mtm1s = (mt0-1)*iridstep
! --- introduction of exponential absolute val table option.
if(ifexpabstable.eq. 0) then
idifs = (abs(irid)-mt0)*iridstep
ridb(irid) = ridb(mt0s)*((ridb(mt0s)/ &
ridb(mtm1s))**(idifs**2))
else if(ifexpabstable.eq. 1) then
idif = abs(irid)-mt0
ridb(irid) = ridb(mt0s)*((ridb(mt0s)/ &
ridb(mtm1s))**(idif))
endif
endif
!
enddo
enddo
!
do irisign=0,1
iristep=(-1)**irisign
do iri= 0,mt*iristep,iristep
! --- Set Ri table values. (See NBP59,63=p#A27,30.)
if(abs(iri).le.mt0) then
ribtbl(iri) = real(iri)*dri
else
mt0s = mt0*iristep
mtm1s = (mt0-1)*iristep
! --- introduction of exponential absolute val table option.
if(ifexpabstable.eq. 0) then
idifs = (abs(iri)-mt0)*iristep
ribtbl(iri) = ribtbl(mt0s)*((ribtbl(mt0s)/ &
ribtbl(mtm1s))**(idifs**2))
else if(ifexpabstable.eq. 1) then
idif = abs(iri)-mt0
ribtbl(iri) = ribtbl(mt0s)*((ribtbl(mt0s)/ &
ribtbl(mtm1s))**(idif))
endif
endif
!
enddo
enddo
!
! --- If using interp2d_expabs introduce ratio between adjacent Richardson
! --- numbers in nonlinear part of table.***
rri = ribtbl(mt0)/ribtbl(mt0-1)
!
do iridsign=0,1
iridstep=(-1)**iridsign
do irid= 0,mt*iridstep,iridstep
do irisign=0,1
iristep=(-1)**irisign
do iri= 0,mt*iristep,iristep
! --- Need to pass back the value of B_1 from oursal2 for use here.
call oursal2_1a(ribtbl(iri),ridb(irid),slq2b(iri,irid), &
smb(iri,irid),shb(iri,irid),ssb(iri,irid), &
c_y0,c_y00,iri,irid)
if(slq2b(iri,irid).lt.0) then
irimax(irid) = iri - 1
go to 15
endif
enddo
15 continue
enddo
!
enddo
enddo
!
! --- Add writes in salinity model case.
!diag if (mnproc.eq.1) then
!diag write(lp,*) "************************************************"
!diag write(lp,*) "New Temperature-Salinity Model"
!diag write(lp,*) "ifsali=",ifsali
!diag write(lp,*) "ifsalback=",ifsalback
!
!diag write(lp,*) "ifepson2=",ifepson2
!diag if(ifepson2.GT.0) then &
!diag write(lp,*) "epson2_ref=",epson2_ref
!diag WRITE(lp,*) "ifdeeplat=",ifdeeplat
!diag IF(ifdeeplat.GT.0) THEN
!diag WRITE(*,*) "eplatidepmin=",eplatidepmin
!diag END IF
!diag WRITE(*,*) "ifbotenhance=",ifbotenhance
!diag IF(ifbotenhance.EQ.1) THEN
!diag WRITE(*,*) "eps_bot0=",eps_bot0
!diag WRITE(*,*) "scale_bot=",scale_bot
!diag END IF
!diag END IF
!*****CD
!
!diag write(lp,*)"ifrafgmax=",ifrafgmax
!diag write(lp,*)"ifbg_theta_interp=",ifbg_theta_interp
!diag write(lp,*) &
!diag " i ", &
!diag " ribtbl(i) "," ridb(i) ", &
!diag "irimax(i) "
!diag do i= -mt,mt
!diag write(lp,9050) i,ribtbl(i),ridb(i),irimax(i)
!diag enddo
!
!diag write(lp,*) " "
!diag write(lp,*) "irid Ri_d Ri(irimax) " &
!diag // "S_M S_H S_S " &
!diag // "S_M/S_H S_S/S_H "
!diag do irid= -mt,mt
!diag write(lp,9100) irid,ridb(irid),ribtbl(irimax(irid)), &
!diag smb(irimax(irid),irid), &
!diag shb(irimax(irid),irid), &
!diag ssb(irimax(irid),irid), &
!diag smb(irimax(irid),irid)/shb(irimax(irid),irid), &
!diag ssb(irimax(irid),irid)/shb(irimax(irid),irid)
!diag enddo
!diag call flush(lp)
!diag endif !1st proc
!
! --- CALCULATE "R_r_Critical" USING CANUTO'S 000228 ANALYTIC FORMULA
! --- FOR "R_rho_Critical". See NBp.000229-3 and 000316-4.
! --- R_rho_Canuto \equiv -Ri_C/Ri_T \equiv -R_r .
! --- In a sheet dated 000228 Canuto gave me:
! --- "R_\rho^{cr} = {1 \over \Deta} [1 {+\over-} \sqrt{1 - \Delta^2}]
! --- \Delta \equiv {{\pi_2(1 + {15 \over 7} \pi_3)} \over
! --- {\pi_3 - \pi_2 + (15 \over 14} \pi_3^2}} ".
! --- Note that the + and - choices are reciprocals so this covers
! --- both the Salt Fingering and Double Diffusive Critical R_\rho's.
! --- From Ocean Turbulence III paper have:
! --- \pi_{1,2,3,4,5} =
! --- (\tau_pc,\tau_c\theta,\tau_c,\tau_p\theta,\tau_\theta)/\tau
! --- R_r_Crit = [-1 -/+ \sqrt{1 - \Delta^2}]/Delta
! --- \Delta = {{{\tau_c\theta \over \tau} ( 1 + (15/7)*{\tau_c \over \tau})}
! --- \over {{\tau_c \over \tau} - {\tau_c\theta \over \tau} +
! --- (15/14) {\tau_c \over \tau}^2}}
!
deltanum = tctot*(1. + ((15./7.)*tcot))
deltaden = tcot - tctot + ((15./14.)*(tcot**2))
delta = deltanum/deltaden
rrcrn = (-1. - sqrt(1. - (delta**2)))/delta
rrcrp = (-1. + sqrt(1. - (delta**2)))/delta
theta_rcrn = atan(rrcrn)
theta_rcrp = atan(rrcrp)
!
! --- Make sure the right choice of arctan(R_r)=[\theta_r] is made.
! --- Arctan covers the range (-pi/2,pi/2) while
! --- \theta_r_Crit must be in the range (-pi/4,3pi/4) (The range of Ri>0.)
!
if(theta_rcrn.lt.-pi/4.) theta_rcrn = theta_rcrn + pi
if(theta_rcrp.lt.-pi/4.) theta_rcrp = theta_rcrp + pi
theta_rcrn_deg = theta_rcrn*(180./pi)
theta_rcrp_deg = theta_rcrp*(180./pi)
!diag if (mnproc.eq.1) then
!diag write(lp,*) " "
!diag write(lp,*) " "
!diag write(lp,*) " "
!diag write(lp,*) " "
!diag write(lp,*) "R_r_Crit+ =",rrcrp
!diag write(lp,*) "R_r_Crit- =",rrcrn
!diag write(lp,*) "\\theta_r_Crit+ =",theta_rcrp
!diag write(lp,*) "\\theta_r_Crit- =",theta_rcrn
!diag write(lp,*) "\\theta_r_Crit+ in degrees =",theta_rcrp_deg
!diag write(lp,*) "\\theta_r_Crit- in degrees =",theta_rcrn_deg
!diag write(lp,*) " "
!diag write(lp,*) " "
!
!diag write(lp,*) " "
!diag write(lp,*) " "
!diag call flush(lp)
!diag endif !1st proc
!
! --- Increments in radial and angular coordinates in (Ri_T,Ri_C) plane.
!
delra_r = 1./real(mt_ra_r)
! deltheta_r = (pi/4.)/real(n_theta_r_oct)
!
! --- Natassa
! if (mnproc.eq.1) then
! write(53,*)nstep,igrid,jgrid,n_theta_r_oct,deltheta_r
! endif !1st proc
!
! --- Calculate the ratio \sigma_sa_max \equiv S_S/S_H as a function
! --- of the angle \theta_r in Ri_T,Ri_C space,
! --- \theta_r \equiv arctan(Ri_C/Ri_T).
! --- The range of angles where unrealizability occurs is
! --- a subset of theta_r = -pi/4 to 3pi/4.
!
!diag if (mnproc.eq.1) then
!diag write(lp,*) "S_S/S_H at pre-maximum Ri as a function of" &
!diag // "\\theta_r \\equiv Arctan(Ri_C/Ri_T)"
!
! --- Absurd default on sisamax \equiv S_S/S_H.
!diag write(lp,*) "Arbitrarily show the absurd value -99.999"
!diag write(lp,*) "at angles where do not have "// &
!diag "a maximum Ri (or radius ra_r)."
!diag write(lp,*) " "
!diag write(lp,*) " \\th_r ^o ra_r " &
!diag // " Ri_T Ri_C Ri Ri_d " &
!diag // " S_M S_H S_S S_S/S_H "
!diag call flush(lp)
!diag endif !1st proc
!
! --- For Ri_T and Ri_C positive find the realizability limits
! --- in polar coordinates in the (Ri_T,Ri_C) plane : (ra_r,theta_r).
!
if(ifpolartablewrite.eq. 1 .and. mnproc.eq.1) then
open(unit=uoff+98,file="turb_ra_th",status="unknown")
endif
do itheta_r = -n_theta_r_oct,3*n_theta_r_oct
! do ihelp = 0,4*n_theta_r_oct
! itheta_r=ihelp-n_theta_r_oct
theta_r = real(itheta_r)*deltheta_r
theta_r_deg = theta_r*(180./pi)
!
! --- Introduce jtheta_r, an angle index that begins at zero
! --- for the purposes of letting OURSAL2 know it starts at the origin.
!
jtheta_r = itheta_r + n_theta_r_oct
!
! --- Initialize sisamax to the impossible negative value of -99.999 to
! --- let places where the realizability limit is not reached stand out.
sisamax(itheta_r) = -99.999
!
! --- Initialize sm_r0,sh_r0,ss_r0 to the INCONSISTENT absurd value -9.999999.
sm_r0 = -9.999999
sh_r0 = -9.999999
ss_r0 = -9.999999
!
! --- Flag ibg determines if the background value of ra_r has been calculated.
if(ifsalback.eq. 6) ibg=0
!
! --- Flag ifunreal determines if realizability limit has been found.
ifunreal=0
!
! --- Make the ra_r max value not too large to try to avoid numerical trouble.
!
do ira_r = 0,(mt_ra_r**2)/4
!
if(ira_r.le.mt_ra_r) then
ra_r = real(ira_r)*delra_r
else
ra_r = ((1.+delra_r)**(ira_r - mt_ra_r)) &
*(real(mt_ra_r)*delra_r)
endif
!
! --- Convert radius and angle, (ra_r,theta_r), to rectangular coordinates.
rit = ra_r*COS(theta_r)
ric = ra_r*SIN(theta_r)
ri_r = rit + ric
rid_r = rit - ric
!
! --- Calculate turbulence functions at this radius and angle in (Ri_T,Ri_C).
!
call oursal2_1a(ri_r,rid_r,slq2_r,sm_r,sh_r,ss_r, &
c_y0,c_y00,ira_r,jtheta_r)
!
if(ifpolartablewrite.eq. 1 .and. mnproc.eq.1) then
write(uoff+98,9001) &
itheta_r,theta_r_deg,ira_r,ra_r,slq2_r,sm_r,sh_r,ss_r
endif
!
! --- Calculate S_M/(S l/q) and find where it's backfact of its origin value.
if(ifsalback.eq. 6) then
smosloq_r = sm_r/sqrt(slq2_r)
if(ira_r.eq. 0) smosloq_0r = smosloq_r
! --- Use radius where dimensionless K_M falls below backfact*origin value.
if((smosloq_r.le.backfact*smosloq_0r).AND. &
(ibg.eq. 0) ) then
ra_r1 = ra_r
rit1 = rit
ric1 = ric
ri_r1 = ri_r
rid_r1 = rid_r
slq2_r1(itheta_r) = slq2_r
sm_r1(itheta_r) = sm_r
sh_r1(itheta_r) = sh_r
ss_r1(itheta_r) = ss_r
ibg=1
endif
endif
!
if(slq2_r.le.0.) then
! --- Use value of last lattice point on this radius with "slq2" positive.
! --- Calculate the ratio of the salt and heat diffusivities there.
sisamax(itheta_r) = ss_r0/sh_r0
!
! --- Store in an array the maximum radius, ra_r, at this angle, theta_r,
! --- in the polar (Ri_T,Ri_C) [that is the (theta_r,ra_r)] plane.
ra_rmax(itheta_r) = ra_r0
!
! --- Determine the background radius, ra_r, at this \theta_r.
if(ifsalback.eq. 5) then
! --- Use a constant fraction of the maximum radius before model breakdown.
back_ra_r(itheta_r) = backfrac*ra_rmax(itheta_r)
!
else if(ifsalback.eq. 6) then
back_ra_r(itheta_r) = ra_r1
endif
!
ifunreal = 1
!
! --- Skip straight to write out when last point reached.
go to 16
endif
!
ra_r0 = ra_r
rit0 = rit
ric0 = ric
ri_r0 = ri_r
rid_r0 = rid_r
slq2_r0 = slq2_r
sm_r0 = sm_r
sh_r0 = sh_r
ss_r0 = ss_r
!
! --- Store c_y as c_y_0 for possible use as a guess in background calc.
c_y_r0(itheta_r) = c_y0
!
enddo
!
! --- Write out stability functions, the S's and sisamax.
16 continue
!diag if (mnproc.eq.1) then
!diag write(lp,9150) theta_r_deg,ra_r0,rit0,ric0,ri_r0,rid_r0, &
!diag sm_r0,sh_r0,ss_r0,sisamax(itheta_r)
!diag call flush(lp)
!diag endif !1st proc
!
! --- Set background ra_r large at angles where unrealizability doesn't occur.
! --- Make the ra_r max value not too large to try to avoid numerical trouble.
if(ifunreal.eq. 0) then
ipenra_r = (mt_ra_r**2)/4-1
back_ra_r(itheta_r) = ((1.+delra_r)**(ipenra_r - mt_ra_r)) &
*(real(mt_ra_r)*delra_r)
endif
!
! --- For ifsalback=5 case get value for initialization of c_y calculation.
if(ifsalback.eq. 5) then
if(jtheta_r.eq. 0) then
c_y001 = c_y0
endif
endif
!
enddo
!
if(ifpolartablewrite.eq. 1 .and. mnproc.eq.1) then
close(uoff+98)
endif
!
! --- Write out stability functions at background ra_r .
if(ifsalback.GT.4) then
do itheta_r = -n_theta_r_oct,3*n_theta_r_oct
theta_r = real(itheta_r)*deltheta_r
theta_r_deg = theta_r*(180./pi)
!
! --- Convert radius and angle, (ra_r,theta_r), to rectangular coordinates.
rit1 = back_ra_r(itheta_r)*COS(theta_r)
ric1 = back_ra_r(itheta_r)*SIN(theta_r)
ri_r1 = rit1 + ric1
rid_r1 = rit1 - ric1
!
! --- Calculation of turbulence functions for ifsalback=5 case.
if(ifsalback.eq. 5) then
!
! --- Calculate turbulence functions at this radius and angle in (Ri_T,Ri_C).
jtheta_r = itheta_r + n_theta_r_oct
!
! --- Set second table index to 1 to use last step's value except at start.
! --- Transform that "last step" value from the most recent angle step to the
! --- final realizable ra_r step at {\it this} angle in hope of more accuracy.
call oursal2_1a(ri_r1,rid_r1,slq2_r1(itheta_r), &
sm_r1(itheta_r),sh_r1(itheta_r),ss_r1(itheta_r), &
c_y_r0(itheta_r),c_y001,jtheta_r,1)
endif
!
!diag if(itheta_r.eq. -n_theta_r_oct) then
!diag if (mnproc.eq.1) then
!diag write(lp,*) " "
!diag write(lp,*) &
!diag "Values at background ra_r=(Ri_T^2 + Ri_C^2)^(1/2)"
!diag write(lp,*) "\\th_r ^o ra_r " &
!diag // "Ri_T Ri_C Ri Ri_d " &
!diag // "(Sl/q)^2 S_M S_H S_S S_S/S_H "
!diag write(lp,*) " "
!diag call flush(lp)
!diag endif !1st proc
!diag endif
!
sisa1 = ss_r1(itheta_r)/sh_r1(itheta_r)
!
! if (mnproc.eq.1) then
! write(lp,*)
! & 'itheta_r,theta_r_deg = ',itheta_r,theta_r_deg
! write(lp,*)
! & 'back_ra_r,slq2_r1 = ',
! & back_ra_r(itheta_r),slq2_r1(itheta_r)
! write(lp,*)
! & 'sm_r1,sh_r1,ss_r1 = ',
! & sm_r1(itheta_r),sh_r1(itheta_r),ss_r1(itheta_r)
! call flush(lp)
! endif !1st proc
!diag if (mnproc.eq.1) then &
!diag write(lp,9160) theta_r_deg,back_ra_r(itheta_r), &
!diag rit1,ric1,ri_r1,rid_r1,slq2_r1(itheta_r), &
!diag sm_r1(itheta_r),sh_r1(itheta_r),ss_r1(itheta_r), &
!diag sisa1
!diag call flush(lp)
!diag endif !1st proc
!
if(slq2_r1(itheta_r).lt.0.) then
if (mnproc.eq.1) then
write(lp,*) &
"Negative (Sl/q)^2 in table of Background vs. \\theta_r."
write(lp,*) "itheta_r=",itheta_r, &
" slq2_r1(itheta_r)=",slq2_r1(itheta_r)
write(lp,*) "Program is stopping in turb_2."
endif !1st proc
call xcstop('(inigiss)')
stop '(inigiss)'
endif
enddo
endif
!
!
9001 format(2(I8,' ',1pe11.3),8(1pe11.3))
9050 format(I8,' ',2E16.4,I8,' ')
9100 format(' ',I8,' ',2E12.4,3F11.6,2F11.4)
9150 format(F11.3,5E12.4,3F10.6,F9.3)
9160 format(F11.3,1x,6(E10.4,1x),3(F10.6,1x),F9.3)
9200 format(I12,' ',5E16.6)
!
return
end
!
subroutine oursal2_1a(ri,rid,slq2,sm,sh,sc,c_y0,c_y00,iri,irid)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
implicit none
!
! --- Replace the numerical value of 6.25 by 1/(tpvot**2) .
! --- Version in which following OTsalche/plot000127
! --- the timescale ratios are calculated in the 'smshsc' routine
! --- and passed back hrough the common block /bb/
! --- to simplify the process of adjustment of timescale ratios.
! --- Submodule to calculate turbulence functions (Sl/q)^2 and S_M,S_H,S_S
! --- of Ri(=Ri_T+Ri_C) and Ri_d(=Ri_T-Ri_C) in our NCAR turbulence module.
! --- Stripped and adapted from plot981007.f.
! --- Program to generate contour and 1 variable plots vs. Ri,Ri_d based on
! --- Program to generate contour plots vs. Ri_T and Ri_C based on
! --- Program to generate plots vs. Ri_T at different Ri_C values based on
! --- .or.eC.eD PROGRAM WITH .eW VAL.e OF "p10". 'p10 = tpt*tct/(tc**2)'
! --- Program to generate K_X/((l^2) S) for Canuto based on plot980609.f:
! --- Program to generate data for plots of turbulence functions including
! --- S_{M,H,C} and Canuto's new y = (\tau_pv S)^2
! --- and n,c as functions of stability parameters in the concentration theory
! --- (structure is a 1 point closure like the generalized Mellor-Yamada,
! --- but the constants are derived based on Dubovikov's model according
! --- to Ye Cheng). The concentration theory dimensionless parameters
! --- associated with the squares of shear, temperature contribution to
! --- Brunt Vaisala frequency and concentration contribution to it,
! --- the new y,n,c are represented in this program by the variables
! --- c_y,c_n,c_c.
! --- Adapted from Cheng's program mike_12.f_980528 for the Dubovikov model.
!-----------------------------------------------------------------------
!
! --- y=(tau*s)**2
! --- tau=2*e/epsilon=b1*l/q
! --- km=e*tau*sm=1/2*(b1*l)**2*s/y**(1/2)*sm
! --- kh=e*tau*sh=1/2*(b1*l)**2*s/y**(1/2)*sh
! --- ks=e*tau*ss=1/2*(b1*l)**2*s/y**(1/2)*ss
!
! --- X = {M,H,C} .
! --- Cheng above gives K_X = (1/2)((B_1*l)^2) (S/(((\tau S)**2)^(1/2))) S_X
! --- The "old" y used above is (\tau S)^2.
! --- The "new" y (c_y in the program) is (\tau_pv S)^2.
! --- The program variable "slq2" is (S l/q)^2 = y (B_1)^(-2),
! --- since \tau=B_1 l/q. (S l/q)^2 = (\tau \over \tau_pv)^2 c_y (B_1)^(-2) .
! --- c_y = (S l/q)^2 * [(B_1)^2 * (\tau_pv \over \tau)^2] .
!
! --- Take \tau_pv/\tau as being calculated in the smshsc routine instead.
! --- From the printed notes Canuto gave me on 980601 have:
! --- \tau_pv = {2 \over 5} \tau (B.1) or parameter(tpvot = 0.4)
!
real ri,rid,slq2,sm,sh,sc,c_y0,c_y00
real eeps,c_yst,c_yst0,c_y,val,c_n,c_c
!DBI: all eps ==> eeps in this routine!
integer iri,irid,iend,ier
real rit,ric
common /bb/rit,ric !rit is the temperature's part of
!Ri and ric the concentration's.
save /bb/
!
parameter(c_yst0 = 8.527882) !Need a guess for c_y for the solver
!for the neutral case, c_yst. Take
!c_yst = 8.527882, the approximate value
!calculated at rit=ric=0. A variable c_y00
!is intended to hold the Ri=0 value of c_y
!from the previous Ri_d row in a table the
!subroutine is being called to make and a
!variable c_y0 is intended to hold the
!previous Ri value from the current Ri_d
!row of that table.
b1=16.6
!
! --- Commented excerpt from the file "sx"
!
! --- sgmt := 0.72;
!
! --- tpt := 1/(5*(1+1/sgmt))*tau;
! --- tpt = .08372093019*tau
!
! --- tpc := 1/(5*(1+1/sgmt))*tau;
! --- tpc = .08372093019*tau
!
! --- tt := sgmt*tau;
! --- tt = .72*tau
!
! --- tc := sgmt*tau;
! --- tc = .72*tau
!
! --- tct := 2/15*sgmt*tau;
! --- tct = .09599999998*tau
!
! --- Calculate the timescale ratios in the 'smshsc' routine instead of here.
! --- Set \sigma_t0. sgmt = .72
!
! --- Calculate {\tau_C \over \tau} and {\tau_{C\theta} \over \tau}.
! --- tcot = sgmt
! --- tctot = (2./15.)*sgmt
! --- "tpt/tau" and "tpc/tau" from the "sx" excerpt
! --- tptot = 1./(5.*(1+1/sgmt))
! --- tpcot = 1./(5.*(1+1/sgmt))
!
! --- Timescale ratios are now calculated in the 'smshsc' subroutine.
! --- Make dummy call with c_y=c_n=c_c=0 to get their values for initial use.
call smshsc_a3(0.,0.,0.,sm,sh,sc)
!
eeps=1.e-6
iend=300
!
! --- rimax= ?
! --- rtwi finds the root of x=fct_sal(x)
! --- Need a guess at the root, c_yst. Use neighboring solution.
! --- Initial guess for c_yst for this value of Ri_d.
if(iri.eq.0.and.irid.eq.0) then
c_yst = c_yst0
else if(iri.eq.0) then
c_yst = c_y00
else
c_yst = c_y0
endif
!
! --- Calculate Ri_T =(Ri + Ri_d)/2 and Ri_C =(Ri - Ri_d)/2.
rit = (ri + rid)/2.
ric = (ri - rid)/2.
call rtwi(c_y,val,c_yst,eeps,sm,sh,sc,iend,ier)
!
if(ier.ne.0) then
! --- Make error message more specific.
if (mnproc.eq.1) then
write(lp,*) "In oursal2 subroutine"
write(lp,*) "c_y00=",c_y00," c_y0=",c_y0
write(lp,*) "ri=",ri," rid=",rid
write(lp,*) "rit=",rit," ric=",ric
write(lp,*) "Initial guess for rtwi c_yst=",c_yst
!
write(lp,*) "rtwi call problem, ier=",ier
endif !1st proc
call xcstop('(oursal2_1a)')
stop '(oursal2_1a)'
endif
!
! --- Calculate (S l/q)^2[=program variable "slq2"] from c_y.**
! --- (S l/q)^2 = (\tau \over \tau_pv)^2 c_y (B_1)^(-2) .
! --- (S l/q)^2 = (\tau_pv \over \tau)^(-2) c_y (B_1)^(-2) .
slq2 = c_y/((b1*tpvot)**2)
!
! --- Store value of c_y for future guesses.
if(c_y.ge.0) then
c_y0=c_y
else
! --- Turbulence model becomes unphysical for c_y negative.
! --- Realizability for negative Ri
if(ri.lt.0) then
if (mnproc.eq.1) then
write(lp,*) "c_y negative at negative Ri"
write(lp,*) "Ri=",ri," c_y=",c_y
write(lp,*) "Unstable realizability limit unexpected:"
write(lp,*) "stopping in oursal2."
endif !1st proc
call xcstop('(oursal2_1a)')
stop '(oursal2_1a)'
endif
endif
!
if(iri.eq.0) c_y00=c_y
if((iri.eq.0).and.(irid.eq.0).and. &
(abs(c_y - c_yst0).gt.1.e-6)) then
if (mnproc.eq.1) then
write(lp,*) "Inconsistency in neutral value of c_y"
write(lp,*) "Value used =",c_yst0
write(lp,*) "Value calculated =",c_y
write(lp,*) "Program stopping in oursal2"
endif !1st proc
call xcstop('(oursal2_1a)')
stop '(oursal2_1a)'
endif
!
! --- From last page (#5) of "980608 AH Concentration Work" handwritten
! --- sheetsC have:
! --- n = -{{\tau_C \tau_{C\theta}} \over {\tau_{pv}}^2 } y Ri_T
! --- c = - {{\tau_C}^2 \over {\tau_{pv}}^2} y Ri_C
! --- Decide to use the parameter "tpvot" instead of its value 2/5 \tau .
! --- n = -{{(\tau_C/\tau) (\tau_{C\theta}/\tau)} \over {\tau_{pv}/\tau}^2 }
! --- y Ri_T
! --- c = - {{\tau_C/\tau}^2 \over {\tau_{pv}/\tau}^2} y Ri_C
!
c_n = -(tcot*tctot/(tpvot**2))*c_y*rit
c_c = -((tcot**2)/(tpvot**2))*c_y*ric
call smshsc_a3(c_y,c_n,c_c,sm,sh,sc)
!
!
1003 format(12(I8))
1004 format(12(1pe14.5))
end
!-----------------------------------------------------------------------
function fct_sal(sm,sh,sc,c_y)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
implicit none
!
real fct_sal,c_n,c_c,c_y,sm,sh,sc
!
real rit,ric
common /bb/rit,ric
save /bb/
!
! --- Decide to use the parameter "tpvot" instead of its value 2/5 \tau .
c_n = -((tcot*tctot)/(tpvot**2))*c_y*rit
c_c = -((tcot**2)/(tpvot**2))*c_y*ric
call smshsc_a3(c_y,c_n,c_c,sm,sh,sc)
!
! --- y(S_\nu - Ri_T S_h - Ri_C S_c) = 8/25 . 8/25 = 0.32 . S_\nu = sm.
! --- y = 0.32/(S_\nu - Ri_T S_h - Ri_C S_c).
fct_sal=(2.*(tpvot**2))/(sm-rit*sh-ric*sc)
return
end
!-----------------------------------------------------------------------
subroutine smshsc_a3(yyy,nnn,ccc,sm,sh,sc)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
implicit none
!
! --- .eW SUBROUTI.e WHICH calculates the "p's" from the timescale ratios.
! --- BA.eD on "smshsc2":
! --- SUBROUTI.e WHICH CALCULA.eS "p's" from "sgmt". BA.eD ON "smshsc1":
! --- .eW SUBROUTI.e WHICH U.eS .e C.eNG'S .orTRAN CO.e TO CALCULA.e CONSTANTS
! --- FROM T.e "p's" .eNT TO .e BY HIM TODAY. BA.eD ON "smshsc0".
! --- **.or.eCT T.e VAL.e OF "p10".**
! --- p_10 = {\tau_{p \theta} \tau_{c \theta}} \over {\tau_c ^ 2}
!
! --- Replace Cheng's smsh with smshsc, which includes concentration.
! --- The y,n,c used here are Canuto's "y,n,c" called c_y,c_n,c_c
! --- elsewhere in this program.
real yyy,nnn,ccc,sm,sh,sc
real Nm,Nh,Nc
!
real p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p1m,p2m
real a0,a1,a2,a3,a4,a5
real d0,d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12,d13,d14,d15
real D
!
integer ifrecall,ifmodelconstout
!
! --- Switch for whether(1) or not(0) to output p's a's and d's to a file.
parameter(ifmodelconstout=0)
!
! --- Add `\tau_pv \over \tau' to the common block with timescale ratios.
!
! --- Calculate the p's.
p1 = 0.832
p2 = 0.545
p3 = (5./2.)*tpcot
p4 = (1./5.)*tpcot*(tcot**(-2))
p5 = tpcot*tctot*(tcot**(-2))
p6 = (1./5.)*(tcot**(-1))*(tctot**(-1))*tptot
p7 = 5.*tctot
p8 = (5./2.)*tptot
p9 = ttot*tptot*((tcot*tctot)**(-1))
p10 = tctot*tptot*(tcot**(-2))
p11 = tpcot*(tcot**(-1))
p1m = 1. - p1
p2m = 1. - p2
!
!-----------------------------------------------------------------------
!results.2_1
! --- Values of a's and d's calculated from p's using Cheng's Fortran code
! --- to do so, from today's email from him, cheng990513.results.2_1 .
! --- results.2_1
!##########################
!## Fortran code:
!##########################
A0 = 12
A1 = p11*(12*p9+8*p6-30*p6*p8-5*p6*(p1m+3*p2m))
A2 = 5*(2*p4*p6*p7-p4*p9-p6*p11)*(p1m+3*p2m)+8*p6*p11+8*p4*p9- &
16*p4*p6*p7+12*p11*p9+12*p11*p10-12*p4*p7**2*p6- &
30*p6*p11*p8+30*p4*p6*p7*p8+30*p6*p4*p7*p3-30*p4*p9*p3
A3 = p10*(12*p11+8*p4-30*p3*p4-5*p4*(p1m+3*p2m))
A4 = -p6*(8-30*p8-5*p1m-15*p2m)-12*p9-12*p11
A5 = -p4*(8-30*p3-5*p1m-15*p2m)-12*p10-12*p11
D0 = 24
D1 = p11*((-p6-2*p9)*p1m**2+(p6+6*p9)*p2m**2+2*p6*p8*(p1m-3*p2m))
D2 = (2*p4*p6*p7-p4*p9-p6*p11)*(p1m**2-p2m**2)+ &
2*(-p11*p10-p11*p9+p4*p7**2*p6)*(p1m**2-3*p2m**2)+ &
2*(-p6*p4*p7*p3-p4*p6*p7*p8+p4*p9*p3+p6*p11*p8)*(p1m-3*p2m)
D3 = p10*((-p4-2*p11)*p1m**2+2*p4*p3*(p1m-3*p2m)+(6*p11+p4)*p2m**2)
D4 = -4*p6*p11*(3*p9+2*p6)
D5 = 4*p4*p6**2*p7*(4+3*p7)-4*p4*p9*(3*p11+2*p6)- &
4*p6*p11*(3*p9+3*p10+2*p4+2*p6)
D6 = 4*p4**2*p6*p7*(4+3*p7)-4*p4*p9*(2*p4+3*p11)- &
8*p4*p6*(p11+p10)-12*p10*p11*(p4+p6)
D7 = -4*p4*p10*(2*p4+3*p11)
D8 = (2*p9+2*p11+p6)*p1m**2-2*p6*p8*(p1m-3*p2m)- &
(p6+6*p9+6*p11)*p2m**2
D9 = (2*p10+p4+2*p11)*p1m**2-2*p4*p3*(p1m-3*p2m)- &
(p4+6*p10+6*p11)*p2m**2
D10 = 8*p6**2+4*(7*p11+3*p9)*p6+24*p11*p9
D11 = -8*(4+3*p7)*p4*p6*p7+4*p4*(4*p6+7*p9+3*p11)+ &
4*p6*(3*p10+7*p11)+24*p11*(p10+p9)
D12 = 4*p10*(7*p4+6*p11)+4*p4*(2*p4+3*p11)
D13 = 6*p2m**2-2*p1m**2
D14 = -28*p6-24*p9-24*p11
D15 = -24*p10-28*p4-24*p11
!results.2_1
!-----------------------------------------------------------------------
!
! --- Write out the p's.
! --- Writeout the timescale ratios as well.
ifrecall=1
if(ifrecall.eq.0 .and. mnproc.eq.1) then
write(lp,*) "tau_pv/tau =",tpvot
write(lp,*) "tau_ptheta/tau =",tptot
write(lp,*) "tau_pc/tau =",tpcot
write(lp,*) "tau_theta/tau =",ttot
write(lp,*) "tau_c/tau =",tcot
write(lp,*) "tau_ctheta/tau =",tctot
write(lp,*) " "
write(lp,*) "p1 =",p1
write(lp,*) "p2 =",p2
write(lp,*) "p3 =",p3
write(lp,*) "p4 =",p4
write(lp,*) "p5 =",p5
write(lp,*) "p6 =",p6
write(lp,*) "p7 =",p7
write(lp,*) "p8 =",p8
write(lp,*) "p9 =",p9
write(lp,*) "p10=",p10
write(lp,*) "p11=",p11
!
! --- Write out the a's and d's as well.
write(lp,*) "a0=",a0
write(lp,*) "a1=",a1
write(lp,*) "a2=",a2
write(lp,*) "a3=",a3
write(lp,*) "a4=",a4
write(lp,*) "a5=",a5
write(lp,*) "d0=",d0
write(lp,*) "d1=",d1
write(lp,*) "d2=",d2
write(lp,*) "d3=",d3
write(lp,*) "d4=",d4
write(lp,*) "d5=",d5
write(lp,*) "d6=",d6
write(lp,*) "d7=",d7
write(lp,*) "d8=",d8
write(lp,*) "d9=",d9
write(lp,*) "d10=",d10
write(lp,*) "d11=",d11
write(lp,*) "d12=",d12
write(lp,*) "d13=",d13
write(lp,*) "d14=",d14
write(lp,*) "d15=",d15
!
! --- Output p#, a# and d# to the file model_constants if the switch is set.
! --- Writeout the timescale ratios as well.
if(ifmodelconstout.eq.1 .and. mnproc.eq.1) then
open(unit=uoff+98,file='model_constants',status='unknown')
write(uoff+98,*) "tau_pv/tau =",tpvot
write(uoff+98,*) "tau_ptheta/tau =",tptot
write(uoff+98,*) "tau_pc/tau =",tpcot
write(uoff+98,*) "tau_theta/tau =",ttot
write(uoff+98,*) "tau_c/tau =",tcot
write(uoff+98,*) "tau_ctheta/tau =",tctot
write(uoff+98,*) " "
write(uoff+98,*) "p1 =",p1
write(uoff+98,*) "p2 =",p2
write(uoff+98,*) "p3 =",p3
write(uoff+98,*) "p4 =",p4
write(uoff+98,*) "p5 =",p5
write(uoff+98,*) "p6 =",p6