bustr bvstr units confusion

[Honolulu_Wang]

Hi all,
I met some problem and confusion for the bustr/bvstr units.
In the ROMS code: Modules/mod_forces.F:
! Bottom momentum stresses. !
! !
! bustr Kinematic bottom momentum flux (bottom stress) in !
! the XI-direction (m2/s2) at horizontal U-points. !
! bvstr Kinematic bottom momentum flux (bottom stress) in !
! ETA-direction (m2/s2) at horizontal V-points. !
It tells the unit is m2/s2.
But in the var_info.dat file it said the uiit is N/m2.
My understanding of this inconsistency is that, ROMS did a scale transformation by a function FUNCTION nf_fwrite2d, making the scale equates -rho for scale transformation, so we will get N/m^2 for bvstr/bustr in the outputfile directly, named " bottom U-momentum stress". I guess ROMS did this for convenience.

! Write out bottom U-momentum stress.
!
IF (Hout(idUbms,ng)) THEN
scale=-rho0
gtype=gfactor*u2dvar
status=nf_fwrite2d(ng, iNLM, HIS(ng)%ncid, HIS(ng)%Vid(idUbms), &
& HIS(ng)%Rindex, gtype, &
& LBi, UBi, LBj, UBj, scale, &
& GRID(ng) % umask_io, &
& FORCES(ng) % bustr)
IF (status.ne.nf90_noerr) THEN
IF (Master) THEN
WRITE (stdout,10) TRIM(Vname(1,idUbms)), HIS(ng)%Rindex
END IF
exit_flag=3
ioerror=status
RETURN
END IF
END IF


MODULE nf_fwrite2d_mod
!
!svn $Id: nf_fwrite2d.F 585 2012-01-03 18:44:28Z arango $
!================================================== Hernan G. Arango ===
! Copyright (c) 2002-2012 The ROMS/TOMS Group !
! Licensed under a MIT/X style license !
! See License_ROMS.txt !
!=======================================================================
! !
! This function writes out a generic floating point 2D array into an !
! output NetCDF file. !
! !
! On Input: !
! !
! ng Nested grid number. !
! model Calling model identifier. !
! ncid NetCDF file ID. !
! ncvarid NetCDF variable ID. !
! tindex NetCDF time record index to write. !
! gtype Grid type. If negative, only write water points. !
! LBi I-dimension Lower bound. !
! UBi I-dimension Upper bound. !
! LBj J-dimension Lower bound. !
! UBj J-dimension Upper bound. !
! Amask land/Sea mask, if any (real). !
! Ascl Factor to scale field before writing (real). !
! A Field to write out (real). !
! SetFillVal Logical switch to set fill value in land areas !
! (optional). !
! !
! On Output: !
! !
! nf_fwrite Error flag (integer).


But for the ROMS coding calculating itself, bustr/bvstr units are still the same m2/s2,and its value remain the one before scale/unit transformation and remain same units m2/s2 for its subroutine and biological module and sediment module.
This could better explain in the following code calculation tke and bustr in the mod_mixing.F

tke(i,j,0,nnew)=MAX(cmu_fac3*0.5_r8* &
& SQRT((bustr(i,j)+bustr(i+1,j))**2+ &
& (bvstr(i,j)+bvstr(i,j+1))**2), &
& gls_Kmin(ng))
So units between bvstr, tke, gls_Kmin should be consistent:m2/s2

Is this same from your understanding?
What I am doing now will need the value of bvstr/bustr for some extended subroutine, so hopefully have a better understanding of value.

Thanks for your answer.

[wilkin]

Yes, internally ROMS carries the surface and bottom stresses (sustr, bustr, etc.) in kinematic units of stress divided by reference density (parameter rho0 in ROMS), which is then units of m2/s2.

This is clear in set_vbc.F for simple bottom drag formulae such as quadratic:

Code: Select all

#   elif defined UV_QDRAG
!
!  Set quadratic bottom stress.
!
      DO j=Jstr,Jend
        DO i=IstrU,Iend
          cff1=0.25_r8*(v(i  ,j  ,1,nrhs)+                              &
     &                  v(i  ,j+1,1,nrhs)+                              &
     &                  v(i-1,j  ,1,nrhs)+                              &
     &                  v(i-1,j+1,1,nrhs))
          cff2=SQRT(u(i,j,1,nrhs)*u(i,j,1,nrhs)+cff1*cff1)
          bustr(i,j)=0.5_r8*(rdrag2(i-1,j)+rdrag2(i,j))*                &
     &               u(i,j,1,nrhs)*cff2

Here the components of velocity (u,v) are being averaged to the u-point on the staggered grid (as is the drag coefficient, which can be spatially varying and is notionally defined at the rho-point position on the staggered grid) before computing the velocity magnitude (cff2), then bustr is the velocity magnitude times drag coefficient times u-component of velocity.

bustr has units m2/s2 and is defined on the u-point of the grid.

Similarly, bvstr will be defined at the v-points grid.

The magnitude of the vector [bustr,bvstr] is the familiar "u-star" in fluid dynamics, being the bottom stress divided by rho0.

If you wish to use bottom stress in a parameterization of, say, particulate matter resuspension rate or a settlement criterion for larvae, then you need to calculate the stress magnitude by averaging to a common location on the staggered grid (most rationally the rho-points) and work with that. e.g.:

Code: Select all

       TauB=rho0*SQRT((0.5_r8*(bustr(i,j)+bustr(i+1,j)))**2+ &
     &            (0.5_r8*(bvstr(i,j)+bvstr(i,j+1)))**2)

Here, TauB will be at rho-point (i,j) in units of Pascal = Newton/m2.