[Mitgcm-support] Re: Bottom Drag Terms

mitgcm-support at dev.mitgcm.org mitgcm-support at dev.mitgcm.org
Wed Jul 9 15:51:16 EDT 2003


Alistair,

  I don't really remember, but I think the if(no_slip_bottom) part was simply
historical.  I developed my adjustment of the original code keeping the
no_slip_bottom flag.  This did prove useful for me to debug the implicit
diffusion problem, since I could let no_slip_bottom be false, and return to
your original code.  At this point, I don't think there's much reason to keep
it.

The drag term in the equations of motion is (conventionally)

du/dt ... = ... + (1/rho)ddz(u'w')


Quadratic:
-(u'w')@bottom = tau_b = Cd rho |u| u
Cd, the quadratic drag coeff, is non-dimensional.
Units:
tau_b ~ N/m^2 = kg /ms^2
rho |u|u ~ kg/m^3 m/s m/s ~ kg/m s^2 

Linear:
-(u'w')@bottom = tau_b = r rho u
r, the linear drag coeff, is in units m/s.
r rho u ~ m/s kg/m^3 m/s ~ kg/m s^2

For shallow water flow, the divergence of the stresses should lead to
du/dt ... = ... - ru/H -Cd|u|u/H
which shows an equivalent check for r (m/s) and Cd (nd).


Haven't yet tried the flux-corrected transport.  Good seeing you Friday.

                                                -Chris

On 15-Feb-2001 Alistair Adcroft wrote:
> Hi Chris (E),
> 
> Did you take a look at c35 yet?
> 
> I'm in the process of re-organizing the calc_mom_rhs.F to allow vector
> invariant form and noticed these lines near the top:
>       IF (no_slip_bottom) THEN
>        bottomDragTerms=.TRUE.
>       ELSE
>        bottomDragTerms=.FALSE.
>       ENDIF
> 
> which imply we can only use the linear of quadratic drag if
> we also use the no-slip boundary condition for viscosity too.
> I know I wrote the above but can't quite figure the reasoning!
> Probably just a quick decision to get it done before you left
> that day. Except for very large viscosities it probably doesn't
> matter but it seems like an unnecessary inflexibility.
> Any reason not to fix this?
> 
> Also, the quantity
>      &      2.*KappaRU(i,j,kp1)*rkFac*rdrckp1
>      &     + bottomDragLinear
>      &     + bottomDragQuadratic*sqrt(KE(i,j)+KE(i-1,j))
>      &    )*(1.-maskDown)*uVel(i,j,k,bi,bj)
> is meant to be the divergence of a stress (the rho's get cancelled).
> Do we have the conventional units for bottomDragLinear
> and bottomDragQuaratic? I think CNH asked me this earlier but I
> didn't know.
> 
> A.

-- 
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Christopher Edwards                     christopher.edwards at uconn.edu
Department of Marine Sciences           phone: (860) 405-9173
University of Connecticut               fax: (860) 405-9153
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