[MITgcm-support] Diagnostic calculation of buoyancy frequency with nonlinear equation of state

[Martin Losch]

Hi Sonya,

with MDJWF the pressure in the EOS is not simply depth, but pressure as the depth levels, computed from the hydrostatic pressure equation, so computing density offline is a little more complicated.

I would use the diagnostics field DRHODR, which gives the vertical gradient of density, as the model uses it, to compute buoyancy, i,e. N2 = -r/rho0 * DRHODR.

Martin

> On 8. Sep 2022, at 17:36, Sonya Legg - NOAA Affiliate <sonya.legg at noaa.gov> wrote:
> 
> Hi all, 
> 
> I'd like to hear about your experiences diagnosing the buoyancy frequency in simulations with a nonlinear equation of state. Here's what I am doing: 
> 
> - I'm using the MDJWF eos
> - I'm assuming that the pressure used in the equation of state is simply given by the depth, i.e. pressure(k) = -Z(k)
> - I'm using centered differencing, i.e. N2 = -g/rho0*(rho(k)-rho(k+1))/(Z(k) -Z(k+1)), where k increases downward following MITgcm convention. Z=RC
> - I calculate the density of both the upper and lower parcel if they were at the pressure corresponding to the intermediate location, i.e. at (Z(k) + Z(k+1))/2
> -  This mostly produces sensible looking results. However, the particular simulation that I am analyzing has some deep layers of almost homogeneous fluid (remnants of earlier mixing), which are giving N2< 0 results (where I would expect N2=0), despite no indication of any convective velocities in those regions. (In these nonhydrostatic simulations there are other regions with overturns and plenty of turbulence). 
> 
> I'm thinking there must be something I'm missing, having grown up in linear-eos world. 
> Anyone have a matlab N2 routine for nonlinear eos I can compare with?
> 
> Thanks
> Sonya
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