[MITgcm-support] ISOMIP compressibility

[Christopher Pitt Wolfe]

The difference between the “truly” incompressible and the semi-compressible Boussinesq equations is all in the equation of state. In the “truly” impressible equations, density does not depend on pressure at all while the semi-compressible equations allow the density to depend on the hydrostatic pressure due to the reference density. This is the standard set used in oceanography and most people just call these the Boussinesq or incompressible equations since the compressibility doesn’t affect dynamics, just thermodynamics.

The ISOMIP reference experiment uses the JMD95Z equation of state, which depends on the above hydrostatic pressure. So the ISOMIP experiment would be using the semi-compressible equations.

Christopher

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Christopher L. Pitt Wolfe
Associate Professor (Physical Oceanography)
School of Marine and Atmospheric Sciences
Stony Brook University
christopher.wolfe at stonybrook.edu             631-632-3152
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> On Nov 4, 2021, at 6:11 AM, Martin Losch <Martin.Losch at awi.de> wrote:
> 
> Arran,
> 
> the isomip verification experiment uses hydrostatic (because nonHydrostatic=.FALSE. in data, defining ALLOW_NONHYDROSTATIC only compiles the code) and incompressible equations.
> 
> In general, I have always thought the the non-hydrostatic code always uses incompressible equations.
> 
> I am not entirely sure about the documentation, but 1.5.1.4 (where you find eq 1.98-1.103) also contains the statement that “it is the hydrostatic () form of these equations that are used throughout the ocean modelling community …”
> I agree that this is a little misleading. But note, that 1.100 (non-divergent velocity field) implies incompressibility, so I am not quite sure what the section heading means here, maybe someone else can explain.
> 
> Martin
> 
>> On 3. Nov 2021, at 21:11, Arran Whiteford <arran.whiteford at vuw.ac.nz> wrote:
>> 
>> Hullo,
>> 
>> I'm trying to figure out what versions of the Boussinesq equations the ISOMIP tutorial example is solving 
>> https://github.com/MITgcm/MITgcm/tree/master/verification/isomip
>> 
>> It includes non hydrostatic code.
>> #define ALLOW_NONHYDROSTATIC https://github.com/MITgcm/MITgcm/blob/master/verification/isomip/code/CPP_OPTIONS.h
>> 
>> In the MITgcm documents it explains:
>> 1.3.4.4.2. Ocean
>> Non-hydrostatic forms of the incompressible Boussinesq equations in z- coordinates are supported - see eqs. (1.98) to (1.103).
>> 
>> BUT eqns (1.98) to (1.103) are not the incompressible eqns, they are the semi-compressible.
>> https://mitgcm.readthedocs.io/en/latest/overview/hydrostatic.html
>> 
>> In the non-hydrostatic ocean model all terms in equations Eqs.(1.29 →
>> 1.31) are retained.
>> 
>> Which is true? Is the nonhydrostatic code running incompressible or semi-compressible Boussinesq equations?
>> 
>> Thanks,
>> Arran
>> 
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