## Set geostrphically balanced initial current

General scientific issues regarding ROMS

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chenxufsu
Posts: 8
Joined: Thu Apr 09, 2015 6:35 pm
Location: Florida State University

### Set geostrphically balanced initial current

Hello Everyone,
I am trying to set a initial condition of geostrophically balanced current in a channel.
I set velocity field first and calculate the temperature field through geostrophic balance and linear relationship between the density and temperature as salinity is set to be zero. However, strong internal wave generated and break the geostrophic field. Anyone have a suggestion on how to set a geostrophic flow for initial condition? Thank you!

shchepet
Posts: 185
Joined: Fri Nov 14, 2003 4:57 pm

### Re: Set geostrphically balanced initial current

I set velocity field first and calculate the temperature field through geostrophic balance
It is usually works the other way around: density field + free surface (via level of no motion or some other idea of this sort) ==> pressure field ==> pressure gradient ==> velocity field

chenxufsu
Posts: 8
Joined: Thu Apr 09, 2015 6:35 pm
Location: Florida State University

### Re: Set geostrphically balanced initial current

Thank you very much! it works well now!
shchepet wrote:
I set velocity field first and calculate the temperature field through geostrophic balance
It is usually works the other way around: density field + free surface (via level of no motion or some other idea of this sort) ==> pressure field ==> pressure gradient ==> velocity field

shchepet
Posts: 185
Joined: Fri Nov 14, 2003 4:57 pm

### Re: Set geostrphically balanced initial current

There is one more thing to add to this topic specifically related to the fact that you may
want not just geostrophic balance, but the geostrophic balance as it would be felt by the
discrete model
, i.e., ROMS.

ROMS uses C-grid, which means that discrete us and vs in Coriolis terms are
subject to 4-point horizontal averaging, so the discrete geostrophic balance exists in a bit
awkward sense: <4-point-averaged u> = -(1/f) * (1/rho0) * dp/dy
and <4-point-averaged v> = +(1/f) * (1/rho0) * dp/dx where p is defined at rho-points.

The problem is that imagine that p contains checker-board mode, so dp/dy and dp/dx would
contain it as well because the differencing is only over 1 dx and 1 dy in each direction.
However 4-pint averaged velocity components cannot admit it, so there is no way to balance.

To address this one have to ensure that checkerboard mode should be excluded entirely from
the pressure and tracer fields defined at RHO points. This leads to a rather simple recipe
how to generate analytical geostrophically-balanced initial conditions in ROMS (or any other
C-gridded model):

1. Define temporal T,S (or density field) and free surface at horizontal vorticity points and
place them into scratch arrays.

2. Compute U and V by vertically integrating density computed from these temporal field
(still defined at vorticity points) and differencing the resultant pressure field (naturally
differencing over 1 dx in each direction).

3. Horizontally average T,S and vorticity fields defined in (1) using 4-point averaging, so
the outcome in at RHO-points. Accept them as the final fields.

chenxufsu
Posts: 8
Joined: Thu Apr 09, 2015 6:35 pm
Location: Florida State University

### Re: Set geostrphically balanced initial current

shchepet wrote:There is one more thing to add to this topic specifically related to the fact that you may
want not just geostrophic balance, but the geostrophic balance as it would be felt by the
discrete model
, i.e., ROMS.

ROMS uses C-grid, which means that discrete us and vs in Coriolis terms are
subject to 4-point horizontal averaging, so the discrete geostrophic balance exists in a bit
awkward sense: <4-point-averaged u> = -(1/f) * (1/rho0) * dp/dy
and <4-point-averaged v> = +(1/f) * (1/rho0) * dp/dx where p is defined at rho-points.

The problem is that imagine that p contains checker-board mode, so dp/dy and dp/dx would
contain it as well because the differencing is only over 1 dx and 1 dy in each direction.
However 4-pint averaged velocity components cannot admit it, so there is no way to balance.

Thank you! really helpful

To address this one have to ensure that checkerboard mode should be excluded entirely from
the pressure and tracer fields defined at RHO points. This leads to a rather simple recipe
how to generate analytical geostrophically-balanced initial conditions in ROMS (or any other
C-gridded model):

1. Define temporal T,S (or density field) and free surface at horizontal vorticity points and
place them into scratch arrays.

2. Compute U and V by vertically integrating density computed from these temporal field
(still defined at vorticity points) and differencing the resultant pressure field (naturally
differencing over 1 dx in each direction).

3. Horizontally average T,S and vorticity fields defined in (1) using 4-point averaging, so
the outcome in at RHO-points. Accept them as the final fields.