# Ocean Modeling Discussion

ROMS/TOMS

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 Post subject: Akt, Akv, VISC2 and TNU2 coefficientsPosted: Fri Oct 21, 2011 9:17 am

Joined: Mon Mar 07, 2011 5:37 pm
Posts: 52
Location: HYDRATEC
Hi Roms users,

I want to simulate influence of wind upon a stratified basin. So I use ANA_SMFLUX, and GLS_MIXING. But I have some questions about ocean.in file:

1. What is the difference between R0 (density for state equation) and RHO0 (mean density)?
2. How can I determine values of mixing coefficients (both vertical, Akt and Akv, and horizontal, VISC2 and TNU2), or are there common values?

Antoine

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 Post subject: Re: Akt, Akv, VISC2 and TNU2 coefficientsPosted: Fri Oct 21, 2011 5:38 pm

Joined: Wed Jul 02, 2003 5:29 pm
Posts: 3633
Location: IMS/UAF, USA
antoinemarie wrote:
1. What is the difference between R0 (density for state equation) and RHO0 (mean density)?
You've got it - it is in how they are used. If you study the equations of motion, there is a rho0 that appears in places as the mean density. There is also a rho that varies in space and time, computed in the equation of state.
Quote:
2. How can I determine values of mixing coefficients (both vertical, Akt and Akv, and horizontal, VISC2 and TNU2), or are there common values?
The vertical mixing is a whole field in itself. You are obtaining those values from the GLS scheme that you've chosen.

For the horizontal, you usually just want something small to keep things smooth and numerically stable. There are some pointers in the back of the manual which I should probably put on the wiki somewhere - like here

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 Post subject: Re: Akt, Akv, VISC2 and TNU2 coefficientsPosted: Fri Oct 21, 2011 11:27 pm

Joined: Wed Feb 26, 2003 4:41 pm
Posts: 1078
Location: IMCS, Rutgers University
The RHO0 is a very important quantity in ROMS and is due to the Boussinesq approximation: the horizontal density gradients are very small so it can be neglected, except where they appear in the governing equations multiplied by the acceleration due to gravity, g, which is assumed constant. This is used in terms like the pressure gradient, buoyancy, etc. The inertia in the fluid is very small compared to the gravity exerted over the fluid. Therefore, this is a very important approximation constant and have values of the order of RHO0=1025 kg/m3.

Contrarily, R0 is a less important constant and rarely used except when the linear equation of state is invoked. The linear equation of state is only used in highly idealized ROMS applications. The seawater is a nonlinear function of temperature, salinity, and pressure. It you derive the linear equation of state using calculus of variations, you will see where R0 comes from. R0 is in term of density anomalies and has a typical value of R0=25 kg/m3.

Therefore, RHO0 and R0 are a very different constants...

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