Question about the scalar transport equation used in ROMS

[Diego]

I am writing an ecosystem-focused manuscript (we used ROMS with BIO_FENNEL). At the moment I am writing the equations and I am a bit confused about the scalar transport equation used in ROMS. Maybe someone can help me out:


Below is a general scalar transport equation commonly used by biological oceanographers to show how physical and biological fields are coupled:

General scalar transport equation

Eq1.jpg (66.25 KiB) Viewed 1637 times

Below is the scalar transport equation from WikiROMS

Scalar transport equation from WikiROMS (Jul 2010)

Eq2.jpg (38.67 KiB) Viewed 1637 times

Everything is straightforward to me with the exception of the diffusive term (Dc). I was reading the Wiki section about Transverse Stress Tensors and also Wajsowicz (1993), and it is not clear to me whether Dc is equal to the horizontal turbulent diffusivity terms from the first equation. Or in other words, is the equation below is correct??:

Is this correct???

Eq3.jpg (35.71 KiB) Viewed 1637 times

If anybody can give me a hand with my "diffusivity problems"... it would be greatly appretiated!

Regards,

Diego

[arango]

Actually, you are looking at the wrong equations. The above equations are the generic primitive equations in Cartesian coordinates. The tracer equations that ROMS are solving are in flux form and curvilinear coordinates. They are also shown in WikiROMS in the curvilinear coordinates transformation page.

The deviatory stress tensor is a viscosity formulation. It is for the momentum equations only. The terms for this tensor are show also in WikiROMS in the horizontal mixing page.

The vertical and horizontal diffusion depends on your C-preprocessing options for tracer diffusion. The isopycnal diffusion is based on the Redy tensor. The equations are not in WikiROMS but in my hand written notes which are available in the ROMS website. The vertical and horizontal diffusion are split. The vertical diffusion looks like the one that you have above but in flux form (see equation 5 above).