Final set of model constants for the GLS turbulence closures

[lanerolle]

I have noticed that for each different version of ROMS released, the constants sets/names associated with the GLS eddy-viscosity parameterizations appear to change. For example, normally we have GLS MY, GLS k-epsilon, GLS k-omega, GLS k-tau as options and the current version of ROMS I am using (3.0 and higher) does not appear to have GLS MY, GLS k-tau but instead has GLS k-kl and something called "gen" (all this is from the documentation in ocean_X.in). Sometimes, the constants associated with the same GLS parameterization (eg. k-omega, k-tau, etc.) appear to be different in different versions of the ROMS (released).

I have done some experiments with a meteorologically forced 1d mixing model problem and found that the eddy-viscosities/diffusivities coming out of the different GLS parametizations (and the MY2.5) are drastically different to each other.

Could someone please confirm:

(1) what the final set of parameterizations associated with the GLS scheme are? and,
(2) what the final set of model constants associated with each of these parameterizations are?

[jcwarner]

The GLS closure is a formulation of a two-equation turbulence closure model with variable coeffcients. The advantage of this scheme is that only one formulation needs to be implemented numerically. Then the user sets values for the coefficients and the closure scheme will become numerically equivalent to any number of two-equation models. For example, the user sets specific values for 'p', 'm', and 'n' and the closure method will be equivalent to the k-epsilon model, and a different set of 'p''m'and 'n' values will yield a closure scheme of k-omega (for example). I appologize if the scheme names have changed over the years, but, well, things change.

I believe the coefficeints are mostly the same as that appearing in our Ocean Modeling paper, "Performance of four turbulence closure models implemented using a generic length scale method " by Warner, Sherwood, Arango, and Signell, Ocean Modelling 8 (2005) 81–113.
In that paper, Table 1, p.87, are coefficient sets for:
1) k-epsilon, or sometimes k_e, or k-e.
2) k-omega, or sometimes k_w, or k-w.
3) k-gen, or sometimes just gen. This is setting the coefficients as described in the Umlauf and Burchard 2003 paper.
4) k-kl , or sometime k_kl, which is a version of the Mellor Yamada 2.5 closure. They used q^2 and q^2 l (el), where k=1/2 q^2. I wanted to be very clear that using GLS with this set of coefficients was not exactly equivalent to MY25, because of the way the length scale limitations were imposed (see discussion in the paper). Since all the others were k-something, i think i was the one who started to use k-kl, just to be consistent. If i am mistaken, someone can correct me.

There are a plethora of other two-equation models out there. Some work, some do not work. For example, there is a k-tau, k-omega^2, etc etc. I had not tested all these, and I did not feel comfortable providing coefficient set values for closures that I did not try. So i removed some of them along the way. The ones that are described in the ocean*.in files are the ones that we used in our Ocean Modeling paper, and they have been tested and i feel comfortable supporting those sets. If you want to try other coefficients sets, go ahead. That is the beauty of coding in the GLS method. All you have to do is change the coefficient values.

I am comparing the values in the ocean*.in files to our paper, and i see some subtle changes. But use the values in the ocean*.in files. There have been some slight changes along the way, but i recommend to use the values in the ocean*.in files. If you have specific questions, post them back here and i can dig thru the notes for more information.
-john

[susonic]

Hi Dr. Warner,

I've got some questions about various GLS vertical mixing schemes.
According to Warner et al(2005) on table no.2,
1. if I use k-epsilon with the Kantha and Clayson stability function,
is nessasary to change the GLS_CMU0 value from 0.5477(ocean.in) to 0.5544(from the paper)?
2. What about the GLS_CMU0 value if I want to use CanutoA stability function for each of k-epsilon, k-omega, k-kl and gen?
3. What is the GLS_CMU0 value supposed to be if I use the Galperin stability function ?
I'm not understanding... Please help me.

Regrads,

-Peter

[jcwarner]

A lot of these coefficients are empirical. Some of the values could have been modified over the past few years, i have not kept up well with that literature. A good place to check would be what the GOTM crowd is doing. From the paper, the gls_cmuo value should be 0.5544 when used with the KC stability function for any selection of p-m-n values. Table 2 shows the cmuo values for Canuto A and B, for any choice of the p-m-n sets. For Galperin i would suggest the KC values.

[susonic]

Thanks for your quik reply, Dr. Warner.

In your previous article which is right above my question, you mentioned this

but i recommend to use the values in the ocean*.in files.

and you just wrote that

From the paper, the gls_cmuo value should be 0.5544 when used with the KC stability function for any selection of p-m-n values.

I'm little bit confused...
So based on the paper, for the k-epsilon with Kantha Clayson, GLS_CMU0 value should be 0.5544.
Then based on which stability function is the GLS_CMU0 value in ocean.in(0.5477)?