Need help on the understanding of Mellor-Yamada model

[Mary Zhu]

Hi, 

         I'm new in studying about different kinds of turbulence closure, and I would appreciate it if anyone can help answer the following questions. 

         1. The first question starts at the settings of using MellorYamada model(see the table below). 

	./channel/MellorYamada.xml	./entrainment/MellorYamada.xml	./couette/MellorYamada.xml
turb_method	3	3	2
tke_method	3	3	3
len_scale_method	9	9	9

              In these three xml files, the turb_methods differ.  Which one should I choose if I want to use MY82 model? Or they are actually the same?

        2. I've  been taking MY82(no matter level 1, 2, 2.5, 3 or 4) as  second-order Reynolds-stress models for a long time. Are they all second-order models? Are they Reynolds-stress models? 

             I'm not sure about whether they are Reynolds stress models because According to the book Turbulent Flows written by S. B. Pope,  in a  Reynolds-stress model 'model transport equations are solved for the individual Reynolds stresses <uiuj> and for the dissipation. Consequently, the turbulent-viscosity hypothesis is not needed'. But after going through the whole process of GOTM computation I found that no matter turb_method=2 or turb_method=3, it eventually comes to the computation of  viscosity and diffusion. So it seems that MY82 adopts the turbulence-viscosity hypothesis. Was it a Reynolds-stress model? or Did I make a misunderstanding about MY82?

           

Best regards

Mary

[Lars Umlauf]

Hi Mary,

For MY82, you should use 3/3/9, as you write below. This solves two transport equations for the TKE and the product of  TKE and some integral length scale, exactly as described in MY82. Please have a look at their paper and our documentation:

http://www.gotm.net/pages/documentation/manual/devel/html/node73.html
http://www.gotm.net/pages/documentation/manual/devel/html/node75.html

Regarding your other questions: GOTM does not solve the full (differential) equations for all the second moments. These equations are made algebraic, using some assumptions that are summarized in the attached review paper. It turns out that, in many cases, the full set of algebraic second moment equations can be condensed to vertical gradient laws involving an eddy diffusivity that is proportional to a so-called "stability function" (see attached paper).

In gotmturb.nml, you need to tell the model which coefficient you want to use for your second-moment model. For MY82, this would be scnd_coeff=2. Many people, however, prefer the more recent version by Kantha and Clayson (1994), which would be scnd_coeff=3.

Hope that helps.

Lars

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Lars Umlauf

Physical Oceanography and Instrumentation
Leibniz-Institute for Baltic Sea Research

phone : ++49 381 5197 223
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