[Edited] Vertical profiles of EKE budget terms

[flq321]

Hi all,
I am trying to obtain vertical profiles of terms in the EKE budget where the fluctuations are defined with respect to the zonal mean. I am using 3 months of ROMS output at 3 km resolution from a simulation of the Kuroshio region. All my analysis is offline using the instantaneous history files. Because the vertical grid varies in space and time in ROMS, I am following these steps:

1. At each time, for each (x,y), interpolate the vertical column of fields onto predefined depths (10 m, 20 m, 30 m, etc.). This gives me a new 3d spatial array for the fields at each time where the vertical coordinate is now uniform.

2. For each 'y' location, compute zonally-averaged terms in the EKE budget using the newly created 3d arrays in step 1. Repeat this at each 'y' and average across 'y'. Accumulate the terms in time.

3. Average each term over time to get the time-averaged EKE budget.

I am attaching a couple of figures, one plotting the terms and the other showing the expressions I am using. (Nothing fancy here, just standard EKE analysis)

[EDIT: In the writeup, I forgot to add two more contributions to the shear term which are included in the plot:

- <u'v'> dU/dy - <v'v'> dV/dy
]

When I try the above steps, a couple of terms look problematic: the subgrid mixing terms and the pressure-work terms.

The subgrid mixing term appears to be quite large (too large?) as I am expecting the budget to be at least in approximate balance. Note I have not split the subgrid term into a negative-definite term ("destruction") and a "diffusion" term. As a result, the subgrid term can have either sign.

Secondly, the pressure-work term occasionally jumps to large values deep down in the interior. Am not entirely clear why is this happening.

I have seen lots of papers report depth-integrated EKE budgets but have not come across too many that show the full vertical profile of each term in the EKE budget over the entire water column (any references are welcome).

Thanks for your help.

[PS: I have additional questions regarding the computation of spectral fluxes of terms in the EKE budget. I will post them in a subsequent thread.]

[larspr]

Hi flq321,
I don't know if it's relevant, but for some years my colleagues and myself did some work where we struggled with making suitable energy budget calculations for terrain-following as well as layered coordinate ocean models. Four of the resulting publications are listed below. In these papers we worked out what we defined as mean kinetic energy (MKE), eddy kinetic energy (EKE), mean available gravitational potential energy (MAGE) and eddy available gravitational potential energy (EAGE). We also worked out the time rate of change of each of the energy parts and thereby all the reversible and irreversible energy conversion terms. It tuns out that there is an ambiguity in the conversion term between total AGE and total KE, as for instance explained in Røed (1999). This ambiguity has a decisive impact on the various conversion terms. Perhaps the most relevant papers to you are Albretsen (2007) and Fossum and Røed (2004, 2006), which include examples of use for terrain-following coordinate models (ROMS and POM).

Røed, Mon. Wea. Rev. (1999) 127 (8): 1897–1911, DOI 10.1175/1520-0493(1999)127<1897:APEDSF>2.0.CO;2
Røed & Fossum, Ocean Dynamics (2004) 54: 197–220, DOI 10.1007/s10236-003-0076-1
Fossum & Røed, Journal of Marine Research, 64, 319–353, 2006, DOI 10.1357/002224006778189617
Albretsen: Ocean Dynamics (2007) 57:287–304, DOI 10.1007/s10236-007-0121-6

Best regards
Lars Petter Røed

[arango]

Thank you, Lars. Those are great references. I added them to my reading list. A couple of decades ago, I tried to derive an energy conservation equation for ROMS, so the only way to add energy to the system is from external forcing. I was unable to eliminate the pressure gradient term because of the terrain-following coordinates. I tried all the tricks that I knew, but I never got a satisfactory solution. The question that I was trying to answers is: Does terrain-following coordinating conserve total energy?

[flq321]

Thanks very much for the references! I will check them out.