[MITgcm-support] increased total energy (kinetic and potential energy) in mitgcm model

[Andrew Hogg]

Hi Yang

I suspect what is happening here is that you have a vertical diffusion of buoyancy (explicit, numerical or both) which is acting to increase the centre of mass of the water column, thereby increasing the background potential energy. A better metric of the total energy of the flow is mechanical energy =  kinetic + available potential energy. Finding available potential energy is a non-trivial task - it requires you to subtract background potential energy from the total potential energy, but I may be able to provide a script to do this for you. If you're interested, first have a read of this paper:

G. O. HUGHES, A. McC. HOGG & R. W. GRIFFITHS (2009). Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr., 39, 3130-3146.

and then get back to me.

Cheers
Andy

On 18/08/2013, at 10:18 AM, "Jiao, Yang" <yj10 at my.fsu.edu<mailto:yj10 at my.fsu.edu>>
 wrote:


I should add that the order of this growth is very small O(10^4) compared to the magnitude of total energy O(10^8), and was mainly contributed by growth in potential energy.


Yang

From: Jiao, Yang [yj10 at my.fsu.edu<mailto:yj10 at my.fsu.edu>]
Sent: Saturday, August 17, 2013 7:42 PM
To: MITgcm-support at mitgcm.org<mailto:MITgcm-support at mitgcm.org>
Subject: [MITgcm-support] increased total energy (kinetic and potential energy) in mitgcm model


Hi everyone,


I'm having problem in the total energy (kinetic and potential energy) evolution of my non-hydrostatic models. I was trying to simulate a water flow in a rectangular channel (cross section 24km*1km) with an initial condition, a current satisfying some instability criterion (all variables are y-independent, which is the direction along the channel).


The total energy is supposed to decrease all the time, but when I used a 4800*3*500 (nx*ny*nz) grid points model to simulate the flow and choose different horizontal eddy viscosity parameters (Ah=0.05~0.5m^2/s), the total energy will increase for small Ah values. And I used 1600*3*500  model to simulate a similar initial condition but without satisfying the instability criterion, the total energy had a perfect linear growth during the whole model run, and it didn't change much no matter what Ah I choose in the 0.05~0.5 range.


I used area integration of the cross section of the channel to get the energy using matlab. Kinetic energy is u^2/2 and potential energy is -z*b (negative depth*buoyancy) for each cell. I used 3 second time interval but using smaller values won't help. Adding density into the energy also won't change anything.


Does anyone also have this kind of issue before? Is there any clue on what caused this?


Thanks,

Yang
Graduate student
EOAS, Physical Oceanography
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