[MITgcm-support] Re: single layer run

[Baylor Fox-Kemper]

I agree with Jason that eventually, all motion will die.   However, 
much could occur in the interim...The time scales are, roughly in order 
for small viscosity and drag:

L/sqrt(g*H) for surface gravity wave radiation, kelvin wave 
propagation, and tsunamis

1/f for (nearly inviscid geostrophic flow adjustment to inertial 
oscillations about the final state)

1/grad(U) for the growth rate of barotropic instabilities off of the 
inertially-oscillating flow

L_basin/(beta*L^2) is the timescale for the Rossby wave to propagate 
west, send a kelvin wave around the basin and radiate from the eastern 
boundary to fill the hole (although it will not produce a steady state 
when it gets there unless friction acts).

1/r for bottom drag (r is bottom drag, in time^-1 units)

L^2/nu for lateral friction (L is scale of pressure anomaly, nu is 
viscosity)

So, you can see that if there is very little friction, interesting 
things may happen at first, but eventually the friction will slow 
everything down to a motionless state.  The degree to which the initial 
adjustment will be geostrophic rather than tsunami-like, should depend 
on the magnitude of the initial pressure change, I suppose.  If 
U/sqrt(gH) > 1, then you get a hydraulic jump and a tsunami carries a 
lot of fluid away, else if U<<sqrt(gH) the gravity waves don't carry 
away much fluid, only energy and the geostrophic adjustment and 
subsequent ageostrophic resettlement wins.

Cheers,
-Baylor

On May 13, 2005, at 10:55 AM, Martin Losch wrote:

> Hi,
>
> I guess I have to give in (o:
> If there were only no dissipation ...
>
> Martin
>
> On May 13, 2005, at 4:45 PM, Jason Goodman wrote:
>
>> On May 13, 2005, at 10:15 AM, Dimitris Menemenlis wrote:
>>
>>> Martin wrote:
>>>
>>>> I am convinced that even in the case of constant (in time) pressure
>>>> forcing you should end up with a steady state that is non-zero, also
>>>> in the case of a single layer.
>>>>
>>>
>>> Martin and Sergey, I have been following your discussion with some 
>>> interest.  I don't understand why a constant in time surface 
>>> pressure forcing would establish a non-zero circulation at steady 
>>> state.  Isn't the inverse barometer adjustment meant to insure that 
>>> there is no such circulation, i.e., that (for a flat ocean) the 
>>> pressure at the bottom of be constant?
>>
>> I'd say so.  Martin's equation
>>
>> f*v + g*d(ssh)/dx + (1/rho0)*dp/dx = 0
>>
>> leaves out the bottom drag term.  While it is true that a transient 
>> circulation parallel to atmospheric pressure contours should occur at 
>> first, the inclusion of a bottom-drag term means the flow will have a 
>> small down-pressure-gradient component.  Thus, water will pile up in 
>> the low-atmospheric-pressure zones, until the second two terms in 
>> Martin's equation balance and the flow goes to zero.  This is a 
>> stable solution.
>>
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support