[MITgcm-support] Orlanski radiation condition parameters

[Burns, Paul]

Hi Jody,

Thanks for your message.

My understanding is that the Orlanski scheme is suitable for cases where a spectrum of waves is excited.  In Orlanski (1976) it shows that the scheme uses a variable phase velocity (varying in time, location along boundary, and with each prognostic variable) to try and account for different waves reaching the boundary (shown in equation (2.2)).  Orlanski also performed tests, computing the evolution of a collapsing bubble in stratified flow, which excited many different internal waves, with the results showing only small distortion using the boundary condition (2.2).  In the same paper it is also said that the sponge condition is not perfect and may create small distortions.  It seems that neither boundary condition is perfect.

My understanding is that the parameter Cmax that the users sets in MITgcm sets only the maximum phase speed that the Orlanski scheme accounts for, but that the scheme still computes variable phase speeds below this limit.

I've performed some initial tests using the Orlanski scheme and I'm not seeing obvious reflections at the boundary, with flow structures apparently leaving the domain without big distortions.  But I wish to confirm things further than visual inspection, which isn't sufficient alone.


Cheers,
Paul





Dr Paul Burns MInstP FRMetS

Research Fellow

Geophysical and Astrophysical Fluid Dynamics Group

Department of Mathematics

Harrison Building

University of Exeter

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From: MITgcm-support <mitgcm-support-bounces at mitgcm.org> on behalf of Jody Klymak <jklymak at uvic.ca>
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Subject: Re: [MITgcm-support] Orlanski radiation condition parameters

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Hi Paul,

Others should correct me if I am mistaken, but I don’t think Orlanski will work particularly well for this case because you do not have one dominant wave speed in your problem.  Rather, you might try a gentle sponge.

Cheers,   Jody


On Apr 12, 2022, at 11:58 AM, Burns, Paul <P.Burns2 at exeter.ac.uk<mailto:P.Burns2 at exeter.ac.uk>> wrote:

Hi,

This is a bit basic, but I would like to check my implementation of my lateral boundary conditions.  I am running a 2D simulation and prescribe (Dirichlet conditions) a Garrett-Munk spectrum of waves on my left boundary, which then propagate into my domain.  I would like to allow the motions in the interior solution to radiate away through my right boundary, so I've asked the model to use the Orlanski condition on the right boundary.

In Orlanski (1976) it states that the (variable) phase velocity C must be less than the maximum numerical velocity, which for my setup is dx/dt = 25/1 = 25 m/s.  So in data.obcs I've set Cmax = 20 m/s.  This is quite different to the value used in the 'Gravity Plume On a Continental Slope' tutorial, which has a similar domain size to mine, but this is because of my much smaller timestep due to my fine vertical grid required for my features of interest.  I realise I am using large aspect ratio cells, but this is to keep the simulation feasible with the compute resources I have.  I will try and test sensitivity of my results to horizontal resolution.

Can someone confirm how you fix the remaining parameter of the Orlanski scheme? That is,
 cVelTimeScale



Many thanks,
Paul




Dr Paul Burns MInstP FRMetS
Research Fellow
Geophysical and Astrophysical Fluid Dynamics Group
Department of Mathematics
Harrison Building
University of Exeter

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