OBC for barotropic channel flow

[linzhenhua]

Hi,I have a question about the open boundary conditions of barotropic channel flow,take an east-west channel as example.What I want to simulate is an east-west barotropic surface elevation difference driven flow,and hope the model could reach a steady state.The Coriolis effect is not considered.

For the west FSOBC,I have only one choice,clamped boundary condition,e.g.,0.1m,constant with time.The problem is with the eastern boundary,since I want to have constant surface slope driven flow,the model becomes unstable if I set clamped OBC,e.g.,0.0m for the east FSOBC,this may be anticipated because the reflection of waves caused by the clamped east open boundary condition.

But if I set other east OBC,such as chapman OBC,I could not maintain the surface slope to drive the flow after some time,the surface elevation in the domain could become totally 0.1m later.

I wonder whether this model setup is possble with combination of the available OBCs in roms,or could some experts tell me whether this setup is physically or numerically possible?

[m.hadfield]

I suggest you try xxxx_FSCLAMPED with xxxx_M2REDUCED and/or xxxx_FSCHAPMAN with xxxx_M2FLATHER. With the Flather boundary conditions you need to specify normal velocity as well as SSH at the boundary. If you have a way of estimating normal velocity, then you should use it; otherwise you can leave it at zero, but then you should be aware that the actually SSH will not exactly match the value you have prescribed.

[m.hadfield]

PS: Your query is timely, as I have just spent several days mucking about with simulations of barotropic flow through an idealised strait, not dissimilar to Cook Strait, which separates the North and South Islands of New Zealand. I can give more information about my results and what I've learned from them.

[linzhenhua]

Hi,m.hadfield.Thanks for your reply.I'd like to expand your reply with my comprehension.

First,I'm not quite sure about the word "and/or".If I remember correctly,when I tried xxxx_FSCLAMPED with xxxx_FSCHAPMAN in one setup for two BCs,I could not maintain the surface slope to drive the flow. So I reject this combination first.

Now there are only two selections left.One is to use both OBCs with FSCLAMPED.I have tried this combination with M2GRADIENT,the model blow up for the reflection.Later I will try your suggestion,with FSCLAMPED and M2REDUCED.

Another is to use both OBCs with FSCHAPMAN with M2FLATHER,then I need to prescribe SSH and M2 at both OBCs.

As to the estimate of M2,how about using the balance of pressure gradient and bottom friction to evaluate it?

For example, g*depth*delta_zeta/delta_x=cd*u*u,then for a surface slope 6mm/km,cd=3*10**(-3),25m depth

9.8*25*6e-3/1000=3e-3*u**2 u=0.7

Is this kind of method reasonable for such estimation?

Any comments?

[m.hadfield]

Hi,m.hadfield.Thanks for your reply.I'd like to expand your reply with my comprehension.

First,I'm not quite sure about the word "and/or".If I remember correctly,when I tried xxxx_FSCLAMPED with xxxx_FSCHAPMAN in one setup for two BCs,I could not maintain the surface slope to drive the flow. So I reject this combination first.

xxxx_FSCLAMPED and xxxx_FSCHAPMAN are not meant to be used together. One will override the other (I think).

By "and/or", I meant you could try xxxx_FSCLAMPED with xxxx_M2REDUCED, or you could try xxxx_FSCHAPMAN with xxxx_M2FLATHER, or you could try both (in separate simulations, I mean).

Now there are only two selections left. One is to use both OBCs with FSCLAMPED.I have tried this combination with M2GRADIENT,the model blow up for the reflection.

The model blows up with this combination because GRADIENT boundary conditions are unstable. (That instability could be suppressed with nudging, but ROMS doesn't currently offer this option.)

Later I will try your suggestion,with FSCLAMPED and M2REDUCED.

Another is to use both OBCs with FSCHAPMAN with M2FLATHER,then I need to prescribe SSH and M2 at both OBCs.

Yes, that was one of my suggestions.

As to the estimate of M2,how about using the balance of pressure gradient and bottom friction to evaluate it?

For example, g*depth*delta_zeta/delta_x=cd*u*u,then for a surface slope 6mm/km,cd=3*10**(-3),25m depth

9.8*25*6e-3/1000=3e-3*u**2 u=0.7

Is this kind of method reasonable for such estimation?

Yes if you have any way of estimating boundary velocities, you should use it.

Flather boundaries are resistive, ie. if the normal M2 velocity differs from the prescribed value, the SSH will be lowered (for inward flow) or raised (for outward flow) relative to the prescribed SSH. The resistance is sqrt(g/h). So prescribing an incorrect velocity will affect the pressure field, but you may be able to estimate approximately how large this effect will be.

[linzhenhua]

Hi,Thanks for your information and sorry for the late test report.

First to clarify the "and/or" issue. I know that EAST_FSCLAMPED and EAST_CHAPMAN could not used at the same time. I just want to say that if I use WEST_FSCLAMPED and EAST_CHAPMAN at the same time,I could not maintain the surface slope.

About the other two suggestion.
Combination of xxxx_CLAMPED and xxxx_REDUCED does not work for me.After some time the model still blow up,I could see the reflection at the outlet open boundary.

The combination of xxxx_FLATHER and xxxx_CHAPMAN seems to be stable.For reference,I use no initial surface elevation,a initial SSH difference about 48mm/8km,M2 is 0.7m/s at both OBC.
I check the result after 80 Hour. The vertical averaged velocities near the inflow,middle domain,near outflow are all around 0.695m/s.The initial zero FS first oscillates in the first few hours and then become stable,about +7.5mm near the infow and -7.5mm near the outflow. So maybe I could conclude that the FS adjust itself to M2.Finally the total(FS+SSH) difference between the infow and outflow is 48mm+15mm=63mm.

The problem for me is then to adjust M2 to get the desired barotropic gradient,right?

Any comments?

[thomas.roc]

Hi, I'm currently facing the same problems. I'm trying to run a barotropic simulation of a simple east-west channel with a homogeneous bathymetry. In this case zeta_west is gently increasing up to a threshold of 0.4m and zeta_east remains the same (thanks to ANA_FSOBC).

The boundary conditions are the following:
- #define WEST_M2FLATHER
#define WEST_FSCHAPMAN
- #define EAST_M2REDUCED
#define EAST_FSCLAMPED

I'm using ANA_M2OBC to define ubar_west as equal to SQRT(2*g*(zeta_west-zeta_east)).
Here are the rest of my CPP options:
#define UV_QDRAG
#define ANA_GRID
#define ANA_INITIAL
#define ANA_FSOBC
#define ANA_SMFLUX
#define NORTHERN_WALL
#define SOUTHERN_WALL
#define FSOBC_REDUCED

In spite of the numerous OBC combinations or ways to perturb or initialize the system I've tried, I haven't reached any steady solution. I might missed something obvious !?

Does anybody have a clue on this one ?

Cheers

[thomas.roc]

My mistake !

My supervisor pointed out the problem in my simulation.
I was calculating west_ubar as function of another unknown(zeta_west-zeta_east). Thus non linear behaviours pop up.
By using a fixed (zeta_west-zeta_east) and using the proper time step, the simulation reaches a steady solution.

Cheers