Simulating an estuary with constant depth and width

[schen]

Hi all,
I'm setting up tidal forcing (only M2) for an estuarine channel (20 m deep) and encountered some problems. I'll appreciate if somebody can kindly give me some hints:

The first configuration is a channel with one open boundary. I used
#define NORTHERN_WALL
#define SOUTHERN_WALL
#define EASTERN_WALL
#define WEST_FSCHAPMAN
#define WEST_M2FLATHER
#define WEST_M3RADIATION
#define WEST_TRADIATION
#define ANA_FSOBC
#define ANA_M2OBC

in analytical.F

BOUNDARY(ng)%ubar_west(j)=1.0_r8*SIN(omega)
BOUNDARY(ng)%zeta_west(j)=1.0_r8*COS(omega)


Then I compared the model result (zeta) with the analytical solution for 1st order tides, and the comparison is very promising (standing waves).

Then, I made the eastern boundary open:

#undef EASTERN_WALL
#define EAST_FSRADIATION
#define EAST_M2RADIATION
#define EAST_M3RADIATION
#define EAST_TRADIATION

The surface elevation behaved like a simple sine wave (what we expect), but the magnitude of zeta decreased with time !! (for example,
in the beginning, zeta is from -1.5 to 1.5. At the end of simulation, zeta became from -2.5 to 0.5). And the time interval of writing output files is small. So the decreasing is not due to samping error.

Questions:

1. Is the decrease in zeta due to leaking mass ? (I didn't enforce volume conservation at both boundaries). I tried to enforce EAST_VOLCON and WEST_VOLCON, but tides can not propagate in.

2. How do I properly simulate M2 tides for open channel ? Do I need to specify ubar and zeta with a phase difference that depends on domain length and tidal wave speed ?

3. My ultimate goal is to enable both tides and fresh water discharge for a curvy channel with varying depth. What kinds of boundary conditions for both East (tide) and West (river) will be more appropriate ?

Thanks a lot !!!
Best regards,
Shih-Nan

[jcwarner]

There are several choices for open boundary conditions that may provide reasonable performance for the estuary test. For the conditions that you impose the western conditions that you suggested can work well, as they impose the tidal conditions that you are specificying while allowing tidal harmonics generated within the domain to leave the system. However, the eastern bc's that you suggest are less than ideal. If you only use radiation conditions on the eastern end, then there is no restoring force to keep water in the system - it can just drain away.

There is a setup for an estuary test case provided in the distributed code. Here we use a river flow on the eastern end with m2clamped condition. For the western end we specify a tidal elevation and use west_m2reduced to calculate the barotropic mass flux. These are alternative choices to the ones you specified. Please see cppdefs.h and analytical.F for the full set of options for this test case.

john

[schen]

Hi John,
Thanks for your reply. I'm actually using the test case you set up (ESTUARY_TEST). I applied the same OBC as yours but used constant depth.

#define EAST_FSGRADIENT
#define EAST_M2CLAMPED
#define EAST_M3GRADIENT
#define EAST_TCLAMPED
#define WEST_FSCLAMPED
#define WEST_M2REDUCED
#define WEST_M3GRADIENT
#define WEST_TRADIATION

I found that the EAST_M2CLAMPED condition served like a wall so that the tidal wave reflected back and formed standing waves. Do you have any good suggestions on getting tidal waves to radiate out but at the same time keeping constant (nearly) freshwater influx?

Also, I found that for the flat bottom case, the salt intrusion (I used 1psu as an index) was kept pushing toward the ocean side. Its position oscillated with tides, but it seemed that the solution couldn't reach a quasi-steady. May I have your suggestion on this as well?
Thanks

Shih-Nan