about tidal forcing

[chenjung]

Hi, everybody
I set up the 2D idealisze case to test the M2 tide.
I used closed boundary conditon for north, west and south sides.
M2 tide with 1m amplitude just input from east side, and it's worked fine.
But when i change the domain depth from 150m to 50m, the result of tide amplitude at boundary point is only 0.4m.
I think it should be 1m.
Could anybody tell me why or give a suggest.
Thaks a lot.


This is my cpp file:
#define UV_LDRAG
#define EAST_FSCHAPMAN
#define EAST_M2FLATHER
#define NORTHERN_WALL
#define WESTERN_WALL
#define SOUTHERN_WALL
#define ANA_GRID
#define ANA_INITIAL
#define ANA_SMFLUX <-- set to zero
#define ANA_FSOBC
#define ANA_M2OBC <-- set to zero

Domain of my case is 200x100, resulotion is 1 km and all domain depth is set the same.

[kate]

You need to think about tides and how they work in a semi-enclosed basin. I see that you have your M2OBC set to zero - this is likely the problem. In any case, you will have an incoming tide and an outgoing tide and having them cancel is not so surprising.

[jzavala]

As far as I can remember the appropriate boundary condition for tides is

u - p/c = Flux (= A*cos(w*t) in your case)

with u = ubar, p = g*zeta, c = sqrt(gh)

so you need to define ubar in ana_m2obc accordingly.

Jvr

[chenjung]

Thanks for reply. I'll try it.
But I don't understand is that why the depth could affect the amplitude at boundary??

[m.hadfield]

Thanks for reply. I'll try it.
But I don't understand is that why the depth could affect the amplitude at boundary??

The Flather boundary conditions requires that you prescribe the tidal variations in sea surface height and normal velocity at the zero. There is an inconsistency between the height and normal velocity you have prescribed (the latter being zero). The effect of that inconsistency varies with the water depth, which affects both correct value of the normal velocity and and the impedance of the boundary.

[crowley]

In addition to the boundary condition problem, you should think about the behavior of tides in a semi-enclosed basin, as Kate said. Changing the depth of the basin will change the speed of the wave, hence the transit time through your basin. Think about what that can do to the relative phases of the incoming/outgoing waves and what happens when they combine.

If I remember the formula correctly, a 200 m long basin resonates as a quarter-wave oscillator, with the node at the open boundary, at a depth of about 35 m.