Blowup. Boundary condtition problem?

[michele]

I have a bowup problem.
I probably need some basic help in the chioce of boundary conditions.

I have a fairly regular bathymetry 300 m x 2040 m, with DX=5 m and DY=10 m
with the coast at SOUTH (beach in Y=0, the rear land reaching level + 5 m in Y=-40 m)
the open sea at NORTH (Y=2000m, depth of 10 m),
a smooth profile at WEST (X=0) and EAST (X=300m).

The tide Z(t) and the longshore velocity U(t) are known
in form of sinusoidal functions with max 1.2 m and 0.5 m/sec
starting from zero.

Activated options are
UV_VIS2
MIX_S_UV
WET_DRY (minimum depth=0.5)
UV_ADV
TS_MPDATA
DJ_GRADPS
MASKING plus ANA_MASK
SOLVE3D plus (default activated options)
SPLINES
UV_QDRAG
SEDIMENT plus ..
GLS_MIXING plus ..
All the rest is zero

DT=1 sec, NDTFAST=20

Boundary conditions are:
SOUTHERN_WALL

EAST_FSGRADIENT
EAST_M2CLAMPED --> U_BAR=U(t) in file ana_m2obc.h
EAST_M3GRADIENT

WEST_FSCLAMPED --> Z=Z(t) in file ..
WEST_M2GRADIENT
WEST_M3GRADIENT

NORTH_FSGRADIENT
NORTH_M2GRADIENT
NORTH_M3GRADIENT

The application blows up after approx. 4000 time steps.
I checked the generated dirichlet conditions of U(t) and Z(t):
they are the expected ones.
Some disturbance of the velocity arise in the domain and
a localised disturbance develops from mid boundary, at WEST (i.e.
where zero gradient velocity is prescribed; bottom here is very regular, depth is around 8 m).

Before blow-up,
velocity is smooth, around 0.02 m/s,
except at some peaks where it is 0.2 m/s.
Water level is flat.

I believe there is a problem with boundary conditions
Indeed a similar application, with prescribed sinusoidal
water level at NORTH, radiation stress (derived from SWAN) in the domain and with the boundary condition EW_PERIODIC, runs smoothly.

Could anybody suggest the proper boundary conditions (for the 3 open sides) when tides and longshore currents are known?

Thanks in advance.
Michele.

[jcwarner]

perhaps try the M2FLATHER or M2REDUCED type BC's on the east and west. If the longshore tranposrt is to the west, then try east_m2reduced and west_m2flather. You may need to try a few different options to see what works best for your application.

[nobuhitomori]

perhaps try the M2FLATHER or M2REDUCED type BC's on the east and west. If the longshore tranposrt is to the west, then try east_m2reduced and west_m2flather. You may need to try a few different options to see what works best for your application.

From my experience, I recommend use following combination.
FS -> Chapman or Clamped
M2 -> Flather
You may also use M2REDUCED for only free surface given condition as jcwarner suggested.

[michele]

Thanks john and thanks nobu!

I have not solved the problem yet...


The longshore tidal current U(t) must be prescribed and can not be derived by the surface gradient. Therefore I cannot use M2reduced.
Further, I do not have a main current direction.. since the current is sinusoidal... so no main longshore transport.

My feeling is that I need to prescribe at one of the 2 sides, e.g. at east:
A) the longshore velocity ubar_east=U(t), vbar_east=0 in ANA_M2OBC, with condition M2_Clamped and
B) a pressure gradient which is related to the (time derivative of the) prescribed velocity. A sort of FS_reduced.. (not to be confused with FSOBC_reduced, which is similar to M2_reduced)

... or is it totally wrong?

[michele]

I have tried with
Fsclamped and m2reduced
both at the eastern and western boundaries.

At the beginning, elevation grows. the velocity computed by m2_reduced is positive at west, negative at east. Almost symmetric.
(water enters from both sides....)
As always, the blowup occurs when tidal elevation is still a few centimeters.
As usual: the greater instability is localised close to the western boundary and it spreads toward north (reaching the offshore boundary).

I also tried DG_GRADP rather than DG_GRADPS. There is a hole in the center of the bathymetry but it does not justify any problems with regard to the pressure gradient algorithm and as expected the change had no effect. Also, I remind you that with EW_periodic (and an additional external forcing) the application runs.

Any additional suggestion?