[CIG-LONG] Hydrostatic Pressure and linear side stress boundary conditions

[Karen Paczkowski]

I am a graduate student at Yale University.  I am trying to model a  
subduction zone, where the mantle passively responds to the slab  
movement.  To do this I would like to specify some shapes where within  
these I set velocities to represent the slab, but then only specify  
stresses as the boundary conditions on the larger simulation domain.   
So I like to just have the bottom, side and top boundary conditions be  
the equilibrium stress conditions of the system so that the flow field  
in the mantle will just organize itself naturally as a passive  
response to the subducting slab's movement.

I thought this would mean that I should specify:
1)  the bottom boundary condition as a stress acting up (in the y  
direction) equal to the stress from the force of gravity acting down
2)  the top boundary condition would just be the hydrostatic term
3)  the side boundary condition would be a linear gradient going from  
the value at the bottom to that at the top.

I started by just creating a box in gale with no subducting slab  
shapes, so everything should be static.  I set the side boundary  
conditions to zero velocity and specified the bottom boundary  
condition as a stress acting of equal magnitude and in opposite  
direction as the weight of the simulation box.  I find that when I  
don't put in a hydrostatic term for the top boundary I get a linear  
gradient of stress with depth.  But, if I put in the hydrostatic term  
I get a bulging of the simulation box as time progresses.

So my main questions are:
1)  How can i specify a linear stress gradient for the side boundary  
condition
2)  Why does including both the bottom stress boundary condition and  
the hydrostatic stress top boundary condition cause this bulging.   
Should I only be specifying the bottom and not including the  
hydrostatic pressure?  Should I be altering the stress applied to the  
bottom when the hydrostatic pressure is included?

I have attached the test input file where everything should be  
static.  It is a 2D box, with dimensions 2 x 0.5, density=1,  
gravity=1, and viscosity=1.  The side boundary conditions are  
currently just vx=vy=0.  The bottom boundary condition is a stress of  
0.5 (=rho*g*ymax).  When the hydrostatic term is left in (like it is  
currently) I get the bulging I described above.  When it is commented  
out I get a linear stress gradient with depth.

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Thank you,
Karen