I would like to set up a thermal wind balanced channel flow. The channel will
have flat bottom for now, later I will put a cylinder or an island into the
domain. I basically follow the setup in the article "Island Wakes in Deep
Water" by Changming Dong.
http://www.atmos.ucla.edu/~cdong/papers ... _final.pdf
This is part of the final work for my mathematics bachelor's degree, and my
professor wants me to treat the equations analytically as far as
possible. That's why I'm looking for the simplest possible set of equations.
The vertical mixing poses a problem, because it's complicated.
This work is not meant to gain insight into realistic processes, but to gain
experience into mathematical modelling and numerical methods.
If I understand correctly, the simplest scheme in ROMS is the Brunt Vaisala
frequency mixing. It modifies Akt and Akv depending on whether the regime is
stable, neutreal or unstable. If it's stable, Akt and Akv are functions of
bvf.
The initial density profile for my setup will be stably stratified and
I will take care that the Richardson number is bigger than 1/4 in the
domain. If velocity and density profile stay termal wind balanced, there
should be no reason to get statically unstable regime, right? So I'm
thinking about setting Akt and Akv to the same value for all cases.
That would simplfy the formulas.
Do you think that's a good idea?
If yes, is it possible to set akv=akv_bak to zero? I.e., is there some
implicit numerical diffusion like in the horizontal?
Thanks,
--Stefan
Simplest vertical mixing
The simplest vertical mixing is indeed a constant or other specified function for Akt, Akv. This can be done with ANA_VMIX. As for setting the background values to zero, I don't know if that will work or not. You can always try it and report back here. 
The reason I say that is because the vertical mixing is handled implicitly, with a tridiagonal solve over a vertical stack of points.
The vertical advection scheme will indeed have errors, though it's the third-order scheme that has errors looking like diffusion. The options I see for tracers are spline vertical advection, fourth-order Akima, and second- and fourth-order centered advection. The even-orders will be more dispersive than diffusive.
The reason I say that is because the vertical mixing is handled implicitly, with a tridiagonal solve over a vertical stack of points.
The vertical advection scheme will indeed have errors, though it's the third-order scheme that has errors looking like diffusion. The options I see for tracers are spline vertical advection, fourth-order Akima, and second- and fourth-order centered advection. The even-orders will be more dispersive than diffusive.
I see. Thanks.
Another question:
In my mathematical model, I will have water flowing in a channel from north to south, with u=w=0 and a vertical shear in v (just like in the paper above). This implies a horizontal density gradient wich I want to impose by using a linear equation of state. A tilted free surface is also necessary. Then I'd like to use periodic boundary conditions, and set the viscosity and thermal diffusivity to zero in all directions. I think in principle, this should yield a perfect steady state. The rate of change of total energy for the whole system should then be zero.
The problem is that the numerical diffusion will dissipate energy, so the system must break down into non-steady state after some time. Is there a way to estimate the rate of energy loss by numerical dissipation for a given velocity profile, i.e. for a given total kinetic energy, by numerical dissipation?
Do you think that matter is important in setting up a balanced channel flow of that kind?
Thanks,
--Stefan
Another question:
In my mathematical model, I will have water flowing in a channel from north to south, with u=w=0 and a vertical shear in v (just like in the paper above). This implies a horizontal density gradient wich I want to impose by using a linear equation of state. A tilted free surface is also necessary. Then I'd like to use periodic boundary conditions, and set the viscosity and thermal diffusivity to zero in all directions. I think in principle, this should yield a perfect steady state. The rate of change of total energy for the whole system should then be zero.
The problem is that the numerical diffusion will dissipate energy, so the system must break down into non-steady state after some time. Is there a way to estimate the rate of energy loss by numerical dissipation for a given velocity profile, i.e. for a given total kinetic energy, by numerical dissipation?
Do you think that matter is important in setting up a balanced channel flow of that kind?
Thanks,
--Stefan