I would like to calculate the numerical horizontal dissipation occurring in my simulation, given that there is no explicit horizontal dissipation being modeled in it. My goal with this is to add in the effect of the horizontal mixing with the vertical closure scheme turbulent kinetic energy so as to have a total turbulent kinetic energy for my simulation.
I am using the 3rd order upstream advection of momentum (UTOPIA) scheme. My approach here has been to assume that the majority of the horizontal dissipation taking place is numerical dissipation coming out of the advection of momentum. I have been trying to work out the form of the truncation error of the scheme using Taylor series analysis in order to calculate the terms from my model output, but it hasn't been working out. The UTOPIA scheme used in ROMS for advection of momentum is given on the https://www.myroms.org/wiki/index.php/N ... der_Upwind in semi-discretized form, and I went to the code itself in rhs3d.F to see what the discretization actually looks like, to do the Taylor series error analysis.
After spending a lot of time of this with what seems to be limited success of many terms dropping out and giving me an appropriate-ordered error term, I thought I'd reach out to see if anyone has already done this.
I'll note here too that I have found a form of the truncation error for the original 1D Leonard 1979 advection of a tracer equation, but the form on the wiki for advection of momentum is distinct from that for advection of a tracer, so I don't think that helps me.
Thanks for any advice here!