Well, I kind of have an idea of what do you want to compute. You need a cross-section of Eulerian, Lagrangian, and Stokes velocities for your application. I will never get that from your initial posting above

Still, I don't understand the role of passive tracers and much less the need to NaN lateral boundary conditions. In my opinion, your approach has lot of holes. If you publish this and describe your approach, you will get into a lot of troubles with the reviewers.

The velocities that you seek involve wave-induced circulation using a formulation of the radiation stress tensor. The Eulerian, Lagrangian, and Stokes velocities have a lot of physics that are just missing by computing Lagrangian trajectories and whatever

labels mean. So you need to model the radiation stress properly. There are several methodologies for this. One approach was proposed by Mellor (2005, 2008, ...). He has several sequential papers about this with corrections to his methodology. There is a lot of criticism in the literature about his approach. Another approach is the vortex-force formalism (Uchiyama, 2010, Ocean Modelling, ROMS-UCLA). Also Fabrice Ardhuin has several papers for radiation stress formulations.

John Warner has been working on this for several years. Our version of ROMS has the Mellor (2005, 2008) formulation. See CPP

NEARSHORE_MELLOR**. Notice that ROMS already output the velocities that you seek when this is activated. However, as I mentioned above, there is criticism with the Mellor's formulation.

If this is the main part of your dissertation, you need to experiment with these methodologies instead. I am not an expert on this but I know others that may help you. Perhaps, John Warner can advise you about this and comment on his experiences with these algorithms.