Module that advects particles in two-dimensional flow

[glwagner]

As requested by @natschil.

[miniufo]

Just about to open a new issue on this, but found it here which is years ago. I see there is a PassiveTracerFlows.jl. Is it possible to make a similar ParticleTrackingFlows.jl for online Lagrangian particle tracking?

After a quick look at PassiveTracerFlows.jl, I find it is still evolving the tracer in spectral space. For tracking, we need to solve:

$$ \begin{equation} d\mathbf{x} = \mathbf{v} dt \end{equation} $$

which would be easier on grid points. When calculate the nonlinear terms, I guess all the variables in spectral space will be transformed back to grid space. This may make the tracking implementable. SpeedyWeather is doing a similar job, but on a spherical geometry.

How about doing this offline, by saving the outputs at a relatively high frequency? I am worrying about the stochastic forcing, which has no memory in time. The offline tracking may not respect this fact and renders a longer memory in particle trajectories (by output frequency and interpolation between outputs).