Advection-diffusion of passive tracer using a turbulent flow

[jbisits]

This PR adds the ability to advect-diffuse a passive tracer using a flow generated by the MultiLayerQG module from the GeophysicalFlows.jl package with a constant diffusivity. To implement this another method has been added to TracerAdvectionDiffusion.Problem that takes in a MultiLayerQG.Problem as an argument. The TracerAdvectionDiffusion.Problem is then setup on the same size grid and number of layers as the MultiLayerQG.Problem. Additional arguments are \kappa and \eta, the constant diffusivity, the stepper and the tracer_release. The tracer_release argument allows the user to specify some length of time to run the flow for (e.g. so the flow reaches a statistical equilibrium) prior to releasing the tracer into the flow.

I have written an example ,turbulent_advection-diffusion.jl, showing how the module works. In doing this I have added Plots.jl to the Project.toml which I did not want to do (nor does it need to be there). I have no experience setting up the example to be run and rendered into a GitHub page so this is why it has occured.

I have not implemented it yet but as a test for the function I will set the MultilayerQG.Problem to produce noflow (i.e. flow fields are 0 for the whole simulation) and check the diffusion of a tw-dimensional Gaussian in a similar manner to one of the tests that is already in the test_traceradvectiondiffusion.jl file.

I am not sure if this is the best way to implement this functionality into the PassiveTracerFlows.jl package but I have used it a lot over the last year or so and it has been very reliable and reasonably quick even on the much larger domains I was using.

[navidcy]

@jbisits I made some changes:

• dropped Plots from package depot
• added your example in the literated list
• use latest FourierFlows and GeophysicalFlows version
• updated syntax to work for any number of layers

[navidcy]

made a few remarks
I will have a closer look over the weekend!

[jbisits]

@navidcy thanks for making the changes above, all of the package organisation is new to me!

[navidcy]

taking the absolute value of the tracer doesn't seem right... :(
let me try to heal the instabilities

[navidcy]

  stepforward!(ADprob)
  stepforward!(params.MQGprob)
  MultiLayerQG.updatevars!(params.MQGprob)

the MultiLayerQG.updatevars!(params.MQGprob) was missing... thus the advecting velocities were not updated...

This seems to have fixed it. Have a look:

turbulentflow_advection-diffusion.mp4

The proper solution would be to define an abstract type of a CoupledProblem that would include both the PassiveTracerFlows.Problem and the MultiLayerQG.Problem and then define a new method for stepforward! for this coupled problem, e.g.,

function stepforward!(coupled_prob::CoupledProblem)
  stepforward!(coupled_prob.ADprob)
  stepforward!(coupled_prob.MQGprob)
  MultiLayerQG.updatevars!(coupled_prob.MQGprob)
end

But we can defer this for a future PR?

[navidcy]

@jbisits feel free to merge when tests pass if you don't have anything else to add.

Sorry it took so long.

[navidcy]

oh I guess you probably don't have the right to merge? I'll do it ;)

[jbisits]

taking the absolute value of the tracer doesn't seem right... :( let me try to heal the instabilities

Yeah taking absolute value was something we did on larger domains at the start of simulations where some values were really small and negative.

[jbisits]

  stepforward!(ADprob)
  stepforward!(params.MQGprob)
  MultiLayerQG.updatevars!(params.MQGprob)

the MultiLayerQG.updatevars!(params.MQGprob) was missing... thus the advecting velocities were not updated...

This seems to have fixed it. Have a look:

turbulentflow_advection-diffusion.mp4

This is great!!

The proper solution would be to define an abstract type of a CoupledProblem that would include both the PassiveTracerFlows.Problem and the MultiLayerQG.Problem and then define a new method for stepforward! for this coupled problem, e.g.,

function stepforward!(coupled_prob::CoupledProblem)
  stepforward!(coupled_prob.ADprob)
  stepforward!(coupled_prob.MQGprob)
  MultiLayerQG.updatevars!(coupled_prob.MQGprob)
end

But we can defer this for a future PR?

Agreed.

[jbisits]

@jbisits feel free to merge when tests pass if you don't have anything else to add.

Sorry it took so long.

Did not take too long! Thanks for all your help!!!

[jbisits]

I can have a look at some of these tests in a bit