Development of a "Field" abstraction for solutions in 1, 2, and 3 dimensions

[glwagner]

It'd be nice to have a (lightweight) abstraction for a "Field" in FourierFlows. The FourierFlows field could store either data in physical/grid space, or data in transform/coefficient space, or both (we should decide on semantics as well).

Type information can also be used to indicate whether the coefficient-space data is in "conjugate symmetric" form (currently we hack a fragile query into functions like parsevalsum that attempts to diagnose this fact from the size of the array with an if-statement, rather than using multiple dispatch on types).

Syntax could get a little nicer because we can define a function compute_grid_space!(field) and compute_coefficient_space!(field) functions that do fourier transforms (rather than requiring users / external packages like GeophysicalFlows to manually write FFTs).

Food for thought.

[navidcy]

I like this; will try to do it.

In MultilayerQG module in GeophysicalFlows.jl we have something towards that direction...
https://github.com/FourierFlows/GeophysicalFlows.jl/blob/b15419e4fe093666c0b72cf1191328e631c5ed20/src/multilayerqg.jl#L258-L259
But what you suggest is better.

Will field though always carry along both physical space and Fourier space values?