Source-Only Fetch-Limited Growth

Source-only models use advection=nothing, matching the Oceananigans and Breeze convention that absent physics is represented by nothing. This column combines wind input and whitecapping dissipation and approaches an analytic equilibrium.

using Oceananigans, Ripple, CairoMakie

Base.include(@__MODULE__, joinpath(@__DIR__, "..", "scripts", "example_visuals.jl"))

output_dir = example_output_directory("source_only_fetch_limited_growth")
plot_paths = String[]
animation_paths = String[]
output_paths = String[]

case = only(filter(c -> c.name == :fetch_limited_source_balance,
                   default_validation_cases()))
result = run_validation(case)

grid = RectilinearGrid(CPU(); size=(1, 1, 1), x=(0, 1), y=(0, 1), z=(0, 1))
spectral_grid = PolarWaveVectorGrid(Float64; κ=[1.0], φ=[0.0])

target_growth_rate = 1.2
directional_growth_weight = Ripple.wind_directional_weight(spectral_grid, 1, 1, 0.0, 2)
growth_rate = target_growth_rate / directional_growth_weight
whitecapping_rate = 4.8
saturation_threshold = 0.5

sources = SourceTermSet((
    ExponentialWindInput(rate=growth_rate, direction=0.0, spreading_power=2),
    WhitecappingDissipation(rate=whitecapping_rate,
                             saturation_threshold=saturation_threshold,
                             saturation_power=1.0,
                             wavenumber_power=0.0),
))

model = SpectralWaveModel(; grid,
                            spectral_grid,
                            advection=nothing,
                            sources,
                            timestepper=:SemiImplicitEuler)

weight = spectral_weight(spectral_grid, 1, 1)
equilibrium_m0 = saturation_threshold * (1 + target_growth_rate / whitecapping_rate)
set!(model, N=saturation_threshold / (20 * weight))

step_count = example_mode() == :small ? 40 : 240
dt = 0.02
times = [model.clock.time]
moments = [m0(model.action)[1, 1, 1]]

for n in 1:step_count
    time_step!(model, dt)
    push!(times, model.clock.time)
    push!(moments, m0(model.action)[1, 1, 1])
end

frame_indices = unique(round.(Int, range(1, length(moments); length=min(length(moments), 12))))
line_frames = [vcat(moments[1:i], fill(moments[i], length(moments) - i))
               for i in frame_indices]

push!(plot_paths,
      write_line(joinpath(output_dir, "fetch_limited_growth.png"),
                 times, (moments, fill(equilibrium_m0, length(times)));
                 title="Fetch-limited source balance",
                 xlabel="time", ylabel="m0",
                 names=("column m0", "analytic equilibrium")))

push!(animation_paths,
      write_line_animation(joinpath(output_dir, "fetch_limited_growth_animation.mp4"),
                           times, line_frames;
                           title="Approach to source equilibrium",
                           xlabel="time", ylabel="m0"))

writer_model = SpectralWaveModel(grid;
                                  spectral_grid,
                                  advection=nothing,
                                  sources,
                                  timestepper=:SemiImplicitEuler)
set!(writer_model, N=saturation_threshold / (20 * weight))
writer_simulation = Simulation(writer_model; Δt=dt, stop_iteration=1, verbose=false)
writer_path = joinpath(output_dir, "fetch_limited_growth.jld2")
writer_simulation.output_writers[:action] =
    JLD2Writer(writer_model, (; N=writer_model.action);
               filename=writer_path,
               schedule=IterationInterval(1),
               overwrite_existing=true)
run!(writer_simulation)
push!(output_paths, writer_path)

@assert validation_passed(result)
@assert last(moments) <= equilibrium_m0 + 1e-2
@assert all(diff(moments) .>= -1e-12)
@assert all(isfile, plot_paths)
@assert all(isfile, animation_paths)
@assert all(isfile, output_paths)

@show validation_passed(result)
@show result.metrics[:equilibrium_tendency_error]
@show result.metrics[:final_m0_error]
@show result.metrics[:monotonicity_error]
@show last(moments)
@show plot_paths
@show animation_paths

Running The Example

From the repository root:

julia --startup-file=no --project=. examples/source_only_fetch_limited_growth.jl

Set RIPPLE_EXAMPLE_MODE=small for the fast smoke-test version.

This literate page is generated from examples/source_only_fetch_limited_growth.jl.