A two-dimensional turbulence example

using Oceananigans
using TurbulentWords
using CairoMakie

We construct a simulation with a word and run it.

simulation = word_to_simulation("hello", pad_to_square=true)
simulation.stop_time = 15

model = simulation.model
u, v, w = model.velocities
outputs = (; ζ = ∂x(v) - ∂y(u))
filename = "hello_turbulence"
simulation.output_writers[:fields] = JLD2OutputWriter(model, outputs,
                                                      schedule = TimeInterval(0.2),
                                                      filename = filename * ".jld2",
                                                      overwrite_existing = true)

run!(simulation)

[ Info: Initializing simulation...
[ Info: Iteration: 0, time: 0.0, wall time: 12.271 seconds, Δt: 0.011000000000000001
[ Info:     ... simulation initialization complete (6.830 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (3.467 seconds).
[ Info: Iteration: 10, time: 0.11000000000000004, wall time: 8.888 seconds, Δt: 0.011000000000000001
[ Info: Iteration: 20, time: 0.21100000000000002, wall time: 3.576 seconds, Δt: 0.011000000000000001
[ Info: Iteration: 30, time: 0.32100000000000006, wall time: 3.569 seconds, Δt: 0.011000000000000001
[ Info: Iteration: 40, time: 0.42200000000000004, wall time: 3.606 seconds, Δt: 0.011000000000000001
[ Info: Iteration: 50, time: 0.5320000000000001, wall time: 3.604 seconds, Δt: 0.012100000000000001
[ Info: Iteration: 60, time: 0.6484000000000001, wall time: 3.611 seconds, Δt: 0.012100000000000001
[ Info: Iteration: 70, time: 0.7694000000000001, wall time: 3.580 seconds, Δt: 0.012100000000000001
[ Info: Iteration: 80, time: 0.8847, wall time: 3.618 seconds, Δt: 0.012100000000000001
[ Info: Iteration: 90, time: 1.0, wall time: 3.622 seconds, Δt: 0.012100000000000001
[ Info: Iteration: 100, time: 1.121, wall time: 3.643 seconds, Δt: 0.013310000000000002
[ Info: Iteration: 110, time: 1.23993, wall time: 3.635 seconds, Δt: 0.013310000000000002
[ Info: Iteration: 120, time: 1.3730299999999993, wall time: 3.648 seconds, Δt: 0.013310000000000002
[ Info: Iteration: 130, time: 1.4931699999999997, wall time: 3.642 seconds, Δt: 0.013310000000000002
[ Info: Iteration: 140, time: 1.61331, wall time: 3.659 seconds, Δt: 0.013310000000000002
[ Info: Iteration: 150, time: 1.7464099999999994, wall time: 3.639 seconds, Δt: 0.014641000000000003
[ Info: Iteration: 160, time: 1.8878460000000008, wall time: 3.679 seconds, Δt: 0.014641000000000003
[ Info: Iteration: 170, time: 2.0292820000000003, wall time: 3.659 seconds, Δt: 0.014641000000000003
[ Info: Iteration: 180, time: 2.1756920000000015, wall time: 3.653 seconds, Δt: 0.014641000000000003
[ Info: Iteration: 190, time: 2.317128000000001, wall time: 3.632 seconds, Δt: 0.014641000000000003
[ Info: Iteration: 200, time: 2.458564000000001, wall time: 3.638 seconds, Δt: 0.016105100000000004
[ Info: Iteration: 210, time: 2.6161051000000004, wall time: 3.649 seconds, Δt: 0.016105100000000004
[ Info: Iteration: 220, time: 2.7771561000000036, wall time: 3.620 seconds, Δt: 0.016105100000000004
[ Info: Iteration: 230, time: 2.928840800000003, wall time: 3.644 seconds, Δt: 0.016105100000000004
[ Info: Iteration: 240, time: 3.0805255000000016, wall time: 3.680 seconds, Δt: 0.016105100000000004
[ Info: Iteration: 250, time: 3.232210200000001, wall time: 3.665 seconds, Δt: 0.017715610000000007
[ Info: Iteration: 260, time: 3.4000000000000004, wall time: 3.595 seconds, Δt: 0.017715610000000007
[ Info: Iteration: 270, time: 3.5771561000000025, wall time: 3.578 seconds, Δt: 0.017715610000000007
[ Info: Iteration: 280, time: 3.741724880000002, wall time: 3.559 seconds, Δt: 0.017715610000000007
[ Info: Iteration: 290, time: 3.9062936600000016, wall time: 3.606 seconds, Δt: 0.017715610000000007
[ Info: Iteration: 300, time: 4.070862440000003, wall time: 3.602 seconds, Δt: 0.019487171000000008
[ Info: Iteration: 310, time: 4.238974342, wall time: 3.650 seconds, Δt: 0.019487171000000008
[ Info: Iteration: 320, time: 4.419487171, wall time: 3.666 seconds, Δt: 0.019487171000000008
[ Info: Iteration: 330, time: 4.6000000000000005, wall time: 3.609 seconds, Δt: 0.019487171000000008
[ Info: Iteration: 340, time: 4.794871709999998, wall time: 3.606 seconds, Δt: 0.019487171000000008
[ Info: Iteration: 350, time: 4.975384538999998, wall time: 3.603 seconds, Δt: 0.021435888100000012
[ Info: Iteration: 360, time: 5.171487104800001, wall time: 3.554 seconds, Δt: 0.021435888100000012
[ Info: Iteration: 370, time: 5.371487104800001, wall time: 3.549 seconds, Δt: 0.021435888100000012
[ Info: Iteration: 380, time: 5.571487104800001, wall time: 3.544 seconds, Δt: 0.021435888100000012
[ Info: Iteration: 390, time: 5.771487104800001, wall time: 3.560 seconds, Δt: 0.021435888100000012
[ Info: Iteration: 400, time: 5.971487104800001, wall time: 3.553 seconds, Δt: 0.023579476910000015
[ Info: Iteration: 410, time: 6.188635815280002, wall time: 3.602 seconds, Δt: 0.023579476910000015
[ Info: Iteration: 420, time: 6.4, wall time: 3.596 seconds, Δt: 0.023579476910000015
[ Info: Iteration: 430, time: 6.623579476910001, wall time: 3.584 seconds, Δt: 0.023579476910000015
[ Info: Iteration: 440, time: 6.847158953820001, wall time: 3.567 seconds, Δt: 0.023579476910000015
[ Info: Iteration: 450, time: 7.0707384307300005, wall time: 3.609 seconds, Δt: 0.025937424601000018
[ Info: Iteration: 460, time: 7.329687123005002, wall time: 3.598 seconds, Δt: 0.025937424601000018
[ Info: Iteration: 470, time: 7.581561972207004, wall time: 3.629 seconds, Δt: 0.025937424601000018
[ Info: Iteration: 480, time: 7.825937424601001, wall time: 3.605 seconds, Δt: 0.025937424601000018
[ Info: Iteration: 490, time: 8.077812273803001, wall time: 3.607 seconds, Δt: 0.025937424601000018
[ Info: Iteration: 500, time: 8.329687123005003, wall time: 3.607 seconds, Δt: 0.02853116706110002
[ Info: Iteration: 510, time: 8.599718169427701, wall time: 3.603 seconds, Δt: 0.02853116706110002
[ Info: Iteration: 520, time: 8.8285311670611, wall time: 3.684 seconds, Δt: 0.02853116706110002
[ Info: Iteration: 530, time: 9.0855935011833, wall time: 3.587 seconds, Δt: 0.02853116706110002
[ Info: Iteration: 540, time: 9.342655835305502, wall time: 3.580 seconds, Δt: 0.02853116706110002
[ Info: Iteration: 550, time: 9.599718169427701, wall time: 3.584 seconds, Δt: 0.031384283767210024
[ Info: Iteration: 560, time: 9.86276856753442, wall time: 3.613 seconds, Δt: 0.031384283767210024
[ Info: Iteration: 570, time: 10.156921418836049, wall time: 3.598 seconds, Δt: 0.031384283767210024
[ Info: Iteration: 580, time: 10.43138428376721, wall time: 3.614 seconds, Δt: 0.031384283767210024
[ Info: Iteration: 590, time: 10.72553713506884, wall time: 3.688 seconds, Δt: 0.031384283767210024
[ Info: Iteration: 600, time: 11.0, wall time: 3.629 seconds, Δt: 0.03452271214393103
[ Info: Iteration: 610, time: 11.338090848575723, wall time: 3.638 seconds, Δt: 0.03452271214393103
[ Info: Iteration: 620, time: 11.669045424287862, wall time: 3.618 seconds, Δt: 0.03452271214393103
[ Info: Iteration: 630, time: 12.0, wall time: 3.599 seconds, Δt: 0.03452271214393103
[ Info: Iteration: 640, time: 12.338090848575723, wall time: 3.634 seconds, Δt: 0.03452271214393103
[ Info: Iteration: 650, time: 12.669045424287862, wall time: 3.640 seconds, Δt: 0.03797498335832414
[ Info: Iteration: 660, time: 13.0, wall time: 3.622 seconds, Δt: 0.03797498335832414
[ Info: Iteration: 670, time: 13.351899933433293, wall time: 3.650 seconds, Δt: 0.03797498335832414
[ Info: Iteration: 680, time: 13.675949966716647, wall time: 3.646 seconds, Δt: 0.03797498335832414
[ Info: Iteration: 690, time: 14.0, wall time: 3.625 seconds, Δt: 0.03797498335832414
[ Info: Iteration: 700, time: 14.351899933433293, wall time: 3.616 seconds, Δt: 0.04177248169415655
[ Info: Iteration: 710, time: 14.72531744508247, wall time: 3.607 seconds, Δt: 0.04177248169415655
[ Info: Simulation is stopping after running for 4.480 minutes.
[ Info: Simulation time 15 seconds equals or exceeds stop time 15 seconds.

Now we load the saved output

ζt = FieldTimeSeries(filename * ".jld2", "ζ")
times = ζt.times

0.0:0.2:15.0

and make a movie

fig = Figure(size = (600, 600))
ax = Axis(fig[1, 1])
hidedecorations!(ax)
hidespines!(ax)

n = Observable(1)

ζn = @lift ζt[$n]

ζlim = 0.8
heatmap!(ax, ζn; colormap = :balance, colorrange = (-ζlim, ζlim))

stillframes = 20
framerate = 32
movingframes = length(times)

record(fig, filename * ".mp4"; framerate) do io
    [recordframe!(io) for _ = 1:stillframes]

    for nn in 1:movingframes
        n[] = nn
        recordframe!(io)
    end

    for nn in movingframes:-1:1
        n[] = nn
        recordframe!(io)
    end

    [recordframe!(io) for _ = 1:stillframes]
end

"hello_turbulence.mp4"

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