Wind- and convection-driven mixing in an ocean surface boundary layer

This example simulates mixing by three-dimensional turbulence in an ocean surface boundary layer driven by atmospheric winds and convection. It demonstrates:

• How to set-up a grid with varying spacing in the vertical direction
• How to use the SeawaterBuoyancy model for buoyancy with TEOS10EquationOfState.
• How to use a turbulence closure for large eddy simulation.
• How to use a function to impose a boundary condition.

Install dependencies

First let's make sure we have all required packages installed.

using Pkg
pkg"add Oceananigans, CairoMakie, SeawaterPolynomials, CUDA"

We start by importing all of the packages and functions that we'll need for this example.

using Oceananigans
using Oceananigans.Units

using CUDA
using Random
using Printf
using CairoMakie
using SeawaterPolynomials.TEOS10: TEOS10EquationOfState

The grid

We use 128²×64 grid points with 1 m grid spacing in the horizontal and varying spacing in the vertical, with higher resolution closer to the surface. Here we use a stretching function for the vertical nodes that maintains relatively constant vertical spacing in the mixed layer, which is desirable from a numerical standpoint:

Nx = Ny = 128    # number of points in each of horizontal directions
Nz = 64          # number of points in the vertical direction

Lx = Ly = 128    # (m) domain horizontal extents
Lz = 64          # (m) domain depth

refinement = 1.2 # controls spacing near surface (higher means finer spaced)
stretching = 12  # controls rate of stretching at bottom

# Normalized height ranging from 0 to 1
h(k) = (k - 1) / Nz

# Linear near-surface generator
ζ₀(k) = 1 + (h(k) - 1) / refinement

# Bottom-intensified stretching function
Σ(k) = (1 - exp(-stretching * h(k))) / (1 - exp(-stretching))

# Generating function
z_interfaces(k) = Lz * (ζ₀(k) * Σ(k) - 1)

grid = RectilinearGrid(GPU(),
                       size = (Nx, Nx, Nz),
                       x = (0, Lx),
                       y = (0, Ly),
                       z = z_interfaces)

128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CUDAGPU with 3×3×3 halo
├── Periodic x ∈ [0.0, 128.0) regularly spaced with Δx=1.0
├── Periodic y ∈ [0.0, 128.0) regularly spaced with Δy=1.0
└── Bounded  z ∈ [-64.0, 0.0] variably spaced with min(Δz)=0.833413, max(Δz)=1.96618

We plot vertical spacing versus depth to inspect the prescribed grid stretching:

fig = Figure(size=(1200, 800))
ax = Axis(fig[1, 1], ylabel = "z (m)", xlabel = "Vertical spacing (m)")

lines!(ax, zspacings(grid, Center()))
scatter!(ax, zspacings(grid, Center()))

fig

Buoyancy that depends on temperature and salinity

We use the SeawaterBuoyancy model with the TEOS10 equation of state,

ρₒ = 1026 # kg m⁻³, average density at the surface of the world ocean
equation_of_state = TEOS10EquationOfState(reference_density=ρₒ)
buoyancy = SeawaterBuoyancy(; equation_of_state)

SeawaterBuoyancy{Float64}:
├── gravitational_acceleration: 9.80665
└── equation_of_state: BoussinesqEquationOfState{Float64}

Boundary conditions

We calculate the surface temperature flux associated with surface cooling of 200 W m⁻², reference density ρₒ, and heat capacity cᴾ,

Q = 200   # W m⁻², surface _heat_ flux
cᴾ = 3991 # J K⁻¹ kg⁻¹, typical heat capacity for seawater

Jᵀ = Q / (ρₒ * cᴾ) # K m s⁻¹, surface _temperature_ flux

4.884283985946938e-5

Finally, we impose a temperature gradient dTdz both initially (see "Initial conditions" section below) and at the bottom of the domain, culminating in the boundary conditions on temperature,

dTdz = 0.01 # K m⁻¹

T_bcs = FieldBoundaryConditions(top = FluxBoundaryCondition(Jᵀ),
                                bottom = GradientBoundaryCondition(dTdz))

Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: GradientBoundaryCondition: 0.01
├── top: FluxBoundaryCondition: 4.88428e-5
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)

Note that a positive temperature flux at the surface of the ocean implies cooling. This is because a positive temperature flux implies that temperature is fluxed upwards, out of the ocean.

For the velocity field, we imagine a wind blowing over the ocean surface with an average velocity at 10 meters u₁₀, and use a drag coefficient cᴰ to estimate the kinematic stress (that is, stress divided by density) exerted by the wind on the ocean:

u₁₀ = 10  # m s⁻¹, average wind velocity 10 meters above the ocean
cᴰ = 2e-3 # dimensionless drag coefficient
ρₐ = 1.2  # kg m⁻³, approximate average density of air at sea-level
τx = - ρₐ / ρₒ * cᴰ * u₁₀ * abs(u₁₀) # m² s⁻²

-0.00023391812865497074

The boundary conditions on u are thus

u_bcs = FieldBoundaryConditions(top = FluxBoundaryCondition(τx))

Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: -0.000233918
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)

For salinity, S, we impose an evaporative flux of the form

@inline Jˢ(x, y, t, S, evaporation_rate) = - evaporation_rate * S # [salinity unit] m s⁻¹

where S is salinity. We use an evaporation rate of 1 millimeter per hour,

evaporation_rate = 1e-3 / hour # m s⁻¹

2.7777777777777776e-7

We build the Flux evaporation BoundaryCondition with the function Jˢ, indicating that Jˢ depends on salinity S and passing the parameter evaporation_rate,

evaporation_bc = FluxBoundaryCondition(Jˢ, field_dependencies=:S, parameters=evaporation_rate)

FluxBoundaryCondition: ContinuousBoundaryFunction Jˢ at (Nothing, Nothing, Nothing)

The full salinity boundary conditions are

S_bcs = FieldBoundaryConditions(top=evaporation_bc)

Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: ContinuousBoundaryFunction Jˢ at (Nothing, Nothing, Nothing)
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)

Model instantiation

We fill in the final details of the model here, i.e., Coriolis forces, and the AnisotropicMinimumDissipation closure for large eddy simulation to model the effect of turbulent motions at scales smaller than the grid scale that are not explicitly resolved.

model = NonhydrostaticModel(; grid, buoyancy,
                            tracers = (:T, :S),
                            coriolis = FPlane(f=1e-4),
                            closure = AnisotropicMinimumDissipation(),
                            boundary_conditions = (u=u_bcs, T=T_bcs, S=S_bcs))

NonhydrostaticModel{GPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CUDAGPU with 3×3×3 halo
├── timestepper: RungeKutta3TimeStepper
├── advection scheme: Centered(order=2)
├── tracers: (T, S)
├── closure: AnisotropicMinimumDissipation{ExplicitTimeDiscretization, @NamedTuple{T::Float64, S::Float64}, Float64, Nothing}
├── buoyancy: SeawaterBuoyancy with g=9.80665 and BoussinesqEquationOfState{Float64} with ĝ = NegativeZDirection()
└── coriolis: FPlane{Float64}(f=0.0001)

Note: To use the Smagorinsky-Lilly turbulence closure (with a constant model coefficient) rather than AnisotropicMinimumDissipation, use closure = SmagorinskyLilly() in the model constructor.

Initial conditions

Our initial condition for temperature consists of a linear stratification superposed with random noise damped at the walls, while our initial condition for velocity consists only of random noise.

# Random noise damped at top and bottom
Ξ(z) = randn() * z / model.grid.Lz * (1 + z / model.grid.Lz) # noise

# Temperature initial condition: a stable density gradient with random noise superposed.
Tᵢ(x, y, z) = 20 + dTdz * z + dTdz * model.grid.Lz * 1e-6 * Ξ(z)

# Velocity initial condition: random noise scaled by the friction velocity.
uᵢ(x, y, z) = sqrt(abs(τx)) * 1e-3 * Ξ(z)

# `set!` the `model` fields using functions or constants:
set!(model, u=uᵢ, w=uᵢ, T=Tᵢ, S=35)

Setting up a simulation

We set-up a simulation with an initial time-step of 10 seconds that stops at 2 hours, with adaptive time-stepping and progress printing.

simulation = Simulation(model, Δt=10, stop_time=2hours)

Simulation of NonhydrostaticModel{GPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── Next time step: 10 seconds
├── Elapsed wall time: 0 seconds
├── Wall time per iteration: NaN days
├── Stop time: 2 hours
├── Stop iteration: Inf
├── Wall time limit: Inf
├── Minimum relative step: 0.0
├── Callbacks: OrderedDict with 4 entries:
│   ├── stop_time_exceeded => 4
│   ├── stop_iteration_exceeded => -
│   ├── wall_time_limit_exceeded => e
│   └── nan_checker => }
├── Output writers: OrderedDict with no entries
└── Diagnostics: OrderedDict with no entries

The TimeStepWizard helps ensure stable time-stepping with a Courant-Freidrichs-Lewy (CFL) number of 1.0.

wizard = TimeStepWizard(cfl=1, max_change=1.1, max_Δt=1minute)
simulation.callbacks[:wizard] = Callback(wizard, IterationInterval(10))

Callback of TimeStepWizard(cfl=1.0, max_Δt=60.0, min_Δt=0.0) on IterationInterval(10)

Nice progress messaging is helpful:

# Print a progress message
progress_message(sim) = @printf("Iteration: %04d, time: %s, Δt: %s, max(|w|) = %.1e ms⁻¹, wall time: %s\n",
                                iteration(sim), prettytime(sim), prettytime(sim.Δt),
                                maximum(abs, sim.model.velocities.w), prettytime(sim.run_wall_time))

add_callback!(simulation, progress_message, IterationInterval(40))

We then set up the simulation:

Output

We use the JLD2Writer to save $x, z$ slices of the velocity fields, tracer fields, and eddy diffusivities. The prefix keyword argument to JLD2Writer indicates that output will be saved in ocean_wind_mixing_and_convection.jld2.

# Create a NamedTuple with eddy viscosity
eddy_viscosity = (; νₑ = model.diffusivity_fields.νₑ)

filename = "ocean_wind_mixing_and_convection"

simulation.output_writers[:slices] =
    JLD2Writer(model, merge(model.velocities, model.tracers, eddy_viscosity),
               filename = filename * ".jld2",
               indices = (:, grid.Ny/2, :),
               schedule = TimeInterval(1minute),
               overwrite_existing = true)

JLD2Writer scheduled on TimeInterval(1 minute):
├── filepath: ocean_wind_mixing_and_convection.jld2
├── 6 outputs: (u, v, w, T, S, νₑ)
├── array_type: Array{Float32}
├── including: [:grid, :coriolis, :buoyancy, :closure]
├── file_splitting: NoFileSplitting
└── file size: 63.7 KiB

We're ready:

run!(simulation)

[ Info: Initializing simulation...
Iteration: 0000, time: 0 seconds, Δt: 11 seconds, max(|w|) = 1.3e-05 ms⁻¹, wall time: 0 seconds
[ Info:     ... simulation initialization complete (12.885 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (4.751 seconds).
Iteration: 0040, time: 7.000 minutes, Δt: 8.309 seconds, max(|w|) = 2.5e-05 ms⁻¹, wall time: 18.371 seconds
Iteration: 0080, time: 11.092 minutes, Δt: 4.963 seconds, max(|w|) = 6.6e-03 ms⁻¹, wall time: 18.974 seconds
Iteration: 0120, time: 13.944 minutes, Δt: 4.021 seconds, max(|w|) = 2.3e-02 ms⁻¹, wall time: 19.375 seconds
Iteration: 0160, time: 16.635 minutes, Δt: 4.039 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 19.883 seconds
Iteration: 0200, time: 19.271 minutes, Δt: 4.079 seconds, max(|w|) = 2.5e-02 ms⁻¹, wall time: 20.332 seconds
Iteration: 0240, time: 21.839 minutes, Δt: 3.737 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 20.836 seconds
Iteration: 0280, time: 24.325 minutes, Δt: 3.781 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 21.283 seconds
Iteration: 0320, time: 26.683 minutes, Δt: 3.689 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 21.728 seconds
Iteration: 0360, time: 28.976 minutes, Δt: 3.504 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 22.140 seconds
Iteration: 0400, time: 31.229 minutes, Δt: 3.429 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 22.610 seconds
Iteration: 0440, time: 33.375 minutes, Δt: 3.192 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 23.007 seconds
Iteration: 0480, time: 35.494 minutes, Δt: 3.247 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 23.453 seconds
Iteration: 0520, time: 37.594 minutes, Δt: 3.235 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 23.911 seconds
Iteration: 0560, time: 39.610 minutes, Δt: 3.113 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 24.383 seconds
Iteration: 0600, time: 41.568 minutes, Δt: 3.086 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 24.913 seconds
Iteration: 0640, time: 43.587 minutes, Δt: 3.101 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 25.396 seconds
Iteration: 0680, time: 45.609 minutes, Δt: 2.993 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 25.898 seconds
Iteration: 0720, time: 47.551 minutes, Δt: 2.948 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 26.318 seconds
Iteration: 0760, time: 49.454 minutes, Δt: 2.971 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 26.762 seconds
Iteration: 0800, time: 51.274 minutes, Δt: 2.774 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 27.163 seconds
Iteration: 0840, time: 53.095 minutes, Δt: 2.843 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 27.602 seconds
Iteration: 0880, time: 54.914 minutes, Δt: 2.766 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 28.008 seconds
Iteration: 0920, time: 56.622 minutes, Δt: 2.678 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 28.449 seconds
Iteration: 0960, time: 58.360 minutes, Δt: 2.585 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 28.871 seconds
Iteration: 1000, time: 1 hour, Δt: 2.708 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 29.322 seconds
Iteration: 1040, time: 1.029 hours, Δt: 2.588 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 29.771 seconds
Iteration: 1080, time: 1.056 hours, Δt: 2.671 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 30.169 seconds
Iteration: 1120, time: 1.083 hours, Δt: 2.640 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 30.633 seconds
Iteration: 1160, time: 1.113 hours, Δt: 2.755 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 31.071 seconds
Iteration: 1200, time: 1.142 hours, Δt: 2.693 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 31.532 seconds
Iteration: 1240, time: 1.171 hours, Δt: 2.677 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 31.954 seconds
Iteration: 1280, time: 1.200 hours, Δt: 2.697 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 32.397 seconds
Iteration: 1320, time: 1.230 hours, Δt: 2.674 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 32.830 seconds
Iteration: 1360, time: 1.259 hours, Δt: 2.637 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 33.269 seconds
Iteration: 1400, time: 1.287 hours, Δt: 2.511 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 33.758 seconds
Iteration: 1440, time: 1.315 hours, Δt: 2.482 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 34.216 seconds
Iteration: 1480, time: 1.342 hours, Δt: 2.604 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 34.695 seconds
Iteration: 1520, time: 1.370 hours, Δt: 2.627 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 35.215 seconds
Iteration: 1560, time: 1.399 hours, Δt: 2.501 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 35.722 seconds
Iteration: 1600, time: 1.426 hours, Δt: 2.472 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 36.185 seconds
Iteration: 1640, time: 1.453 hours, Δt: 2.601 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 36.628 seconds
Iteration: 1680, time: 1.481 hours, Δt: 2.515 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 37.026 seconds
Iteration: 1720, time: 1.508 hours, Δt: 2.556 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 37.476 seconds
Iteration: 1760, time: 1.536 hours, Δt: 2.535 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 37.890 seconds
Iteration: 1800, time: 1.563 hours, Δt: 2.539 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 38.333 seconds
Iteration: 1840, time: 1.591 hours, Δt: 2.383 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 38.754 seconds
Iteration: 1880, time: 1.617 hours, Δt: 2.276 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 39.200 seconds
Iteration: 1920, time: 1.643 hours, Δt: 2.427 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 39.628 seconds
Iteration: 1960, time: 1.669 hours, Δt: 2.436 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 40.066 seconds
Iteration: 2000, time: 1.696 hours, Δt: 2.432 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 40.479 seconds
Iteration: 2040, time: 1.723 hours, Δt: 2.408 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 40.917 seconds
Iteration: 2080, time: 1.748 hours, Δt: 2.379 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 41.388 seconds
Iteration: 2120, time: 1.775 hours, Δt: 2.475 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 41.796 seconds
Iteration: 2160, time: 1.801 hours, Δt: 2.427 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 42.245 seconds
Iteration: 2200, time: 1.827 hours, Δt: 2.422 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 42.655 seconds
Iteration: 2240, time: 1.853 hours, Δt: 2.425 seconds, max(|w|) = 6.4e-02 ms⁻¹, wall time: 43.118 seconds
Iteration: 2280, time: 1.880 hours, Δt: 2.379 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 43.526 seconds
Iteration: 2320, time: 1.905 hours, Δt: 2.435 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 43.973 seconds
Iteration: 2360, time: 1.931 hours, Δt: 2.346 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 44.380 seconds
Iteration: 2400, time: 1.957 hours, Δt: 2.410 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 44.821 seconds
Iteration: 2440, time: 1.984 hours, Δt: 2.325 seconds, max(|w|) = 7.3e-02 ms⁻¹, wall time: 45.241 seconds
[ Info: Simulation is stopping after running for 45.517 seconds.
[ Info: Simulation time 2 hours equals or exceeds stop time 2 hours.

Turbulence visualization

We animate the data saved in ocean_wind_mixing_and_convection.jld2. We prepare for animating the flow by loading the data into FieldTimeSeries and defining functions for computing colorbar limits.

filepath = filename * ".jld2"

time_series = (w = FieldTimeSeries(filepath, "w"),
               T = FieldTimeSeries(filepath, "T"),
               S = FieldTimeSeries(filepath, "S"),
               νₑ = FieldTimeSeries(filepath, "νₑ"))

(w = 128×1×65×121 FieldTimeSeries{InMemory} located at (Center, Center, Face) of w at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: w
└── data: 134×1×71×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:68, 1:121) with eltype Float64 with indices -2:131×64:64×-2:68×1:121
    └── max=0.0444131, min=-0.0532021, mean=4.81815e-6, T = 128×1×64×121 FieldTimeSeries{InMemory} located at (Center, Center, Center) of T at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: T
└── data: 134×1×70×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:67, 1:121) with eltype Float64 with indices -2:131×64:64×-2:67×1:121
    └── max=19.9958, min=0.0, mean=18.5885, S = 128×1×64×121 FieldTimeSeries{InMemory} located at (Center, Center, Center) of S at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: S
└── data: 134×1×70×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:67, 1:121) with eltype Float64 with indices -2:131×64:64×-2:67×1:121
    └── max=35.0126, min=0.0, mean=33.0007, νₑ = 128×1×64×121 FieldTimeSeries{InMemory} located at (Center, Center, Center) of νₑ at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: νₑ
└── data: 134×1×70×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:67, 1:121) with eltype Float64 with indices -2:131×64:64×-2:67×1:121
    └── max=0.019322, min=0.0, mean=0.000407261)

We start the animation at $t = 10$ minutes since things are pretty boring till then:

times = time_series.w.times
intro = searchsortedfirst(times, 10minutes)

11

We are now ready to animate using Makie. We use Makie's Observable to animate the data. To dive into how Observables work we refer to Makie.jl's Documentation.

n = Observable(intro)

 wₙ = @lift time_series.w[$n]
 Tₙ = @lift time_series.T[$n]
 Sₙ = @lift time_series.S[$n]
νₑₙ = @lift time_series.νₑ[$n]

fig = Figure(size = (1800, 900))

axis_kwargs = (xlabel="x (m)",
               ylabel="z (m)",
               aspect = AxisAspect(grid.Lx/grid.Lz),
               limits = ((0, grid.Lx), (-grid.Lz, 0)))

ax_w  = Axis(fig[2, 1]; title = "Vertical velocity", axis_kwargs...)
ax_T  = Axis(fig[2, 3]; title = "Temperature", axis_kwargs...)
ax_S  = Axis(fig[3, 1]; title = "Salinity", axis_kwargs...)
ax_νₑ = Axis(fig[3, 3]; title = "Eddy viscocity", axis_kwargs...)

title = @lift @sprintf("t = %s", prettytime(times[$n]))

 wlims = (-0.05, 0.05)
 Tlims = (19.7, 19.99)
 Slims = (35, 35.005)
νₑlims = (1e-6, 5e-3)

hm_w = heatmap!(ax_w, wₙ; colormap = :balance, colorrange = wlims)
Colorbar(fig[2, 2], hm_w; label = "m s⁻¹")

hm_T = heatmap!(ax_T, Tₙ; colormap = :thermal, colorrange = Tlims)
Colorbar(fig[2, 4], hm_T; label = "ᵒC")

hm_S = heatmap!(ax_S, Sₙ; colormap = :haline, colorrange = Slims)
Colorbar(fig[3, 2], hm_S; label = "g / kg")

hm_νₑ = heatmap!(ax_νₑ, νₑₙ; colormap = :thermal, colorrange = νₑlims)
Colorbar(fig[3, 4], hm_νₑ; label = "m s⁻²")

fig[1, 1:4] = Label(fig, title, fontsize=24, tellwidth=false)

fig

And now record a movie.

frames = intro:length(times)

@info "Making a motion picture of ocean wind mixing and convection..."

CairoMakie.record(fig, filename * ".mp4", frames, framerate=8) do i
    n[] = i
end

[ Info: Making a motion picture of ocean wind mixing and convection...

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