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{CUDAGPU, 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{CUDAGPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── Next time step: 10 seconds
├── run_wall_time: 0 seconds
├── run_wall_time / 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 => Callback of stop_time_exceeded on IterationInterval(1)
│   ├── stop_iteration_exceeded => Callback of stop_iteration_exceeded on IterationInterval(1)
│   ├── wall_time_limit_exceeded => Callback of wall_time_limit_exceeded on IterationInterval(1)
│   └── nan_checker => Callback of NaNChecker for u on IterationInterval(100)
└── output_writers: 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.closure_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: 63.8 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 (7.569 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (2.862 seconds).
Iteration: 0040, time: 7.344 minutes, Δt: 7.912 seconds, max(|w|) = 4.2e-05 ms⁻¹, wall time: 11.230 seconds
Iteration: 0080, time: 11.439 minutes, Δt: 4.690 seconds, max(|w|) = 8.7e-03 ms⁻¹, wall time: 11.668 seconds
Iteration: 0120, time: 14.200 minutes, Δt: 3.949 seconds, max(|w|) = 2.2e-02 ms⁻¹, wall time: 12.164 seconds
Iteration: 0160, time: 16.733 minutes, Δt: 3.882 seconds, max(|w|) = 2.5e-02 ms⁻¹, wall time: 12.591 seconds
Iteration: 0200, time: 19.274 minutes, Δt: 4.007 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 13.044 seconds
Iteration: 0240, time: 21.918 minutes, Δt: 3.914 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 13.487 seconds
Iteration: 0280, time: 24.362 minutes, Δt: 3.517 seconds, max(|w|) = 2.5e-02 ms⁻¹, wall time: 13.941 seconds
Iteration: 0320, time: 26.617 minutes, Δt: 3.448 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 14.401 seconds
Iteration: 0360, time: 28.929 minutes, Δt: 3.454 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 14.832 seconds
Iteration: 0400, time: 31.113 minutes, Δt: 3.237 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 15.282 seconds
Iteration: 0440, time: 33.277 minutes, Δt: 3.171 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 15.721 seconds
Iteration: 0480, time: 35.325 minutes, Δt: 3.182 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 16.150 seconds
Iteration: 0520, time: 37.428 minutes, Δt: 3.159 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 16.596 seconds
Iteration: 0560, time: 39.538 minutes, Δt: 3.137 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 17.035 seconds
Iteration: 0600, time: 41.564 minutes, Δt: 3.071 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 17.484 seconds
Iteration: 0640, time: 43.521 minutes, Δt: 3.151 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 17.903 seconds
Iteration: 0680, time: 45.518 minutes, Δt: 3.075 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 18.336 seconds
Iteration: 0720, time: 47.509 minutes, Δt: 3.101 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 18.768 seconds
Iteration: 0760, time: 49.495 minutes, Δt: 2.997 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 19.194 seconds
Iteration: 0800, time: 51.390 minutes, Δt: 2.821 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 19.639 seconds
Iteration: 0840, time: 53.230 minutes, Δt: 2.797 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 20.077 seconds
Iteration: 0880, time: 55.046 minutes, Δt: 2.808 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 20.535 seconds
Iteration: 0920, time: 56.894 minutes, Δt: 2.811 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 20.952 seconds
Iteration: 0960, time: 58.698 minutes, Δt: 2.745 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 21.387 seconds
Iteration: 1000, time: 1.009 hours, Δt: 2.797 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 21.826 seconds
Iteration: 1040, time: 1.039 hours, Δt: 2.813 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 22.274 seconds
Iteration: 1080, time: 1.069 hours, Δt: 2.819 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 22.726 seconds
Iteration: 1120, time: 1.100 hours, Δt: 2.737 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 23.196 seconds
Iteration: 1160, time: 1.130 hours, Δt: 2.771 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 23.630 seconds
Iteration: 1200, time: 1.160 hours, Δt: 2.701 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 24.085 seconds
Iteration: 1240, time: 1.188 hours, Δt: 2.593 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 24.537 seconds
Iteration: 1280, time: 1.216 hours, Δt: 2.710 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 24.976 seconds
Iteration: 1320, time: 1.245 hours, Δt: 2.441 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 25.423 seconds
Iteration: 1360, time: 1.272 hours, Δt: 2.559 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 25.874 seconds
Iteration: 1400, time: 1.300 hours, Δt: 2.647 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 26.338 seconds
Iteration: 1440, time: 1.330 hours, Δt: 2.755 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 26.778 seconds
Iteration: 1480, time: 1.359 hours, Δt: 2.611 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 27.223 seconds
Iteration: 1520, time: 1.387 hours, Δt: 2.476 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 27.690 seconds
Iteration: 1560, time: 1.414 hours, Δt: 2.570 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 28.138 seconds
Iteration: 1600, time: 1.442 hours, Δt: 2.541 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 28.590 seconds
Iteration: 1640, time: 1.469 hours, Δt: 2.488 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 29.043 seconds
Iteration: 1680, time: 1.497 hours, Δt: 2.558 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 29.476 seconds
Iteration: 1720, time: 1.524 hours, Δt: 2.492 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 29.939 seconds
Iteration: 1760, time: 1.551 hours, Δt: 2.480 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 30.395 seconds
Iteration: 1800, time: 1.578 hours, Δt: 2.520 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 30.841 seconds
Iteration: 1840, time: 1.605 hours, Δt: 2.562 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 31.320 seconds
Iteration: 1880, time: 1.633 hours, Δt: 2.513 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 31.765 seconds
Iteration: 1920, time: 1.661 hours, Δt: 2.551 seconds, max(|w|) = 6.9e-02 ms⁻¹, wall time: 32.239 seconds
Iteration: 1960, time: 1.687 hours, Δt: 2.440 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 32.677 seconds
Iteration: 2000, time: 1.714 hours, Δt: 2.468 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 33.122 seconds
Iteration: 2040, time: 1.741 hours, Δt: 2.436 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 33.573 seconds
Iteration: 2080, time: 1.767 hours, Δt: 2.452 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 34.027 seconds
Iteration: 2120, time: 1.794 hours, Δt: 2.370 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 34.463 seconds
Iteration: 2160, time: 1.820 hours, Δt: 2.629 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 34.899 seconds
Iteration: 2200, time: 1.848 hours, Δt: 2.397 seconds, max(|w|) = 7.3e-02 ms⁻¹, wall time: 35.351 seconds
Iteration: 2240, time: 1.874 hours, Δt: 2.539 seconds, max(|w|) = 8.1e-02 ms⁻¹, wall time: 35.781 seconds
Iteration: 2280, time: 1.901 hours, Δt: 2.507 seconds, max(|w|) = 8.0e-02 ms⁻¹, wall time: 36.234 seconds
Iteration: 2320, time: 1.928 hours, Δt: 2.427 seconds, max(|w|) = 6.8e-02 ms⁻¹, wall time: 36.662 seconds
Iteration: 2360, time: 1.955 hours, Δt: 2.516 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 37.100 seconds
Iteration: 2400, time: 1.982 hours, Δt: 2.525 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 37.543 seconds
[ Info: Simulation is stopping after running for 37.821 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=0.0466709, min=-0.063971, mean=-4.9559e-5, 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=35.013, 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=0.0189032, min=0.0, mean=0.000420809)

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...

Julia version and environment information

This example was executed with the following version of Julia:

using InteractiveUtils: versioninfo
versioninfo()

Julia Version 1.12.2
Commit ca9b6662be4 (2025-11-20 16:25 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 9374F 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver4)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 128 virtual cores)
Environment:
  LD_LIBRARY_PATH = 
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /var/lib/buildkite-agent/.julia-oceananigans
  JULIA_PROJECT = /var/lib/buildkite-agent/Oceananigans.jl-27802/docs/
  JULIA_VERSION = 1.12.2
  JULIA_LOAD_PATH = @:@v#.#:@stdlib
  JULIA_VERSION_ENZYME = 1.10.10
  JULIA_PYTHONCALL_EXE = /var/lib/buildkite-agent/Oceananigans.jl-27802/docs/.CondaPkg/.pixi/envs/default/bin/python
  JULIA_DEBUG = Literate

These were the top-level packages installed in the environment:

import Pkg
Pkg.status()

Status `~/Oceananigans.jl-27802/docs/Project.toml`
  [79e6a3ab] Adapt v4.4.0
  [052768ef] CUDA v5.9.5
  [13f3f980] CairoMakie v0.15.8
  [e30172f5] Documenter v1.16.1
  [daee34ce] DocumenterCitations v1.4.1
  [033835bb] JLD2 v0.6.3
  [98b081ad] Literate v2.21.0
  [da04e1cc] MPI v0.20.23
  [85f8d34a] NCDatasets v0.14.10
  [9e8cae18] Oceananigans v0.103.1 `~/Oceananigans.jl-27802`
  [f27b6e38] Polynomials v4.1.0
  [6038ab10] Rotations v1.7.1
  [d496a93d] SeawaterPolynomials v0.3.10
  [09ab397b] StructArrays v0.7.2
  [bdfc003b] TimesDates v0.3.3
  [2e0b0046] XESMF v0.1.6
  [b77e0a4c] InteractiveUtils v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [44cfe95a] Pkg v1.12.0

This page was generated using Literate.jl.