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
├── 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.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: 57.9 MiB

We're ready:

run!(simulation)

[ Info: Initializing simulation...
Iteration: 0000, time: 0 seconds, Δt: 11 seconds, max(|w|) = 1.6e-05 ms⁻¹, wall time: 0 seconds
[ Info:     ... simulation initialization complete (16.227 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (4.779 seconds).
Iteration: 0040, time: 7.344 minutes, Δt: 7.911 seconds, max(|w|) = 3.7e-05 ms⁻¹, wall time: 21.892 seconds
Iteration: 0080, time: 11.440 minutes, Δt: 4.693 seconds, max(|w|) = 8.6e-03 ms⁻¹, wall time: 22.483 seconds
Iteration: 0120, time: 14.066 minutes, Δt: 3.959 seconds, max(|w|) = 2.2e-02 ms⁻¹, wall time: 22.969 seconds
Iteration: 0160, time: 16.692 minutes, Δt: 4.161 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 23.462 seconds
Iteration: 0200, time: 19.356 minutes, Δt: 4.264 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 23.994 seconds
Iteration: 0240, time: 21.884 minutes, Δt: 3.866 seconds, max(|w|) = 2.5e-02 ms⁻¹, wall time: 24.495 seconds
Iteration: 0280, time: 24.378 minutes, Δt: 3.807 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 25.036 seconds
Iteration: 0320, time: 26.780 minutes, Δt: 3.706 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 25.477 seconds
Iteration: 0360, time: 29.119 minutes, Δt: 3.558 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 25.950 seconds
Iteration: 0400, time: 31.461 minutes, Δt: 3.554 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 26.406 seconds
Iteration: 0440, time: 33.664 minutes, Δt: 3.388 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 26.844 seconds
Iteration: 0480, time: 35.909 minutes, Δt: 3.224 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 27.301 seconds
Iteration: 0520, time: 38 minutes, Δt: 3.212 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 27.750 seconds
Iteration: 0560, time: 40.104 minutes, Δt: 3.236 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 28.192 seconds
Iteration: 0600, time: 42.149 minutes, Δt: 2.892 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 28.668 seconds
Iteration: 0640, time: 44.050 minutes, Δt: 2.947 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 29.123 seconds
Iteration: 0680, time: 45.974 minutes, Δt: 2.944 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 29.571 seconds
Iteration: 0720, time: 47.852 minutes, Δt: 2.745 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 29.993 seconds
Iteration: 0760, time: 49.669 minutes, Δt: 2.865 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 30.458 seconds
Iteration: 0800, time: 51.588 minutes, Δt: 2.860 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 30.918 seconds
Iteration: 0840, time: 53.415 minutes, Δt: 2.836 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 31.364 seconds
Iteration: 0880, time: 55.232 minutes, Δt: 2.767 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 31.822 seconds
Iteration: 0920, time: 57.047 minutes, Δt: 2.766 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 32.258 seconds
Iteration: 0960, time: 58.871 minutes, Δt: 2.723 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 32.704 seconds
Iteration: 1000, time: 1.011 hours, Δt: 2.588 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 33.231 seconds
Iteration: 1040, time: 1.040 hours, Δt: 2.552 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 33.667 seconds
Iteration: 1080, time: 1.068 hours, Δt: 2.751 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 34.155 seconds
Iteration: 1120, time: 1.099 hours, Δt: 2.680 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 34.582 seconds
Iteration: 1160, time: 1.128 hours, Δt: 2.780 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 35.035 seconds
Iteration: 1200, time: 1.158 hours, Δt: 2.687 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 35.481 seconds
Iteration: 1240, time: 1.187 hours, Δt: 2.582 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 35.946 seconds
Iteration: 1280, time: 1.216 hours, Δt: 2.706 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 36.431 seconds
Iteration: 1320, time: 1.245 hours, Δt: 2.639 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 36.949 seconds
Iteration: 1360, time: 1.273 hours, Δt: 2.536 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 37.664 seconds
Iteration: 1400, time: 1.301 hours, Δt: 2.582 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 38.601 seconds
Iteration: 1440, time: 1.329 hours, Δt: 2.585 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 39.493 seconds
Iteration: 1480, time: 1.356 hours, Δt: 2.612 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 40.445 seconds
Iteration: 1520, time: 1.386 hours, Δt: 2.631 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 41.434 seconds
Iteration: 1560, time: 1.414 hours, Δt: 2.597 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 42.360 seconds
Iteration: 1600, time: 1.441 hours, Δt: 2.463 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 43.329 seconds
Iteration: 1640, time: 1.467 hours, Δt: 2.435 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 44.319 seconds
Iteration: 1680, time: 1.495 hours, Δt: 2.520 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 45.315 seconds
Iteration: 1720, time: 1.522 hours, Δt: 2.592 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 46.302 seconds
Iteration: 1760, time: 1.550 hours, Δt: 2.582 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 47.252 seconds
Iteration: 1800, time: 1.578 hours, Δt: 2.446 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 48.190 seconds
Iteration: 1840, time: 1.605 hours, Δt: 2.524 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 49.169 seconds
Iteration: 1880, time: 1.631 hours, Δt: 2.413 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 50.152 seconds
Iteration: 1920, time: 1.658 hours, Δt: 2.526 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 51.311 seconds
Iteration: 1960, time: 1.685 hours, Δt: 2.553 seconds, max(|w|) = 6.9e-02 ms⁻¹, wall time: 52.341 seconds
Iteration: 2000, time: 1.713 hours, Δt: 2.487 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 53.328 seconds
Iteration: 2040, time: 1.740 hours, Δt: 2.444 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 54.369 seconds
Iteration: 2080, time: 1.767 hours, Δt: 2.448 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 55.402 seconds
Iteration: 2120, time: 1.793 hours, Δt: 2.442 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 56.381 seconds
Iteration: 2160, time: 1.820 hours, Δt: 2.433 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 57.335 seconds
Iteration: 2200, time: 1.847 hours, Δt: 2.397 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 58.374 seconds
Iteration: 2240, time: 1.873 hours, Δt: 2.355 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 59.360 seconds
Iteration: 2280, time: 1.899 hours, Δt: 2.437 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 1.006 minutes
Iteration: 2320, time: 1.926 hours, Δt: 2.455 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 1.023 minutes
Iteration: 2360, time: 1.952 hours, Δt: 2.463 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 1.040 minutes
Iteration: 2400, time: 1.979 hours, Δt: 2.496 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 1.057 minutes
[ Info: Simulation is stopping after running for 1.071 minutes.
[ 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=0.049421, min=-0.069347, mean=1.02826e-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=18.5886, 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=35.0136, 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=0.0193033, min=0.0, mean=0.000426575)

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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