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|) = 1.2e-05 ms⁻¹, wall time: 0 seconds
[ Info:     ... simulation initialization complete (13.190 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (4.896 seconds).
Iteration: 0040, time: 7 minutes, Δt: 8.310 seconds, max(|w|) = 2.8e-05 ms⁻¹, wall time: 18.742 seconds
Iteration: 0080, time: 11.183 minutes, Δt: 4.840 seconds, max(|w|) = 7.4e-03 ms⁻¹, wall time: 19.223 seconds
Iteration: 0120, time: 14 minutes, Δt: 4.082 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 19.642 seconds
Iteration: 0160, time: 16.672 minutes, Δt: 4.148 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 20.079 seconds
Iteration: 0200, time: 19.349 minutes, Δt: 3.989 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 20.517 seconds
Iteration: 0240, time: 21.890 minutes, Δt: 3.850 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 20.927 seconds
Iteration: 0280, time: 24.322 minutes, Δt: 3.753 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 21.389 seconds
Iteration: 0320, time: 26.688 minutes, Δt: 3.195 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 21.807 seconds
Iteration: 0360, time: 28.942 minutes, Δt: 3.358 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 22.243 seconds
Iteration: 0400, time: 31.111 minutes, Δt: 3.300 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 22.700 seconds
Iteration: 0440, time: 33.219 minutes, Δt: 3.326 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 23.157 seconds
Iteration: 0480, time: 35.267 minutes, Δt: 3.213 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 23.652 seconds
Iteration: 0520, time: 37.372 minutes, Δt: 3.310 seconds, max(|w|) = 3.4e-02 ms⁻¹, wall time: 24.099 seconds
Iteration: 0560, time: 39.481 minutes, Δt: 3.213 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 24.543 seconds
Iteration: 0600, time: 41.579 minutes, Δt: 3.121 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 24.963 seconds
Iteration: 0640, time: 43.550 minutes, Δt: 3.043 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 25.451 seconds
Iteration: 0680, time: 45.491 minutes, Δt: 3.012 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 25.886 seconds
Iteration: 0720, time: 47.390 minutes, Δt: 2.896 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 26.346 seconds
Iteration: 0760, time: 49.291 minutes, Δt: 2.821 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 26.770 seconds
Iteration: 0800, time: 51.143 minutes, Δt: 2.861 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 27.212 seconds
Iteration: 0840, time: 53 minutes, Δt: 2.724 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 27.657 seconds
Iteration: 0880, time: 54.833 minutes, Δt: 2.727 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 28.131 seconds
Iteration: 0920, time: 56.645 minutes, Δt: 2.633 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 28.644 seconds
Iteration: 0960, time: 58.366 minutes, Δt: 2.801 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 29.126 seconds
Iteration: 1000, time: 1.003 hours, Δt: 2.746 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 29.628 seconds
Iteration: 1040, time: 1.033 hours, Δt: 2.730 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 30.096 seconds
Iteration: 1080, time: 1.062 hours, Δt: 2.588 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 30.603 seconds
Iteration: 1120, time: 1.090 hours, Δt: 2.573 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 31.112 seconds
Iteration: 1160, time: 1.117 hours, Δt: 2.500 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 31.641 seconds
Iteration: 1200, time: 1.145 hours, Δt: 2.383 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 32.138 seconds
Iteration: 1240, time: 1.171 hours, Δt: 2.533 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 32.656 seconds
Iteration: 1280, time: 1.200 hours, Δt: 2.609 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 33.173 seconds
Iteration: 1320, time: 1.227 hours, Δt: 2.538 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 33.661 seconds
Iteration: 1360, time: 1.256 hours, Δt: 2.663 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 34.158 seconds
Iteration: 1400, time: 1.285 hours, Δt: 2.639 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 34.632 seconds
Iteration: 1440, time: 1.314 hours, Δt: 2.651 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 35.125 seconds
Iteration: 1480, time: 1.343 hours, Δt: 2.649 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 35.610 seconds
Iteration: 1520, time: 1.372 hours, Δt: 2.518 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 36.136 seconds
Iteration: 1560, time: 1.400 hours, Δt: 2.482 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 36.644 seconds
Iteration: 1600, time: 1.426 hours, Δt: 2.513 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 37.109 seconds
Iteration: 1640, time: 1.454 hours, Δt: 2.473 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 37.644 seconds
Iteration: 1680, time: 1.482 hours, Δt: 2.577 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 38.117 seconds
Iteration: 1720, time: 1.510 hours, Δt: 2.563 seconds, max(|w|) = 6.9e-02 ms⁻¹, wall time: 38.660 seconds
Iteration: 1760, time: 1.538 hours, Δt: 2.526 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 39.196 seconds
Iteration: 1800, time: 1.565 hours, Δt: 2.551 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 39.719 seconds
Iteration: 1840, time: 1.593 hours, Δt: 2.596 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 40.199 seconds
Iteration: 1880, time: 1.621 hours, Δt: 2.470 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 40.699 seconds
Iteration: 1920, time: 1.648 hours, Δt: 2.382 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 41.254 seconds
Iteration: 1960, time: 1.674 hours, Δt: 2.369 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 41.762 seconds
Iteration: 2000, time: 1.700 hours, Δt: 2.371 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 42.288 seconds
Iteration: 2040, time: 1.726 hours, Δt: 2.457 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 42.776 seconds
Iteration: 2080, time: 1.753 hours, Δt: 2.459 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 43.299 seconds
Iteration: 2120, time: 1.780 hours, Δt: 2.442 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 43.770 seconds
Iteration: 2160, time: 1.806 hours, Δt: 2.440 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 44.279 seconds
Iteration: 2200, time: 1.833 hours, Δt: 2.416 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 44.770 seconds
Iteration: 2240, time: 1.860 hours, Δt: 2.428 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 45.276 seconds
Iteration: 2280, time: 1.885 hours, Δt: 2.311 seconds, max(|w|) = 6.4e-02 ms⁻¹, wall time: 45.819 seconds
Iteration: 2320, time: 1.910 hours, Δt: 2.417 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 46.260 seconds
Iteration: 2360, time: 1.936 hours, Δt: 2.353 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 46.791 seconds
Iteration: 2400, time: 1.962 hours, Δt: 2.356 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 47.251 seconds
Iteration: 2440, time: 1.987 hours, Δt: 2.399 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 47.782 seconds
[ Info: Simulation is stopping after running for 48.010 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=0.0569034, min=-0.0584658, mean=-2.53428e-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=35.0135, 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=0.0189381, min=0.0, mean=0.000438569)

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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