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|) = 1.3e-05 ms⁻¹, wall time: 0 seconds
[ Info:     ... simulation initialization complete (7.468 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (2.718 seconds).
Iteration: 0040, time: 7.344 minutes, Δt: 7.911 seconds, max(|w|) = 4.1e-05 ms⁻¹, wall time: 10.935 seconds
Iteration: 0080, time: 11.439 minutes, Δt: 4.652 seconds, max(|w|) = 9.6e-03 ms⁻¹, wall time: 11.405 seconds
Iteration: 0120, time: 14.202 minutes, Δt: 4.163 seconds, max(|w|) = 2.2e-02 ms⁻¹, wall time: 11.820 seconds
Iteration: 0160, time: 16.888 minutes, Δt: 4.183 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 12.247 seconds
Iteration: 0200, time: 19.452 minutes, Δt: 4.044 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 12.667 seconds
Iteration: 0240, time: 21.984 minutes, Δt: 3.825 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 13.096 seconds
Iteration: 0280, time: 24.431 minutes, Δt: 3.736 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 13.528 seconds
Iteration: 0320, time: 26.815 minutes, Δt: 3.646 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 13.950 seconds
Iteration: 0360, time: 29 minutes, Δt: 3.308 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 14.431 seconds
Iteration: 0400, time: 31.175 minutes, Δt: 3.393 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 14.885 seconds
Iteration: 0440, time: 33.391 minutes, Δt: 3.189 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 15.307 seconds
Iteration: 0480, time: 35.473 minutes, Δt: 3.094 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 15.725 seconds
Iteration: 0520, time: 37.465 minutes, Δt: 3.091 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 16.146 seconds
Iteration: 0560, time: 39.453 minutes, Δt: 3.015 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 16.619 seconds
Iteration: 0600, time: 41.447 minutes, Δt: 3.005 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 17.034 seconds
Iteration: 0640, time: 43.355 minutes, Δt: 3.090 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 17.455 seconds
Iteration: 0680, time: 45.285 minutes, Δt: 2.845 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 17.875 seconds
Iteration: 0720, time: 47.091 minutes, Δt: 2.766 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 18.297 seconds
Iteration: 0760, time: 48.958 minutes, Δt: 2.899 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 18.798 seconds
Iteration: 0800, time: 50.850 minutes, Δt: 2.777 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 19.221 seconds
Iteration: 0840, time: 52.673 minutes, Δt: 2.906 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 19.642 seconds
Iteration: 0880, time: 54.570 minutes, Δt: 2.780 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 20.077 seconds
Iteration: 0920, time: 56.360 minutes, Δt: 2.819 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 20.550 seconds
Iteration: 0960, time: 58.184 minutes, Δt: 2.731 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 21.017 seconds
Iteration: 1000, time: 1 hour, Δt: 2.806 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 21.483 seconds
Iteration: 1040, time: 1.031 hours, Δt: 2.747 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 21.950 seconds
Iteration: 1080, time: 1.060 hours, Δt: 2.625 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 22.402 seconds
Iteration: 1120, time: 1.089 hours, Δt: 2.658 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 22.908 seconds
Iteration: 1160, time: 1.117 hours, Δt: 2.719 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 23.370 seconds
Iteration: 1200, time: 1.147 hours, Δt: 2.710 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 23.831 seconds
Iteration: 1240, time: 1.175 hours, Δt: 2.664 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 24.263 seconds
Iteration: 1280, time: 1.204 hours, Δt: 2.600 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 24.692 seconds
Iteration: 1320, time: 1.233 hours, Δt: 2.563 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 25.135 seconds
Iteration: 1360, time: 1.261 hours, Δt: 2.561 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 25.595 seconds
Iteration: 1400, time: 1.289 hours, Δt: 2.514 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 26.061 seconds
Iteration: 1440, time: 1.317 hours, Δt: 2.401 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 26.501 seconds
Iteration: 1480, time: 1.343 hours, Δt: 2.504 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 26.984 seconds
Iteration: 1520, time: 1.369 hours, Δt: 2.392 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 27.427 seconds
Iteration: 1560, time: 1.395 hours, Δt: 2.492 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 27.856 seconds
Iteration: 1600, time: 1.422 hours, Δt: 2.517 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 28.308 seconds
Iteration: 1640, time: 1.450 hours, Δt: 2.554 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 28.744 seconds
Iteration: 1680, time: 1.477 hours, Δt: 2.658 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 29.215 seconds
Iteration: 1720, time: 1.506 hours, Δt: 2.628 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 29.681 seconds
Iteration: 1760, time: 1.535 hours, Δt: 2.573 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 30.113 seconds
Iteration: 1800, time: 1.563 hours, Δt: 2.553 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 30.523 seconds
Iteration: 1840, time: 1.589 hours, Δt: 2.504 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 30.955 seconds
Iteration: 1880, time: 1.617 hours, Δt: 2.484 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 31.420 seconds
Iteration: 1920, time: 1.644 hours, Δt: 2.527 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 31.850 seconds
Iteration: 1960, time: 1.672 hours, Δt: 2.528 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 32.329 seconds
Iteration: 2000, time: 1.699 hours, Δt: 2.376 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 32.756 seconds
Iteration: 2040, time: 1.725 hours, Δt: 2.453 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 33.189 seconds
Iteration: 2080, time: 1.751 hours, Δt: 2.463 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 33.626 seconds
Iteration: 2120, time: 1.778 hours, Δt: 2.468 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 34.058 seconds
Iteration: 2160, time: 1.805 hours, Δt: 2.326 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 34.485 seconds
Iteration: 2200, time: 1.831 hours, Δt: 2.363 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 34.910 seconds
Iteration: 2240, time: 1.856 hours, Δt: 2.395 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 35.357 seconds
Iteration: 2280, time: 1.882 hours, Δt: 2.493 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 35.778 seconds
Iteration: 2320, time: 1.910 hours, Δt: 2.539 seconds, max(|w|) = 7.0e-02 ms⁻¹, wall time: 36.232 seconds
Iteration: 2360, time: 1.937 hours, Δt: 2.464 seconds, max(|w|) = 7.1e-02 ms⁻¹, wall time: 36.675 seconds
Iteration: 2400, time: 1.964 hours, Δt: 2.421 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 37.096 seconds
Iteration: 2440, time: 1.990 hours, Δt: 2.468 seconds, max(|w|) = 6.3e-02 ms⁻¹, wall time: 37.529 seconds
[ Info: Simulation is stopping after running for 37.685 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=0.0470035, min=-0.0492049, mean=-8.28276e-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=35.0124, 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=0.0189301, min=0.0, mean=0.000434534)

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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