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.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 (8.149 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (2.811 seconds).
Iteration: 0040, time: 7.344 minutes, Δt: 7.912 seconds, max(|w|) = 4.1e-05 ms⁻¹, wall time: 11.671 seconds
Iteration: 0080, time: 11.439 minutes, Δt: 4.676 seconds, max(|w|) = 8.5e-03 ms⁻¹, wall time: 12.212 seconds
Iteration: 0120, time: 14.205 minutes, Δt: 3.963 seconds, max(|w|) = 2.3e-02 ms⁻¹, wall time: 12.693 seconds
Iteration: 0160, time: 16.902 minutes, Δt: 4.202 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 13.131 seconds
Iteration: 0200, time: 19.542 minutes, Δt: 4.141 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 13.636 seconds
Iteration: 0240, time: 22.127 minutes, Δt: 3.882 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 14.130 seconds
Iteration: 0280, time: 24.633 minutes, Δt: 3.766 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 14.579 seconds
Iteration: 0320, time: 27.125 minutes, Δt: 3.713 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 15.039 seconds
Iteration: 0360, time: 29.470 minutes, Δt: 3.501 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 15.522 seconds
Iteration: 0400, time: 31.700 minutes, Δt: 3.434 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 16.013 seconds
Iteration: 0440, time: 33.895 minutes, Δt: 3.307 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 16.502 seconds
Iteration: 0480, time: 36 minutes, Δt: 3.161 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 16.982 seconds
Iteration: 0520, time: 38.108 minutes, Δt: 3.152 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 17.447 seconds
Iteration: 0560, time: 40.207 minutes, Δt: 2.938 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 17.889 seconds
Iteration: 0600, time: 42.100 minutes, Δt: 3.085 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 18.341 seconds
Iteration: 0640, time: 44.048 minutes, Δt: 3.006 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 18.801 seconds
Iteration: 0680, time: 46 minutes, Δt: 3.048 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 19.275 seconds
Iteration: 0720, time: 48 minutes, Δt: 2.769 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 19.745 seconds
Iteration: 0760, time: 49.763 minutes, Δt: 2.761 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 20.195 seconds
Iteration: 0800, time: 51.581 minutes, Δt: 2.937 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 20.657 seconds
Iteration: 0840, time: 53.417 minutes, Δt: 2.783 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 21.095 seconds
Iteration: 0880, time: 55.287 minutes, Δt: 2.884 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 21.547 seconds
Iteration: 0920, time: 57.144 minutes, Δt: 2.881 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 22.005 seconds
Iteration: 0960, time: 59 minutes, Δt: 2.767 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 22.439 seconds
Iteration: 1000, time: 1.014 hours, Δt: 2.831 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 22.892 seconds
Iteration: 1040, time: 1.044 hours, Δt: 2.654 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 23.359 seconds
Iteration: 1080, time: 1.073 hours, Δt: 2.720 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 23.808 seconds
Iteration: 1120, time: 1.102 hours, Δt: 2.599 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 24.264 seconds
Iteration: 1160, time: 1.131 hours, Δt: 2.598 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 24.737 seconds
Iteration: 1200, time: 1.160 hours, Δt: 2.686 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 25.207 seconds
Iteration: 1240, time: 1.188 hours, Δt: 2.611 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 25.666 seconds
Iteration: 1280, time: 1.216 hours, Δt: 2.461 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 26.109 seconds
Iteration: 1320, time: 1.242 hours, Δt: 2.435 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 26.549 seconds
Iteration: 1360, time: 1.270 hours, Δt: 2.504 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 27.016 seconds
Iteration: 1400, time: 1.297 hours, Δt: 2.494 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 27.488 seconds
Iteration: 1440, time: 1.324 hours, Δt: 2.500 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 27.955 seconds
Iteration: 1480, time: 1.351 hours, Δt: 2.587 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 28.412 seconds
Iteration: 1520, time: 1.379 hours, Δt: 2.650 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 28.865 seconds
Iteration: 1560, time: 1.407 hours, Δt: 2.516 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 29.330 seconds
Iteration: 1600, time: 1.434 hours, Δt: 2.502 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 29.794 seconds
Iteration: 1640, time: 1.462 hours, Δt: 2.612 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 30.247 seconds
Iteration: 1680, time: 1.490 hours, Δt: 2.628 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 30.746 seconds
Iteration: 1720, time: 1.518 hours, Δt: 2.559 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 31.243 seconds
Iteration: 1760, time: 1.546 hours, Δt: 2.586 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 31.758 seconds
Iteration: 1800, time: 1.574 hours, Δt: 2.372 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 32.233 seconds
Iteration: 1840, time: 1.600 hours, Δt: 2.435 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 32.701 seconds
Iteration: 1880, time: 1.627 hours, Δt: 2.479 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 33.171 seconds
Iteration: 1920, time: 1.654 hours, Δt: 2.481 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 33.631 seconds
Iteration: 1960, time: 1.681 hours, Δt: 2.518 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 34.096 seconds
Iteration: 2000, time: 1.709 hours, Δt: 2.521 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 34.572 seconds
Iteration: 2040, time: 1.736 hours, Δt: 2.462 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 35.071 seconds
Iteration: 2080, time: 1.763 hours, Δt: 2.481 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 35.526 seconds
Iteration: 2120, time: 1.790 hours, Δt: 2.520 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 36.034 seconds
Iteration: 2160, time: 1.818 hours, Δt: 2.498 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 36.529 seconds
Iteration: 2200, time: 1.845 hours, Δt: 2.475 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 37.010 seconds
Iteration: 2240, time: 1.871 hours, Δt: 2.446 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 37.499 seconds
Iteration: 2280, time: 1.898 hours, Δt: 2.391 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 37.966 seconds
Iteration: 2320, time: 1.924 hours, Δt: 2.411 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 38.458 seconds
Iteration: 2360, time: 1.950 hours, Δt: 2.402 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 38.912 seconds
Iteration: 2400, time: 1.975 hours, Δt: 2.315 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 39.388 seconds
Iteration: 2440, time: 2.000 hours, Δt: 2.318 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 39.877 seconds
[ Info: Simulation is stopping after running for 39.890 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=0.0468756, min=-0.0544975, mean=1.58449e-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=18.5884, S = 128×1×64×121 FieldTimeSeries{InMemory} located at (Center, Center, Center) of S at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: S
└── data: 134×1×70×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:67, 1:121) with eltype Float64 with indices -2:131×64:64×-2:67×1:121
    └── max=35.0126, min=0.0, mean=33.0007, νₑ = 128×1×64×121 FieldTimeSeries{InMemory} located at (Center, Center, Center) of νₑ at ocean_wind_mixing_and_convection.jld2
├── grid: 128×128×64 RectilinearGrid{Float64, Periodic, Periodic, Bounded} on CPU with 3×3×3 halo
├── indices: (:, 64:64, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: ocean_wind_mixing_and_convection.jld2
├── name: νₑ
└── data: 134×1×70×121 OffsetArray(::Array{Float64, 4}, -2:131, 64:64, -2:67, 1:121) with eltype Float64 with indices -2:131×64:64×-2:67×1:121
    └── max=0.0174749, min=0.0, mean=0.000420136)

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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