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|) = 1.4e-05 ms⁻¹, wall time: 0 seconds
[ Info:     ... simulation initialization complete (23.627 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (8.942 seconds).
Iteration: 0040, time: 7.000 minutes, Δt: 8.309 seconds, max(|w|) = 3.0e-05 ms⁻¹, wall time: 33.617 seconds
Iteration: 0080, time: 11.092 minutes, Δt: 4.872 seconds, max(|w|) = 6.9e-03 ms⁻¹, wall time: 34.172 seconds
Iteration: 0120, time: 13.874 minutes, Δt: 4.028 seconds, max(|w|) = 2.1e-02 ms⁻¹, wall time: 34.641 seconds
Iteration: 0160, time: 16.552 minutes, Δt: 4.216 seconds, max(|w|) = 2.3e-02 ms⁻¹, wall time: 35.171 seconds
Iteration: 0200, time: 19.220 minutes, Δt: 4.258 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 35.647 seconds
Iteration: 0240, time: 21.934 minutes, Δt: 4.023 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 36.154 seconds
Iteration: 0280, time: 24.433 minutes, Δt: 3.699 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 36.614 seconds
Iteration: 0320, time: 26.808 minutes, Δt: 3.560 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 37.116 seconds
Iteration: 0360, time: 29.057 minutes, Δt: 3.460 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 37.591 seconds
Iteration: 0400, time: 31.214 minutes, Δt: 3.365 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 38.067 seconds
Iteration: 0440, time: 33.392 minutes, Δt: 3.412 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 38.577 seconds
Iteration: 0480, time: 35.605 minutes, Δt: 3.339 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 39.059 seconds
Iteration: 0520, time: 37.683 minutes, Δt: 3.177 seconds, max(|w|) = 3.3e-02 ms⁻¹, wall time: 39.581 seconds
Iteration: 0560, time: 39.812 minutes, Δt: 3.241 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 40.042 seconds
Iteration: 0600, time: 41.879 minutes, Δt: 3.135 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 40.548 seconds
Iteration: 0640, time: 43.874 minutes, Δt: 2.946 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 41.000 seconds
Iteration: 0680, time: 45.716 minutes, Δt: 2.855 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 41.506 seconds
Iteration: 0720, time: 47.574 minutes, Δt: 2.933 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 41.963 seconds
Iteration: 0760, time: 49.495 minutes, Δt: 2.939 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 42.438 seconds
Iteration: 0800, time: 51.382 minutes, Δt: 2.772 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 42.941 seconds
Iteration: 0840, time: 53.133 minutes, Δt: 2.779 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 43.415 seconds
Iteration: 0880, time: 54.995 minutes, Δt: 2.848 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 43.913 seconds
Iteration: 0920, time: 56.779 minutes, Δt: 2.830 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 44.371 seconds
Iteration: 0960, time: 58.583 minutes, Δt: 2.745 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 44.865 seconds
Iteration: 1000, time: 1.006 hours, Δt: 2.806 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 45.322 seconds
Iteration: 1040, time: 1.036 hours, Δt: 2.737 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 45.792 seconds
Iteration: 1080, time: 1.066 hours, Δt: 2.722 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 46.290 seconds
Iteration: 1120, time: 1.096 hours, Δt: 2.703 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 46.762 seconds
Iteration: 1160, time: 1.124 hours, Δt: 2.783 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 47.272 seconds
Iteration: 1200, time: 1.154 hours, Δt: 2.791 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 47.736 seconds
Iteration: 1240, time: 1.183 hours, Δt: 2.548 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 48.231 seconds
Iteration: 1280, time: 1.211 hours, Δt: 2.647 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 48.699 seconds
Iteration: 1320, time: 1.239 hours, Δt: 2.700 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 49.209 seconds
Iteration: 1360, time: 1.268 hours, Δt: 2.627 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 49.671 seconds
Iteration: 1400, time: 1.296 hours, Δt: 2.629 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 50.123 seconds
Iteration: 1440, time: 1.325 hours, Δt: 2.631 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 50.612 seconds
Iteration: 1480, time: 1.354 hours, Δt: 2.621 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 51.083 seconds
Iteration: 1520, time: 1.383 hours, Δt: 2.604 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 51.563 seconds
Iteration: 1560, time: 1.410 hours, Δt: 2.544 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 52.029 seconds
Iteration: 1600, time: 1.437 hours, Δt: 2.494 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 52.528 seconds
Iteration: 1640, time: 1.465 hours, Δt: 2.505 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 52.972 seconds
Iteration: 1680, time: 1.491 hours, Δt: 2.624 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 53.500 seconds
Iteration: 1720, time: 1.519 hours, Δt: 2.536 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 53.955 seconds
Iteration: 1760, time: 1.547 hours, Δt: 2.503 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 54.409 seconds
Iteration: 1800, time: 1.574 hours, Δt: 2.542 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 54.904 seconds
Iteration: 1840, time: 1.601 hours, Δt: 2.523 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 55.373 seconds
Iteration: 1880, time: 1.628 hours, Δt: 2.494 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 55.859 seconds
Iteration: 1920, time: 1.654 hours, Δt: 2.287 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 56.336 seconds
Iteration: 1960, time: 1.679 hours, Δt: 2.428 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 56.833 seconds
Iteration: 2000, time: 1.706 hours, Δt: 2.480 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 57.302 seconds
Iteration: 2040, time: 1.733 hours, Δt: 2.460 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 57.781 seconds
Iteration: 2080, time: 1.759 hours, Δt: 2.498 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 58.294 seconds
Iteration: 2120, time: 1.786 hours, Δt: 2.486 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 58.776 seconds
Iteration: 2160, time: 1.813 hours, Δt: 2.381 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 59.316 seconds
Iteration: 2200, time: 1.839 hours, Δt: 2.329 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 59.829 seconds
Iteration: 2240, time: 1.864 hours, Δt: 2.278 seconds, max(|w|) = 6.4e-02 ms⁻¹, wall time: 1.005 minutes
Iteration: 2280, time: 1.888 hours, Δt: 2.305 seconds, max(|w|) = 8.0e-02 ms⁻¹, wall time: 1.013 minutes
Iteration: 2320, time: 1.913 hours, Δt: 2.300 seconds, max(|w|) = 7.3e-02 ms⁻¹, wall time: 1.022 minutes
Iteration: 2360, time: 1.939 hours, Δt: 2.334 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 1.030 minutes
Iteration: 2400, time: 1.964 hours, Δt: 2.255 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 1.037 minutes
Iteration: 2440, time: 1.988 hours, Δt: 2.231 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 1.046 minutes
[ Info: Simulation is stopping after running for 1.050 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=0.0398717, min=-0.0715062, mean=1.91011e-6, 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=35.0132, 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=0.0185711, min=0.0, mean=0.00042114)

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...

This page was generated using Literate.jl.