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: 63.4 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 (26.327 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (10.396 seconds).
Iteration: 0040, time: 7 minutes, Δt: 8.309 seconds, max(|w|) = 2.9e-05 ms⁻¹, wall time: 38.329 seconds
Iteration: 0080, time: 11.182 minutes, Δt: 4.897 seconds, max(|w|) = 7.0e-03 ms⁻¹, wall time: 38.938 seconds
Iteration: 0120, time: 14 minutes, Δt: 4.093 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 39.597 seconds
Iteration: 0160, time: 16.700 minutes, Δt: 4.346 seconds, max(|w|) = 2.6e-02 ms⁻¹, wall time: 40.178 seconds
Iteration: 0200, time: 19.413 minutes, Δt: 4.110 seconds, max(|w|) = 2.9e-02 ms⁻¹, wall time: 40.823 seconds
Iteration: 0240, time: 22 minutes, Δt: 3.718 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 41.391 seconds
Iteration: 0280, time: 24.444 minutes, Δt: 3.650 seconds, max(|w|) = 2.4e-02 ms⁻¹, wall time: 41.990 seconds
Iteration: 0320, time: 26.749 minutes, Δt: 3.488 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 42.635 seconds
Iteration: 0360, time: 29 minutes, Δt: 3.500 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 43.237 seconds
Iteration: 0400, time: 31.223 minutes, Δt: 3.526 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 43.860 seconds
Iteration: 0440, time: 33.432 minutes, Δt: 3.212 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 44.450 seconds
Iteration: 0480, time: 35.466 minutes, Δt: 3.113 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 45.060 seconds
Iteration: 0520, time: 37.539 minutes, Δt: 3.133 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 45.631 seconds
Iteration: 0560, time: 39.560 minutes, Δt: 3.049 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 46.245 seconds
Iteration: 0600, time: 41.506 minutes, Δt: 3.019 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 46.810 seconds
Iteration: 0640, time: 43.504 minutes, Δt: 2.937 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 47.396 seconds
Iteration: 0680, time: 45.392 minutes, Δt: 2.971 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 47.961 seconds
Iteration: 0720, time: 47.288 minutes, Δt: 2.910 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 48.531 seconds
Iteration: 0760, time: 49.144 minutes, Δt: 2.981 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 49.166 seconds
Iteration: 0800, time: 51 minutes, Δt: 2.999 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 49.740 seconds
Iteration: 0840, time: 52.937 minutes, Δt: 2.983 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 50.370 seconds
Iteration: 0880, time: 54.795 minutes, Δt: 2.922 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 50.967 seconds
Iteration: 0920, time: 56.679 minutes, Δt: 2.893 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 51.594 seconds
Iteration: 0960, time: 58.514 minutes, Δt: 2.755 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 52.169 seconds
Iteration: 1000, time: 1.004 hours, Δt: 2.720 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 52.779 seconds
Iteration: 1040, time: 1.033 hours, Δt: 2.732 seconds, max(|w|) = 4.1e-02 ms⁻¹, wall time: 53.380 seconds
Iteration: 1080, time: 1.063 hours, Δt: 2.780 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 53.947 seconds
Iteration: 1120, time: 1.093 hours, Δt: 2.714 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 54.543 seconds
Iteration: 1160, time: 1.122 hours, Δt: 2.617 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 55.126 seconds
Iteration: 1200, time: 1.151 hours, Δt: 2.618 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 55.708 seconds
Iteration: 1240, time: 1.180 hours, Δt: 2.616 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 56.272 seconds
Iteration: 1280, time: 1.208 hours, Δt: 2.491 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 56.938 seconds
Iteration: 1320, time: 1.235 hours, Δt: 2.595 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 57.529 seconds
Iteration: 1360, time: 1.265 hours, Δt: 2.621 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 58.169 seconds
Iteration: 1400, time: 1.293 hours, Δt: 2.630 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 58.780 seconds
Iteration: 1440, time: 1.320 hours, Δt: 2.397 seconds, max(|w|) = 5.0e-02 ms⁻¹, wall time: 59.412 seconds
Iteration: 1480, time: 1.346 hours, Δt: 2.326 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 1.001 minutes
Iteration: 1520, time: 1.371 hours, Δt: 2.347 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 1.010 minutes
Iteration: 1560, time: 1.397 hours, Δt: 2.441 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 1.020 minutes
Iteration: 1600, time: 1.424 hours, Δt: 2.467 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 1.030 minutes
Iteration: 1640, time: 1.451 hours, Δt: 2.512 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 1.040 minutes
Iteration: 1680, time: 1.477 hours, Δt: 2.466 seconds, max(|w|) = 6.0e-02 ms⁻¹, wall time: 1.050 minutes
Iteration: 1720, time: 1.504 hours, Δt: 2.386 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 1.060 minutes
Iteration: 1760, time: 1.529 hours, Δt: 2.465 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 1.069 minutes
Iteration: 1800, time: 1.556 hours, Δt: 2.356 seconds, max(|w|) = 7.2e-02 ms⁻¹, wall time: 1.080 minutes
Iteration: 1840, time: 1.583 hours, Δt: 2.438 seconds, max(|w|) = 7.8e-02 ms⁻¹, wall time: 1.090 minutes
Iteration: 1880, time: 1.610 hours, Δt: 2.387 seconds, max(|w|) = 7.4e-02 ms⁻¹, wall time: 1.099 minutes
Iteration: 1920, time: 1.636 hours, Δt: 2.478 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 1.109 minutes
Iteration: 1960, time: 1.663 hours, Δt: 2.490 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 1.119 minutes
Iteration: 2000, time: 1.691 hours, Δt: 2.631 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 1.130 minutes
Iteration: 2040, time: 1.719 hours, Δt: 2.365 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 1.140 minutes
Iteration: 2080, time: 1.744 hours, Δt: 2.428 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 1.151 minutes
Iteration: 2120, time: 1.772 hours, Δt: 2.620 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 1.160 minutes
Iteration: 2160, time: 1.800 hours, Δt: 2.528 seconds, max(|w|) = 7.1e-02 ms⁻¹, wall time: 1.170 minutes
Iteration: 2200, time: 1.827 hours, Δt: 2.478 seconds, max(|w|) = 6.5e-02 ms⁻¹, wall time: 1.180 minutes
Iteration: 2240, time: 1.853 hours, Δt: 2.471 seconds, max(|w|) = 6.8e-02 ms⁻¹, wall time: 1.190 minutes
Iteration: 2280, time: 1.880 hours, Δt: 2.438 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 1.200 minutes
Iteration: 2320, time: 1.906 hours, Δt: 2.377 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 1.209 minutes
Iteration: 2360, time: 1.932 hours, Δt: 2.350 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 1.220 minutes
Iteration: 2400, time: 1.957 hours, Δt: 2.378 seconds, max(|w|) = 5.7e-02 ms⁻¹, wall time: 1.229 minutes
Iteration: 2440, time: 1.983 hours, Δt: 2.443 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 1.241 minutes
[ Info: Simulation is stopping after running for 1.247 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=0.0512673, min=-0.0509018, mean=-3.12474e-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=35.0133, 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=0.0180938, min=0.0, mean=0.000442589)

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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