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 (13.899 seconds)
[ Info: Executing initial time step...
[ Info:     ... initial time step complete (5.109 seconds).
Iteration: 0040, time: 7 minutes, Δt: 8.309 seconds, max(|w|) = 2.7e-05 ms⁻¹, wall time: 19.749 seconds
Iteration: 0080, time: 11.182 minutes, Δt: 4.935 seconds, max(|w|) = 7.9e-03 ms⁻¹, wall time: 20.209 seconds
Iteration: 0120, time: 14 minutes, Δt: 4.044 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 20.670 seconds
Iteration: 0160, time: 16.648 minutes, Δt: 3.855 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 21.127 seconds
Iteration: 0200, time: 19.274 minutes, Δt: 4.006 seconds, max(|w|) = 3.8e-02 ms⁻¹, wall time: 21.551 seconds
Iteration: 0240, time: 21.864 minutes, Δt: 3.912 seconds, max(|w|) = 3.9e-02 ms⁻¹, wall time: 22.006 seconds
Iteration: 0280, time: 24.321 minutes, Δt: 3.737 seconds, max(|w|) = 3.6e-02 ms⁻¹, wall time: 22.441 seconds
Iteration: 0320, time: 26.732 minutes, Δt: 3.702 seconds, max(|w|) = 2.8e-02 ms⁻¹, wall time: 22.886 seconds
Iteration: 0360, time: 29.061 minutes, Δt: 3.648 seconds, max(|w|) = 2.7e-02 ms⁻¹, wall time: 23.341 seconds
Iteration: 0400, time: 31.334 minutes, Δt: 3.394 seconds, max(|w|) = 3.1e-02 ms⁻¹, wall time: 23.755 seconds
Iteration: 0440, time: 33.548 minutes, Δt: 3.262 seconds, max(|w|) = 3.2e-02 ms⁻¹, wall time: 24.217 seconds
Iteration: 0480, time: 35.683 minutes, Δt: 3.403 seconds, max(|w|) = 3.0e-02 ms⁻¹, wall time: 24.641 seconds
Iteration: 0520, time: 37.775 minutes, Δt: 3.296 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 25.158 seconds
Iteration: 0560, time: 39.839 minutes, Δt: 3.030 seconds, max(|w|) = 4.9e-02 ms⁻¹, wall time: 25.692 seconds
Iteration: 0600, time: 41.796 minutes, Δt: 2.986 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 26.191 seconds
Iteration: 0640, time: 43.681 minutes, Δt: 2.860 seconds, max(|w|) = 3.5e-02 ms⁻¹, wall time: 26.744 seconds
Iteration: 0680, time: 45.601 minutes, Δt: 3.047 seconds, max(|w|) = 3.7e-02 ms⁻¹, wall time: 27.284 seconds
Iteration: 0720, time: 47.461 minutes, Δt: 2.868 seconds, max(|w|) = 4.3e-02 ms⁻¹, wall time: 27.720 seconds
Iteration: 0760, time: 49.336 minutes, Δt: 2.855 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 28.159 seconds
Iteration: 0800, time: 51.194 minutes, Δt: 2.899 seconds, max(|w|) = 4.4e-02 ms⁻¹, wall time: 28.605 seconds
Iteration: 0840, time: 53.096 minutes, Δt: 2.926 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 29.057 seconds
Iteration: 0880, time: 55 minutes, Δt: 2.789 seconds, max(|w|) = 4.6e-02 ms⁻¹, wall time: 29.470 seconds
Iteration: 0920, time: 56.844 minutes, Δt: 2.835 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 29.924 seconds
Iteration: 0960, time: 58.647 minutes, Δt: 2.728 seconds, max(|w|) = 4.0e-02 ms⁻¹, wall time: 30.356 seconds
Iteration: 1000, time: 1.007 hours, Δt: 2.752 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 30.806 seconds
Iteration: 1040, time: 1.036 hours, Δt: 2.705 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 31.268 seconds
Iteration: 1080, time: 1.065 hours, Δt: 2.549 seconds, max(|w|) = 4.7e-02 ms⁻¹, wall time: 31.685 seconds
Iteration: 1120, time: 1.094 hours, Δt: 2.676 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 32.137 seconds
Iteration: 1160, time: 1.122 hours, Δt: 2.576 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 32.559 seconds
Iteration: 1200, time: 1.150 hours, Δt: 2.791 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 32.996 seconds
Iteration: 1240, time: 1.180 hours, Δt: 2.683 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 33.453 seconds
Iteration: 1280, time: 1.209 hours, Δt: 2.731 seconds, max(|w|) = 4.8e-02 ms⁻¹, wall time: 33.925 seconds
Iteration: 1320, time: 1.238 hours, Δt: 2.628 seconds, max(|w|) = 5.1e-02 ms⁻¹, wall time: 34.371 seconds
Iteration: 1360, time: 1.266 hours, Δt: 2.508 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 34.781 seconds
Iteration: 1400, time: 1.293 hours, Δt: 2.674 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 35.226 seconds
Iteration: 1440, time: 1.322 hours, Δt: 2.604 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 35.648 seconds
Iteration: 1480, time: 1.349 hours, Δt: 2.561 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 36.089 seconds
Iteration: 1520, time: 1.377 hours, Δt: 2.539 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 36.546 seconds
Iteration: 1560, time: 1.405 hours, Δt: 2.595 seconds, max(|w|) = 5.3e-02 ms⁻¹, wall time: 36.978 seconds
Iteration: 1600, time: 1.433 hours, Δt: 2.544 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 37.434 seconds
Iteration: 1640, time: 1.461 hours, Δt: 2.507 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 37.857 seconds
Iteration: 1680, time: 1.487 hours, Δt: 2.389 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 38.296 seconds
Iteration: 1720, time: 1.514 hours, Δt: 2.496 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 38.776 seconds
Iteration: 1760, time: 1.541 hours, Δt: 2.507 seconds, max(|w|) = 4.2e-02 ms⁻¹, wall time: 39.274 seconds
Iteration: 1800, time: 1.569 hours, Δt: 2.530 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 39.986 seconds
Iteration: 1840, time: 1.597 hours, Δt: 2.503 seconds, max(|w|) = 4.5e-02 ms⁻¹, wall time: 40.484 seconds
Iteration: 1880, time: 1.624 hours, Δt: 2.527 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 40.998 seconds
Iteration: 1920, time: 1.651 hours, Δt: 2.514 seconds, max(|w|) = 5.5e-02 ms⁻¹, wall time: 41.442 seconds
Iteration: 1960, time: 1.679 hours, Δt: 2.563 seconds, max(|w|) = 5.6e-02 ms⁻¹, wall time: 41.873 seconds
Iteration: 2000, time: 1.706 hours, Δt: 2.493 seconds, max(|w|) = 5.9e-02 ms⁻¹, wall time: 42.333 seconds
Iteration: 2040, time: 1.734 hours, Δt: 2.442 seconds, max(|w|) = 6.8e-02 ms⁻¹, wall time: 42.764 seconds
Iteration: 2080, time: 1.760 hours, Δt: 2.461 seconds, max(|w|) = 6.7e-02 ms⁻¹, wall time: 43.218 seconds
Iteration: 2120, time: 1.787 hours, Δt: 2.526 seconds, max(|w|) = 7.6e-02 ms⁻¹, wall time: 43.705 seconds
Iteration: 2160, time: 1.814 hours, Δt: 2.493 seconds, max(|w|) = 6.6e-02 ms⁻¹, wall time: 44.134 seconds
Iteration: 2200, time: 1.841 hours, Δt: 2.463 seconds, max(|w|) = 6.2e-02 ms⁻¹, wall time: 44.608 seconds
Iteration: 2240, time: 1.867 hours, Δt: 2.247 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 45.117 seconds
Iteration: 2280, time: 1.891 hours, Δt: 2.394 seconds, max(|w|) = 5.8e-02 ms⁻¹, wall time: 45.603 seconds
Iteration: 2320, time: 1.917 hours, Δt: 2.315 seconds, max(|w|) = 5.2e-02 ms⁻¹, wall time: 46.021 seconds
Iteration: 2360, time: 1.942 hours, Δt: 2.364 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 46.521 seconds
Iteration: 2400, time: 1.967 hours, Δt: 2.352 seconds, max(|w|) = 5.4e-02 ms⁻¹, wall time: 46.973 seconds
Iteration: 2440, time: 1.992 hours, Δt: 2.381 seconds, max(|w|) = 6.1e-02 ms⁻¹, wall time: 47.400 seconds
[ Info: Simulation is stopping after running for 47.528 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=0.0472233, min=-0.0458322, mean=5.01871e-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=35.013, 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=0.0178006, min=0.0, mean=0.000420362)

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.