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 use the SeawaterBuoyancy model for buoyancy with a linear equation of state.
• 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, JLD2, Plots"

We start by importing all of the packages and functions that we'll need for this example.

using Random
using Printf
using Plots
using JLD2

using Oceananigans
using Oceananigans.Units: minute, minutes, hour

The grid

We use 32³ grid points with 2 m grid spacing in the horizontal and 1 m spacing in the vertical,

grid = RegularRectilinearGrid(size=(32, 32, 32), extent=(64, 64, 32))

RegularRectilinearGrid{Float64, Periodic, Periodic, Bounded}
                   domain: x ∈ [0.0, 64.0], y ∈ [0.0, 64.0], z ∈ [-32.0, 0.0]
                 topology: (Periodic, Periodic, Bounded)
  resolution (Nx, Ny, Nz): (32, 32, 32)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (2.0, 2.0, 1.0)

Buoyancy that depends on temperature and salinity

We use the SeawaterBuoyancy model with a linear equation of state,

buoyancy = SeawaterBuoyancy(equation_of_state=LinearEquationOfState(α=2e-4, β=8e-4))

SeawaterBuoyancy{Float64}: g = 9.80665
└── equation of state: LinearEquationOfState{Float64}: α = 2.00e-04, β = 8.00e-04

where $α$ and $β$ are the thermal expansion and haline contraction coefficients for temperature and salinity.

Boundary conditions

We calculate the surface temperature flux associated with surface heating of 200 W m⁻², reference density ρ, and heat capacity cᴾ,

Qʰ = 200  # W m⁻², surface _heat_ flux
ρₒ = 1026 # kg m⁻³, average density at the surface of the world ocean
cᴾ = 3991 # J K⁻¹ s⁻¹, typical heat capacity for seawater

Qᵀ = Qʰ / (ρₒ * cᴾ) # K m⁻¹ s⁻¹, surface _temperature_ flux

4.884283985946938e-5

Finally, we impose a temperature gradient dTdz both initially and at the bottom of the domain, culminating in the boundary conditions on temperature,

dTdz = 0.01 # K m⁻¹

T_bcs = TracerBoundaryConditions(grid,
                                 top = FluxBoundaryCondition(Qᵀ),
                                 bottom = GradientBoundaryCondition(dTdz))

Oceananigans.FieldBoundaryConditions (NamedTuple{(:x, :y, :z)}), with boundary conditions
├── x: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
├── y: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
└── z: CoordinateBoundaryConditions{BoundaryCondition{Gradient,Float64},BoundaryCondition{Flux,Float64}}

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 = 2.5e-3  # dimensionless drag coefficient
ρₐ = 1.225   # kg m⁻³, average density of air at sea-level

Qᵘ = - ρₐ / ρₒ * cᴰ * u₁₀ * abs(u₁₀) # m² s⁻²

-0.0002984892787524367

The boundary conditions on u are thus

u_bcs = UVelocityBoundaryConditions(grid, top = FluxBoundaryCondition(Qᵘ))

Oceananigans.FieldBoundaryConditions (NamedTuple{(:x, :y, :z)}), with boundary conditions
├── x: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
├── y: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
└── z: CoordinateBoundaryConditions{BoundaryCondition{Flux,Nothing},BoundaryCondition{Flux,Float64}}

For salinity, S, we impose an evaporative flux of the form

@inline Qˢ(x, y, t, S, evaporation_rate) = - evaporation_rate * S

where S is salinity. We use an evporation rate of 1 millimeter per hour,

evaporation_rate = 1e-3 / hour

2.7777777777777776e-7

We build the Flux evaporation BoundaryCondition with the function Qˢ, indicating that Qˢ depends on salinity S and passing the parameter evaporation_rate,

evaporation_bc = FluxBoundaryCondition(Qˢ, field_dependencies=:S, parameters=evaporation_rate)

BoundaryCondition: type=Flux, condition=Qˢ(x, y, t, S, evaporation_rate) in Main.ex-ocean_wind_mixing_and_convection at none:1

The full salinity boundary conditions are

S_bcs = TracerBoundaryConditions(grid, top=evaporation_bc)

Oceananigans.FieldBoundaryConditions (NamedTuple{(:x, :y, :z)}), with boundary conditions
├── x: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
├── y: CoordinateBoundaryConditions{BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing},BoundaryCondition{Oceananigans.BoundaryConditions.Periodic,Nothing}}
└── z: CoordinateBoundaryConditions{BoundaryCondition{Flux,Nothing},BoundaryCondition{Flux,Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Nothing,Nothing,Nothing,Nothing,typeof(Main.ex-ocean_wind_mixing_and_convection.Qˢ),Float64,Tuple{Symbol},Nothing,Nothing}}}

Model instantiation

We fill in the final details of the model here: upwind-biased 5th-order advection for momentum and tracers, 3rd-order Runge-Kutta time-stepping, 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 we cannot explicitly resolve.

model = IncompressibleModel(architecture = CPU(),
                            advection = UpwindBiasedFifthOrder(),
                            timestepper = :RungeKutta3,
                            grid = grid,
                            coriolis = FPlane(f=1e-4),
                            buoyancy = buoyancy,
                            closure = AnisotropicMinimumDissipation(),
                            boundary_conditions = (u=u_bcs, T=T_bcs, S=S_bcs))

IncompressibleModel{CPU, Float64}(time = 0 seconds, iteration = 0) 
├── grid: RegularRectilinearGrid{Float64, Periodic, Periodic, Bounded}(Nx=32, Ny=32, Nz=32)
├── tracers: (:T, :S)
├── closure: AnisotropicMinimumDissipation{Oceananigans.TurbulenceClosures.ExplicitTimeDiscretization,Float64,NamedTuple{(:T, :S),Tuple{Float64,Float64}},Float64,NamedTuple{(:T, :S),Tuple{Float64,Float64}},Nothing}
├── buoyancy: SeawaterBuoyancy{Float64,LinearEquationOfState{Float64},Nothing,Nothing}
└── coriolis: FPlane{Float64}

Notes:

• To use the Smagorinsky-Lilly turbulence closure (with a constant model coefficient) rather than AnisotropicMinimumDissipation, use closure = ConstantSmagorinsky() in the model constructor.

• To change the architecture to GPU, replace architecture = CPU() with architecture = GPU()`

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(Qᵘ)) * 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 first build a TimeStepWizard to ensure stable time-stepping with a Courant-Freidrichs-Lewy (CFL) number of 1.0.

wizard = TimeStepWizard(cfl=1.0, Δt=10.0, max_change=1.1, max_Δt=1minute)

TimeStepWizard{Float64,typeof(Oceananigans.Utils.cell_advection_timescale),typeof(Oceananigans.Simulations.infinite_diffusion_timescale)}(1.0, Inf, 1.1, 0.5, 60.0, 0.0, 10.0, Oceananigans.Utils.cell_advection_timescale, Oceananigans.Simulations.infinite_diffusion_timescale)

Nice progress messaging is helpful:

start_time = time_ns() # so we can print the total elapsed wall time

# Print a progress message
progress_message(sim) =
    @printf("i: %04d, t: %s, Δt: %s, wmax = %.1e ms⁻¹, wall time: %s\n",
            sim.model.clock.iteration, prettytime(model.clock.time),
            prettytime(wizard.Δt), maximum(abs, sim.model.velocities.w),
            prettytime((time_ns() - start_time) * 1e-9))

progress_message (generic function with 1 method)

We then set up the simulation:

simulation = Simulation(model, Δt=wizard, stop_time=40minutes, iteration_interval=10,
                        progress=progress_message)

Simulation{IncompressibleModel{CPU, Float64}}
├── Model clock: time = 0 seconds, iteration = 0 
├── Next time step (TimeStepWizard{Float64,typeof(Oceananigans.Utils.cell_advection_timescale),typeof(Oceananigans.Simulations.infinite_diffusion_timescale)}): 10 seconds 
├── Iteration interval: 10
├── Stop criteria: Any[Oceananigans.Simulations.iteration_limit_exceeded, Oceananigans.Simulations.stop_time_exceeded, Oceananigans.Simulations.wall_time_limit_exceeded]
├── Run time: 0 seconds, wall time limit: Inf
├── Stop time: 40 minutes, stop iteration: Inf
├── Diagnostics: OrderedCollections.OrderedDict with 1 entry:
│   └── nan_checker => NaNChecker
└── Output writers: OrderedCollections.OrderedDict with no entries

Output

We use the JLD2OutputWriter to save $x, z$ slices of the velocity fields, tracer fields, and eddy diffusivities. The prefix keyword argument to JLD2OutputWriter indicates that output will be saved in ocean_wind_mixing_and_convection.jld2.

# Create a NamedTuple with eddy viscosity
eddy_viscosity = (νₑ = model.diffusivities.νₑ,)

simulation.output_writers[:slices] =
    JLD2OutputWriter(model, merge(model.velocities, model.tracers, eddy_viscosity),
                           prefix = "ocean_wind_mixing_and_convection",
                     field_slicer = FieldSlicer(j=Int(grid.Ny/2)),
                         schedule = TimeInterval(1minute),
                            force = true)

JLD2OutputWriter scheduled on TimeInterval(1 minute):
├── filepath: ./ocean_wind_mixing_and_convection.jld2
├── 6 outputs: (:u, :v, :w, :T, :S, :νₑ)
├── field slicer: FieldSlicer(:, 16, :, with_halos=false)
├── array type: Array{Float32}
├── including: [:grid, :coriolis, :buoyancy, :closure]
└── max filesize: Inf YiB

We're ready:

run!(simulation)

┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0010, t: 1.667 minutes, Δt: 10 seconds, wmax = 9.0e-06 ms⁻¹, wall time: 19.754 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0020, t: 3 minutes, Δt: 11 seconds, wmax = 8.2e-06 ms⁻¹, wall time: 21.064 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0030, t: 5 minutes, Δt: 12.100 seconds, wmax = 6.1e-06 ms⁻¹, wall time: 22.357 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0040, t: 7 minutes, Δt: 13.310 seconds, wmax = 5.4e-06 ms⁻¹, wall time: 23.574 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0050, t: 9 minutes, Δt: 14.641 seconds, wmax = 7.6e-06 ms⁻¹, wall time: 24.850 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0060, t: 11 minutes, Δt: 12.414 seconds, wmax = 9.7e-06 ms⁻¹, wall time: 26.480 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0070, t: 12.508 minutes, Δt: 10.159 seconds, wmax = 2.6e-05 ms⁻¹, wall time: 27.625 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0080, t: 13.893 minutes, Δt: 8.935 seconds, wmax = 8.0e-05 ms⁻¹, wall time: 28.654 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0090, t: 15.134 minutes, Δt: 8.041 seconds, wmax = 3.0e-04 ms⁻¹, wall time: 29.939 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0100, t: 16.246 minutes, Δt: 7.374 seconds, wmax = 8.2e-04 ms⁻¹, wall time: 30.958 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0110, t: 17.342 minutes, Δt: 6.841 seconds, wmax = 2.4e-03 ms⁻¹, wall time: 31.970 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0120, t: 18.317 minutes, Δt: 6.341 seconds, wmax = 6.1e-03 ms⁻¹, wall time: 32.981 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0130, t: 19.194 minutes, Δt: 5.809 seconds, wmax = 1.3e-02 ms⁻¹, wall time: 34.113 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0140, t: 20.090 minutes, Δt: 5.422 seconds, wmax = 2.6e-02 ms⁻¹, wall time: 35.752 seconds
i: 0150, t: 20.915 minutes, Δt: 4.947 seconds, wmax = 4.0e-02 ms⁻¹, wall time: 36.788 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0160, t: 21.659 minutes, Δt: 4.940 seconds, wmax = 5.2e-02 ms⁻¹, wall time: 37.904 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0170, t: 22.521 minutes, Δt: 5.208 seconds, wmax = 5.6e-02 ms⁻¹, wall time: 39.040 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0180, t: 23.359 minutes, Δt: 5.391 seconds, wmax = 6.0e-02 ms⁻¹, wall time: 40.273 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0190, t: 24.181 minutes, Δt: 5.443 seconds, wmax = 5.7e-02 ms⁻¹, wall time: 41.322 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0200, t: 25.100 minutes, Δt: 5.987 seconds, wmax = 6.0e-02 ms⁻¹, wall time: 42.438 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0210, t: 26.110 minutes, Δt: 6.586 seconds, wmax = 5.8e-02 ms⁻¹, wall time: 44.115 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0220, t: 27.224 minutes, Δt: 6.705 seconds, wmax = 7.7e-02 ms⁻¹, wall time: 45.381 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0230, t: 28.353 minutes, Δt: 7.058 seconds, wmax = 7.2e-02 ms⁻¹, wall time: 46.730 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0240, t: 29.473 minutes, Δt: 7.099 seconds, wmax = 6.2e-02 ms⁻¹, wall time: 48.323 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0250, t: 30.636 minutes, Δt: 7.633 seconds, wmax = 7.0e-02 ms⁻¹, wall time: 49.356 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0260, t: 31.850 minutes, Δt: 7.290 seconds, wmax = 7.1e-02 ms⁻¹, wall time: 50.467 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0270, t: 33 minutes, Δt: 7.689 seconds, wmax = 7.2e-02 ms⁻¹, wall time: 51.762 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0280, t: 34.123 minutes, Δt: 7.358 seconds, wmax = 6.4e-02 ms⁻¹, wall time: 52.810 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0290, t: 35.243 minutes, Δt: 7.287 seconds, wmax = 5.6e-02 ms⁻¹, wall time: 53.918 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0300, t: 36.511 minutes, Δt: 7.661 seconds, wmax = 5.5e-02 ms⁻¹, wall time: 54.938 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0310, t: 37.607 minutes, Δt: 7.278 seconds, wmax = 6.0e-02 ms⁻¹, wall time: 55.972 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0320, t: 38.737 minutes, Δt: 7.372 seconds, wmax = 6.0e-02 ms⁻¹, wall time: 57.011 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0330, t: 39.724 minutes, Δt: 7.237 seconds, wmax = 5.2e-02 ms⁻¹, wall time: 58.122 seconds
┌ Warning: some parameters could not be resolved for type Oceananigans.BoundaryConditions.ContinuousBoundaryFunction{Center,Center,Nothing,32,Main.ex-ocean_wind_mixing_and_convection.#Qˢ,Float64,Tuple{Symbol},Tuple{Int64},Tuple{typeof(Oceananigans.Operators.identity3)}}; reconstructing
└ @ JLD2 /storage7/buildkite-agent/.julia-2624/packages/JLD2/pA6G3/src/data/reconstructing_datatypes.jl:440
i: 0333, t: 40 minutes, Δt: 7.170 seconds, wmax = 4.9e-02 ms⁻¹, wall time: 58.594 seconds
[ Info: Simulation is stopping. Model time 40 minutes has hit or exceeded simulation stop time 40 minutes.

Turbulence visualization

We animate the data saved in ocean_wind_mixing_and_convection.jld2. We prepare for animating the flow by creating coordinate arrays, opening the file, building a vector of the iterations that we saved data at, and defining functions for computing colorbar limits:

# Coordinate arrays
xw, yw, zw = nodes(model.velocities.w)
xT, yT, zT = nodes(model.tracers.T)

# Open the file with our data
file = jldopen(simulation.output_writers[:slices].filepath)

# Extract a vector of iterations
iterations = parse.(Int, keys(file["timeseries/t"]))

""" Returns colorbar levels equispaced between `(-clim, clim)` and encompassing the extrema of `c`. """
function divergent_levels(c, clim, nlevels=21)
    cmax = maximum(abs, c)
    levels = clim > cmax ? range(-clim, stop=clim, length=nlevels) : range(-cmax, stop=cmax, length=nlevels)
    return (levels[1], levels[end]), levels
end

""" Returns colorbar levels equispaced between `clims` and encompassing the extrema of `c`."""
function sequential_levels(c, clims, nlevels=20)
    levels = range(clims[1], stop=clims[2], length=nlevels)
    cmin, cmax = minimum(c), maximum(c)
    cmin < clims[1] && (levels = vcat([cmin], levels))
    cmax > clims[2] && (levels = vcat(levels, [cmax]))
    return clims, levels
end

Main.ex-ocean_wind_mixing_and_convection.sequential_levels

We start the animation at t = 10minutes since things are pretty boring till then:

times = [file["timeseries/t/$iter"] for iter in iterations]
intro = searchsortedfirst(times, 10minutes)

anim = @animate for (i, iter) in enumerate(iterations[intro:end])

    @info "Drawing frame $i from iteration $iter..."

    t = file["timeseries/t/$iter"]
    w = file["timeseries/w/$iter"][:, 1, :]
    T = file["timeseries/T/$iter"][:, 1, :]
    S = file["timeseries/S/$iter"][:, 1, :]
    νₑ = file["timeseries/νₑ/$iter"][:, 1, :]

    wlims, wlevels = divergent_levels(w, 2e-2)
    Tlims, Tlevels = sequential_levels(T, (19.7, 19.99))
    Slims, Slevels = sequential_levels(S, (35, 35.005))
    νlims, νlevels = sequential_levels(νₑ, (1e-6, 5e-3))

    kwargs = (linewidth=0, xlabel="x (m)", ylabel="z (m)", aspectratio=1,
              xlims=(0, grid.Lx), ylims=(-grid.Lz, 0))

    w_plot = contourf(xw, zw, w'; color=:balance, clims=wlims, levels=wlevels, kwargs...)
    T_plot = contourf(xT, zT, T'; color=:thermal, clims=Tlims, levels=Tlevels, kwargs...)
    S_plot = contourf(xT, zT, S'; color=:haline,  clims=Slims, levels=Slevels, kwargs...)

    # We use a heatmap for the eddy viscosity to observe how it varies on the grid scale.
    ν_plot = heatmap(xT, zT, νₑ'; color=:thermal, clims=νlims, levels=νlevels, kwargs...)

    w_title = @sprintf("vertical velocity (m s⁻¹), t = %s", prettytime(t))
    T_title = "temperature (ᵒC)"
    S_title = "salinity (g kg⁻¹)"
    ν_title = "eddy viscosity (m² s⁻¹)"

    # Arrange the plots side-by-side.
    plot(w_plot, T_plot, S_plot, ν_plot, layout=(2, 2), size=(1200, 600),
         title=[w_title T_title S_title ν_title])

    iter == iterations[end] && close(file)
end

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