GitHub

Sea ice advected by an atmospheric anticyclone

using ClimaSeaIce
using ClimaSeaIce.SeaIceMomentumEquations
using ClimaSeaIce.Rheologies
using Oceananigans
using Oceananigans.Units
using Oceananigans.Operators
using Oceananigans.BoundaryConditions
using Printf
using CairoMakie

The experiment found in the paper: Simulating Linear Kinematic Features in Viscous-Plastic Sea Ice Models on Quadrilateral and Triangular Grids With Different Variable Staggering

arch = CPU()

L  = 512kilometers
𝓋ₒ = 0.01 # m / s maximum ocean speed
𝓋ₐ = 30.0 # m / s maximum atmospheric speed modifier
30.0

2 km domain

grid = RectilinearGrid(arch;
                       size = (128, 128),
                          x = (0, L),
                          y = (0, L),
                       halo = (7, 7),
                   topology = (Bounded, Bounded, Flat))

#####
##### Value boundary conditions for velocities
#####

u_bcs = FieldBoundaryConditions(north=ValueBoundaryCondition(0),
                                south=ValueBoundaryCondition(0))

v_bcs = FieldBoundaryConditions(west=ValueBoundaryCondition(0),
                                east=ValueBoundaryCondition(0))

#####
##### Ocean sea-ice stress
#####
Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: ValueBoundaryCondition: 0
├── east: ValueBoundaryCondition: 0
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)

Constant ocean velocities corresponding to a cyclonic eddy

Uₒ = XFaceField(grid)
Vₒ = YFaceField(grid)

set!(Uₒ, (x, y) -> 𝓋ₒ * (2y - L) / L)
set!(Vₒ, (x, y) -> 𝓋ₒ * (L - 2x) / L)
fill_halo_regions!((Uₒ, Vₒ))

τₒ = SemiImplicitStress(uₑ=Uₒ, vₑ=Vₒ)

####
#### Atmosphere - sea ice stress
####

Uₐ = XFaceField(grid)
Vₐ = YFaceField(grid)

τₐ = SemiImplicitStress(; uₑ=Uₐ, vₑ=Vₐ, ρₑ=1.3, Cᴰ=1.2e-3)
ClimaSeaIce.SeaIceMomentumEquations.SemiImplicitStress{Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Float64}(129×128×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Nothing, east: Nothing, south: ZeroFlux, north: ZeroFlux, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 143×142×1 OffsetArray(::Array{Float64, 3}, -6:136, -6:135, 1:1) with eltype Float64 with indices -6:136×-6:135×1:1
    └── max=0.0, min=0.0, mean=0.0, 128×129×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: ZeroFlux, east: ZeroFlux, south: Nothing, north: Nothing, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 142×143×1 OffsetArray(::Array{Float64, 3}, -6:135, -6:136, 1:1) with eltype Float64 with indices -6:135×-6:136×1:1
    └── max=0.0, min=0.0, mean=0.0, 1.3, 0.0012)

Atmospheric velocities corresponding to an anticyclonic eddy moving north-east

@inline center(t) = 256kilometers + 51.2kilometers * t / 86400
@inline radius(x, y, t)  = sqrt((x - center(t))^2 + (y - center(t))^2)
@inline speed(x, y, t)   = 1 / 100 * exp(- radius(x, y, t) / 100kilometers)

@inline ua_time(x, y, t) = - 𝓋ₐ * speed(x, y, t) * (cosd(72) * (x - center(t)) + sind(72) * (y - center(t))) / 1000
@inline va_time(x, y, t) = - 𝓋ₐ * speed(x, y, t) * (cosd(72) * (y - center(t)) - sind(72) * (x - center(t))) / 1000
va_time (generic function with 1 method)

Initialize the stress at time t = 0

set!(Uₐ, (x, y) -> ua_time(x, y, 0))
set!(Vₐ, (x, y) -> va_time(x, y, 0))

fill_halo_regions!((Uₐ, Vₐ))

#####
##### Numerical details
#####

We use an elasto-visco-plastic rheology and WENO seventh order for advection of h and ℵ

momentum_equations = SeaIceMomentumEquation(grid;
                                            top_momentum_stress = τₐ,
                                            bottom_momentum_stress = τₒ,
                                            coriolis = FPlane(f=1e-4),
                                            ocean_velocities = (u = Uₒ, v = Vₒ),
                                            rheology = ElastoViscoPlasticRheology(),
                                            solver   = SplitExplicitSolver(substeps=150))
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Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, σ₂₂::Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, 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Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, uⁿ::Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, 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@NamedTuple{top::ClimaSeaIce.SeaIceMomentumEquations.SemiImplicitStress{Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Float64}, bottom::ClimaSeaIce.SeaIceMomentumEquations.SemiImplicitStress{Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Float64}}, Float64}(FPlane{Float64}(f=0.0001), ClimaSeaIce.Rheologies.ElastoViscoPlasticRheology{Float64}(27500.0, 20.0, 2.0, 2.0e-9, 50.0, 300.0), NamedTuple with 9 Fields on 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo:
├── σ₁₁: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── σ₂₂: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── σ₁₂: 129×129×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Face, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── ζ: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── Δ: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── α: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── uⁿ: 129×128×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── vⁿ: 128×129×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
└── P: 128×128×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing} reduced over dims = (3,) on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU, ClimaSeaIce.SeaIceMomentumEquations.SplitExplicitSolver(150), NamedTuple with 2 Fields on 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo:
├── u: 129×128×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
└── v: 128×129×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU, (top = ClimaSeaIce.SeaIceMomentumEquations.SemiImplicitStress{Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Float64}(129×128×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Nothing, east: Nothing, south: ZeroFlux, north: ZeroFlux, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 143×142×1 OffsetArray(::Array{Float64, 3}, -6:136, -6:135, 1:1) with eltype Float64 with indices -6:136×-6:135×1:1
    └── max=11.035, min=-11.035, mean=5.47742e-16, 128×129×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: ZeroFlux, east: ZeroFlux, south: Nothing, north: Nothing, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 142×143×1 OffsetArray(::Array{Float64, 3}, -6:135, -6:136, 1:1) with eltype Float64 with indices -6:135×-6:136×1:1
    └── max=11.035, min=-11.035, mean=-1.10076e-15, 1.3, 0.0012), bottom = ClimaSeaIce.SeaIceMomentumEquations.SemiImplicitStress{Oceananigans.Fields.Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Oceananigans.Fields.Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center, Nothing, Oceananigans.Grids.RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat, Oceananigans.Grids.StaticVerticalDiscretization{Nothing, Nothing, Float64, Float64}, Float64, Float64, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, OffsetArrays.OffsetVector{Float64, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, Oceananigans.Architectures.CPU}, Tuple{Colon, Colon, Colon}, OffsetArrays.OffsetArray{Float64, 3, Array{Float64, 3}}, Float64, Oceananigans.BoundaryConditions.FieldBoundaryConditions{Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}, Nothing, Nothing, Nothing, Nothing, Oceananigans.BoundaryConditions.BoundaryCondition{Oceananigans.BoundaryConditions.Flux, Nothing}}, Nothing, Oceananigans.Fields.FieldBoundaryBuffers{Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}}, Float64}(129×128×1 Field{Oceananigans.Grids.Face, Oceananigans.Grids.Center, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: Nothing, east: Nothing, south: ZeroFlux, north: ZeroFlux, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 143×142×1 OffsetArray(::Array{Float64, 3}, -6:136, -6:135, 1:1) with eltype Float64 with indices -6:136×-6:135×1:1
    └── max=0.00992188, min=-0.00992188, mean=-2.50039e-20, 128×129×1 Field{Oceananigans.Grids.Center, Oceananigans.Grids.Face, Oceananigans.Grids.Center} on Oceananigans.Grids.RectilinearGrid on Oceananigans.Architectures.CPU
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── boundary conditions: FieldBoundaryConditions
│   └── west: ZeroFlux, east: ZeroFlux, south: Nothing, north: Nothing, bottom: Nothing, top: Nothing, immersed: ZeroFlux
└── data: 142×143×1 OffsetArray(::Array{Float64, 3}, -6:135, -6:136, 1:1) with eltype Float64 with indices -6:135×-6:136×1:1
    └── max=0.00992188, min=-0.00992188, mean=-1.05058e-22, 1026.0, 0.0055)), 0.001, 1.0)

Define the model!

model = SeaIceModel(grid;
                    dynamics = momentum_equations,
                    ice_thermodynamics = nothing, # No ice_thermodynamics here
                    advection = WENO(order=7),
                    boundary_conditions = (u=u_bcs, v=v_bcs))
SeaIceModel{Oceananigans.Architectures.CPU, Oceananigans.Grids.RectilinearGrid}(time = 0 seconds, iteration = 0)
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── ice_thermodynamics: Nothing
├── advection: WENO(order=7)
└── external_heat_fluxes: 
    ├── top: Nothing
    └── bottom: 0

We start with a concentration of ℵ = 1 and an initial height field with perturbations around 0.3 m

h₀(x, y) = 0.3 + 0.005 * (sin(60 * x / 1000kilometers) + sin(30 * y / 1000kilometers))

set!(model, h = h₀)
set!(model, ℵ = 1)

#####
##### Setup the simulation
#####

run the model for 2 days

simulation = Simulation(model, Δt = 2minutes, stop_time = 2days)
Simulation of SeaIceModel
├── Next time step: 2 minutes
├── Elapsed wall time: 0 seconds
├── Wall time per iteration: NaN days
├── Stop time: 2 days
├── Stop iteration: Inf
├── Wall time limit: Inf
├── Minimum relative step: 0.0
├── Callbacks: OrderedDict with 3 entries:
│   ├── stop_time_exceeded => Callback of stop_time_exceeded on IterationInterval(1)
│   ├── stop_iteration_exceeded => Callback of stop_iteration_exceeded on IterationInterval(1)
│   └── wall_time_limit_exceeded => Callback of wall_time_limit_exceeded on IterationInterval(1)
├── Output writers: OrderedDict with no entries
└── Diagnostics: OrderedDict with no entries

Remember to evolve the wind stress field in time!

function compute_wind_stress(sim)
    time = sim.model.clock.time
    @inline ua(x, y) = ua_time(x, y, time)
    @inline va(x, y) = va_time(x, y, time)
    set!(Uₐ, ua)
    set!(Vₐ, va)

    fill_halo_regions!((Uₐ, Vₐ))

    return nothing
end

simulation.callbacks[:top_stress] = Callback(compute_wind_stress, IterationInterval(1))

h = model.ice_thickness
ℵ = model.ice_concentration
u, v = model.velocities

outputs = (; h, u, v, ℵ)

simulation.output_writers[:sea_ice] = JLD2Writer(model, outputs;
                                                       filename = "sea_ice_advected_by_anticyclone.jld2",
                                                       schedule = IterationInterval(5),
                                                       overwrite_existing = true)

wall_time = [time_ns()]

function progress(sim)
    h = sim.model.ice_thickness
    ℵ = sim.model.ice_concentration
    u = sim.model.velocities.u
    v = sim.model.velocities.v

    hmax = maximum(interior(h))
    ℵmin = minimum(interior(ℵ))
    umax = maximum(interior(u)), maximum(interior(v))
    step_time = 1e-9 * (time_ns() - wall_time[1])

    @info @sprintf("Time: %s, Iteration %d, Δt %s, max(vel): (%.2e, %.2e), max(h): %.2f, min(ℵ): %.2f, wtime: %s \n",
                   prettytime(sim.model.clock.time),
                   sim.model.clock.iteration,
                   prettytime(sim.Δt),
                   umax..., hmax, ℵmin, prettytime(step_time))

     wall_time[1] = time_ns()
end

simulation.callbacks[:progress] = Callback(progress, IterationInterval(5))

run!(simulation)

using CairoMakie

htimeseries = FieldTimeSeries("sea_ice_advected_by_anticyclone.jld2", "h")
utimeseries = FieldTimeSeries("sea_ice_advected_by_anticyclone.jld2", "u")
vtimeseries = FieldTimeSeries("sea_ice_advected_by_anticyclone.jld2", "v")
ℵtimeseries = FieldTimeSeries("sea_ice_advected_by_anticyclone.jld2", "ℵ")
128×128×1×289 FieldTimeSeries{Oceananigans.OutputReaders.InMemory} located at (Center, Center, ⋅) of ℵ at sea_ice_advected_by_anticyclone.jld2
├── grid: 128×128×1 RectilinearGrid{Float64, Oceananigans.Grids.Bounded, Oceananigans.Grids.Bounded, Oceananigans.Grids.Flat} on Oceananigans.Architectures.CPU with 7×7×0 halo
├── indices: (:, :, :)
├── time_indexing: Linear()
├── backend: InMemory()
├── path: sea_ice_advected_by_anticyclone.jld2
├── name: ℵ
└── data: 142×142×1×289 OffsetArray(::Array{Float64, 4}, -6:135, -6:135, 1:1, 1:289) with eltype Float64 with indices -6:135×-6:135×1:1×1:289
    └── max=1.0, min=0.0, mean=0.832265

Visualize!

Nt = length(htimeseries)
iter = Observable(1)

hi = @lift(htimeseries[$iter])
ℵi = @lift(ℵtimeseries[$iter])
ui = @lift(utimeseries[$iter])
vi = @lift(vtimeseries[$iter])

fig = Figure()
ax = Axis(fig[1, 1], title = "sea ice thickness")
heatmap!(ax, hi, colormap = :magma, colorrange = (0.23, 0.37))

ax = Axis(fig[1, 2], title = "sea ice concentration")
heatmap!(ax, ℵi, colormap = Reverse(:deep), colorrange = (0.9, 1))

ax = Axis(fig[2, 1], title = "zonal velocity")
heatmap!(ax, ui, colorrange = (-0.1, 0.1))

ax = Axis(fig[2, 2], title = "meridional velocity")
heatmap!(ax, vi, colorrange = (-0.1, 0.1))

CairoMakie.record(fig, "sea_ice_advected_by_anticyclone.mp4", 1:Nt, framerate = 8) do i
    iter[] = i
    @info "doing iter $i"
end
[ Info: doing iter 1
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