Library

BoundaryCondition{C<:BCType}(condition)

Construct a boundary condition of type C with a condition that may be given by a number, an array, or a function with signature:

condition(i, j, grid, time, iteration, U, Φ, parameters) = # function definition

that returns a number and where i and j are indices along the boundary.

Boundary condition types include Periodic, Flux, Value, Gradient, and NoPenetration.

BoundaryFunction{B, X1, X2, F}

A wrapper for user-defined boundary condition functions.

CoordinateBoundaryConditions(left, right)

A set of two BoundaryConditions to be applied along a coordinate x, y, or z.

The left boundary condition is applied on the negative or lower side of the coordinate while the right boundary condition is applied on the positive or higher side.

Dirchlet

An alias for the Value boundary condition type.

FieldBoundaryConditions

An alias for NamedTuple{(:x, :y, :z)} that represents a set of three CoordinateBoundaryConditions applied to a field along x, y, and z.

FieldBoundaryConditions(x, y, z)

Construct a FieldBoundaryConditions using a CoordinateBoundaryCondition for each of the x, y, and z coordinates.

Flux

A type specifying a boundary condition on the flux of a field.

Gradient

A type specifying a boundary condition on the derivative or gradient of a field. Also called a Neumann boundary condition.

Neumann

An alias for the Gradient boundary condition type.

Periodic

A type specifying a periodic boundary condition.

A condition may not be specified with a Periodic boundary condition.

Value

A type specifying a boundary condition on the value of a field. Also called a Dirchlet boundary condition.

ChannelBCs(; north = BoundaryCondition(Flux, nothing),
             south = BoundaryCondition(Flux, nothing),
               top = BoundaryCondition(Flux, nothing),
            bottom = BoundaryCondition(Flux, nothing))

Construct FieldBoundaryConditions with Periodic boundary conditions in the x direction and specified north (+y), south (-y), top (+z) and bottom (-z) boundary conditions for u, v, and tracer fields.

ChannelBCs cannot be applied to the the vertical velocity w.

ChannelSolutionBCs(u=ChannelBCs(), ...)

Construct SolutionBoundaryConditions for a reentrant channel model configuration with solution fields u, v, w, T, and S specified by keyword arguments.

By default ChannelBCs are applied to u, v, T, and S and ChannelBCs(top=NoPenetrationBC(), bottom=NoPenetrationBC()) is applied to w.

Use ChannelBCs when constructing non-default boundary conditions for u, v, w, T, S.

HorizontallyPeriodicBCs(;   top = BoundaryCondition(Flux, nothing),
                         bottom = BoundaryCondition(Flux, nothing))

Construct FieldBoundaryConditions with Periodic boundary conditions in the x and y directions and specified top (+z) and bottom (-z) boundary conditions for u, v, and tracer fields.

HorizontallyPeriodicBCs cannot be applied to the the vertical velocity w.

HorizontallyPeriodicSolutionBCs(u=HorizontallyPeriodicBCs(), ...)

Construct SolutionBoundaryConditions for a horizontally-periodic model configuration with solution fields u, v, w, T, and S specified by keyword arguments.

By default HorizontallyPeriodicBCs are applied to u, v, T, and S and HorizontallyPeriodicBCs(top=NoPenetrationBC(), bottom=NoPenetrationBC()) is applied to w.

Use HorizontallyPeriodicBCs when constructing non-default boundary conditions for u, v, w, T, S.

SolutionBoundaryConditions(tracers, proposal_bcs)

Construct a NamedTuple of FieldBoundaryConditions for a model with fields u, v, w, and tracers from the proposal boundary conditions proposal_bcs, which must contain the boundary conditions on u, v, and w and may contain some or all of the boundary conditions on tracers.

BuoyancyTracer <: AbstractBuoyancy{Nothing}

Type indicating that the tracer b represents buoyancy.

LinearEquationOfState{FT} <: AbstractEquationOfState

Linear equation of state for seawater.

LinearEquationOfState([FT=Float64;] α=1.67e-4, β=7.80e-4)

Returns parameters for a linear equation of state for seawater with thermal expansion coefficient α [K⁻¹] and haline contraction coefficient β [ppt⁻¹]. The buoyancy perturbation associated with a linear equation of state is

Default constants are taken from Table 1.2 (page 33) of Vallis, "Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation" (2ed, 2017).

SeawaterBuoyancy{G, EOS} <: AbstractBuoyancy{EOS}

Buoyancy model for temperature- and salt-stratified seawater.

SeawaterBuoyancy([FT=Float64;] gravitational_acceleration = g_Earth,
                              equation_of_state = LinearEquationOfState(FT))

Returns parameters for a temperature- and salt-stratified seawater buoyancy model with a gravitational_acceleration constant (typically called 'g'), and an equation_of_state that related temperature and salinity (or conservative temperature and absolute salinity) to density anomalies and buoyancy.

Clock{T<:Number}

Clock{T}(time, iteration)

Keeps track of the current time and iteration number.

BetaPlane{T} <: AbstractRotation

A parameter object for meridionally increasing Coriolis parameter (f = f₀ + βy).

BetaPlane([T=Float64;] f₀=nothing, β=nothing,
                       rotation_rate=nothing, latitude=nothing, radius=nothing)

A parameter object for meridionally increasing Coriolis parameter (f = f₀ + βy).

The user may specify both f₀ and β, or the three parameters rotation_rate, latitude, and radius that specify the rotation rate and radius of a planet, and the central latitude at which the β-plane approximation is to be made.

FPlane{FT} <: AbstractRotation

A parameter object for constant rotation around a vertical axis.

FPlane([FT=Float64;] f=nothing, rotation_rate=nothing, latitude=nothing)

Returns a parameter object for constant rotation at the angular frequency f/2, and therefore with background vorticity f, around a vertical axis. If f is not specified, it is calculated from rotation_rate and latitude according to the relation `f = 2rotation_ratesind(latitude).

Also called FPlane, after the "f-plane" approximation for the local effect of Earth's rotation in a planar coordinate system tangent to the Earth's surface.

Field{X, Y, Z, A, G} <: AbstractLocatedField{X, Y, Z, A, G}

A field defined at the location (X, Y, Z) which can be either Cell or Face.

Field(X, Y, Z, arch::AbstractArchitecture, grid)

Construct a Field on architecture arch and grid at location X, Y, Z, where each of X, Y, Z is Cell or Face.

Field(L::Tuple, data::AbstractArray, grid)

Construct a Field on grid using the array data with location defined by the tuple L of length 3 whose elements are Cell or Face.

Field(L::Tuple, arch::AbstractArchitecture, grid)

Construct a Field on architecture arch and grid at location L, where L is a tuple of Cell or Face types.

CellField([T=eltype(grid)], arch, grid)

Return a Field{Cell, Cell, Cell} on architecture arch and grid. Used for tracers and pressure fields.

FaceFieldX([T=eltype(grid)], arch, grid)

Return a Field{Face, Cell, Cell} on architecture arch and grid. Used for the x-velocity field.

FaceFieldY([T=eltype(grid)], arch, grid)

Return a Field{Cell, Face, Cell} on architecture arch and grid. Used for the y-velocity field.

FaceFieldZ([T=eltype(grid)], arch, grid)

Return a Field{Cell, Cell, Face} on architecture arch and grid. Used for the z-velocity field.

Returns a view over the interior points of the field.data.

Set the CPU field u to the array v.

Set the CPU field u data to the function f(x, y, z).

set!(model; kwargs...)

Set velocity and tracer fields of model. The keyword arguments kwargs... take the form name=data, where name refers to one of the fields of model.velocities or model.tracers, and the data may be an array, a function with arguments (x, y, z), or any data type for which a set!(ϕ::AbstractField, data) function exists.

Example

model = Model(grid=RegularCartesianGrid(size=(32, 32, 32), length=(1, 1, 1))

# Set u to a parabolic function of z, v to random numbers damped
# at top and bottom, and T to some silly array of half zeros,
# half random numbers.

u₀(x, y, z) = z/model.grid.Lz * (1 + z/model.grid.Lz)
v₀(x, y, z) = 1e-3 * rand() * u₀(x, y, z)

T₀ = rand(size(model.grid)...)
T₀[T₀ .< 0.5] .= 0

set!(model, u=u₀, v=v₀, T=T₀)

SimpleForcing{X, Y, Z, F, P}

Callable object for specifying 'simple' forcings of x, y, z, t and optionally parameters of type P at location X, Y, Z.

SimpleForcing([location=(Cell, Cell, Cell),] forcing; parameters=nothing)

Construct forcing for a field at location using forcing::Function, and optionally with parameters. If parameters=nothing, forcing must have the signature

`forcing(x, y, z, t)`;

otherwise it must have the signature

`forcing(x, y, z, t, parameters)`.

Examples

julia> const a = 2.1

julia> fun_forcing(x, y, z, t) = a * exp(z) * cos(t)

julia> u_forcing = SimpleForcing(fun_forcing)

julia> parameterized_forcing(x, y, z, t, p) = p.μ * exp(z/p.λ) * cos(p.ω*t)

julia> v_forcing = SimpleForcing(parameterized_forcing, parameters=(μ=42, λ=0.1, ω=π))

ModelForcing(; u=zeroforcing, v=zeroforcing, w=zeroforcing, tracer_forcings...)

Return a named tuple of forcing functions for each solution field.

Example

julia> u_forcing = SimpleForcing((x, y, z, t) -> exp(z) * cos(t))

julia> model = Model(forcing=ModelForcing(u=u_forcing))

Model(; grid, kwargs...)

Construct an Oceananigans.jl model on grid.

Keyword arguments

• grid: (required) The resolution and discrete geometry on which model is solved. Currently the only option is RegularCartesianGrid.
• architecture: CPU() or GPU(). The computer architecture used to time-step model.
• float_type: Float32 or Float64. The floating point type used for model data.
• closure: The turbulence closure for model. See TurbulenceClosures.
• buoyancy: Buoyancy model parameters.
• coriolis: Parameters for the background rotation rate of the model.
• forcing: User-defined forcing functions that contribute to solution tendencies.
• boundary_conditions: User-defined boundary conditions for model fields. Can be eitherSolutionBoundaryConditions or ModelBoundaryConditions. See BoundaryConditions, HorizontallyPeriodicSolutionBCs, and ChannelSolutionBCs.
• parameters: User-defined parameters for use in user-defined forcing functions and boundary condition functions.

ChannelModel(; kwargs...)

Construct a Model with walls in the y-direction. This is done by imposing FreeSlip boundary conditions in the y-direction instead of Periodic.

kwargs are passed to the regular Model constructor.

NonDimensionalModel(; N, L, Re, Pr=0.7, Ro=Inf, float_type=Float64, kwargs...)

Construct a "Non-dimensional" Model with resolution N, domain extent L, precision float_type, and the four non-dimensional numbers:

* `Re = U λ / ν` (Reynolds number)
* `Pr = U λ / κ` (Prandtl number)
* `Ro = U / f λ` (Rossby number)

for characteristic velocity scale U, length-scale λ, viscosity ν, tracer diffusivity κ, and Coriolis parameter f. Buoyancy is scaled with λ U², so that the Richardson number is Ri=B, where B is a non-dimensional buoyancy scale set by the user via initial conditions or forcing.

Note that N, L, and Re are required.

Additional kwargs are passed to the regular Model constructor.

GiB

A Float64 constant equal to 1024MiB. Useful for increasing the clarity of scripts, e.g. max_filesize = 50GiB.

KiB

A Float64 constant equal to 1024.0. Useful for increasing the clarity of scripts, e.g. max_filesize = 250KiB.

MiB

A Float64 constant equal to 1024KiB. Useful for increasing the clarity of scripts, e.g. max_filesize = 100MiB.

TiB

A Float64 constant equal to 1024GiB. Useful for increasing the clarity of scripts, e.g. max_filesize = 2TiB.

day

A Float64 constant equal to 24hour. Useful for increasing the clarity of scripts, e.g. Δt = 0.5day.

hour

A Float64 constant equal to 60minute. Useful for increasing the clarity of scripts, e.g. Δt = 3hour.

minute

A Float64 constant equal to 60second. Useful for increasing the clarity of scripts, e.g. Δt = 15minute.

second

A Float64 constant equal to 1.0. Useful for increasing the clarity of scripts, e.g. Δt = 1second.

pretty_filesize(s, suffix="B")

Convert a floating point value s representing a file size to a more human-friendly formatted string with one decimal places with a suffix defaulting to "B". Depending on the value of s the string will be formatted to show s using an SI prefix from bytes, kiB (1024 bytes), MiB (1024² bytes), and so on up to YiB (1024⁸ bytes).

prettytime(t)

Convert a floating point value t representing an amount of time in seconds to a more human-friendly formatted string with three decimal places. Depending on the value of t the string will be formatted to show t in nanoseconds (ns), microseconds (μs), milliseconds (ms), seconds (s), minutes (min), hours (hr), or days (day).

update_Δt!(wizard, model)

Compute wizard.Δt given the velocities and diffusivities of model, and the parameters of wizard.