Private types

struct Params{T} <: AbstractParams

The parameters for a two-dimensional Navier-Stokes problem:

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• μ::Any: large-scale (hypo)-viscosity coefficient

• nμ::Int64: (hypo)-viscosity order, nμ$≤ 0$

• calcF!::Function: function that calculates the Fourier transform of the forcing, $F̂$

struct Vars{Aphys, Atrans, F, P} <: TwoDNavierStokesVars

The variables for two-dimensional Navier-Stokes problem:

• ζ: relative vorticity

• u: x-component of velocity

• v: y-component of velocity

• ζh: Fourier transform of relative vorticity

• uh: Fourier transform of $x$-component of velocity

• vh: Fourier transform of $y$-component of velocity

• Fh: Fourier transform of forcing

• prevsol: sol at previous time-step

DecayingVars(dev, grid)

Return the variables for unforced two-dimensional Navier-Stokes problem on grid.

ForcedVars(grid)

Return the variables for forced two-dimensional Navier-Stokes on grid.

StochasticForcedVars(grid)

Return the variables for stochastically forced two-dimensional Navier-Stokes on grid.

struct Params{T, Aphys, Atrans, Tℓ, TU} <: SingleLayerQGParams

The parameters for the SingleLayerQG problem.

• β::Any: planetary vorticity $y$-gradient

• deformation_radius::Any: Rossby radius of deformation

• U::Any: Background flow in $x$ direction

• eta::Any: topographic potential vorticity

• etah::Any: Fourier transform of topographic potential vorticity

• μ::Any: linear drag coefficient

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• calcF!::Function: function that calculates the Fourier transform of the forcing, $F̂$

• Qx::Any: array containing $x$-gradient of PV due to eta

• Qy::Any: array containing $y$-gradient of PV due to $U$ and topographic PV

BarotropicQGParams(grid, β, U, eta, μ, ν, nν, calcF)

Return the parameters for a Barotropic QG problem (i.e., with infinite Rossby radius of deformation).

EquivalentBarotropicQGParams(grid, deformation_radius, β, U, eta, μ, ν, nν, calcF)

Return the parameters for an Equivalent Barotropic QG problem (i.e., with finite Rossby radius of deformation).

struct Vars{Aphys, Atrans, F, P} <: SingleLayerQGVars

The variables for SingleLayer QG:

• q: relative vorticity (+ vortex stretching)

• ψ: streamfunction

• u: $x$-component of velocity

• v: $y$-component of velocity

• qh: Fourier transform of relative vorticity (+ vortex stretching)

• ψh: Fourier transform of streamfunction

• uh: Fourier transform of $x$-component of velocity

• vh: Fourier transform of $y$-component of velocity

• Fh: Fourier transform of forcing

• prevsol: sol at previous time-step

DecayingVars(grid)

Return the variables for unforced single-layer QG problem on grid.

ForcedVars(grid)

Return the variables for forced single-layer QG problem on grid.

StochasticForcedVars(grid)

Return the variables for stochastically forced barotropic QG problem on grid.

struct Params{T, Aphys3D, Aphys2D, Atrans4D, Trfft} <: AbstractParams

The parameters for the MultiLayerQG problem.

• nlayers::Int64: number of fluid layers

• f₀::Any: constant planetary vorticity

• β::Any: planetary vorticity $y$-gradient

• b::Tuple: array with Boussinesq buoyancy of each fluid layer

• H::Tuple: array with rest height of each fluid layer

• U::Any: array with imposed constant zonal flow $U(y)$ in each fluid layer

• eta::Any: array containing the topographic PV

• topographic_pv_gradient::Tuple{T, T} where T: tuple containing the $(x, y)$ components of topographic PV large-scale gradient

• μ::Any: linear bottom drag coefficient

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• calcFq!::Function: function that calculates the Fourier transform of the forcing, $F̂$

• g′::Tuple: array with the reduced gravity constants for each fluid interface

• Qx::Any: array containing $x$-gradient of PV due to eta in each fluid layer

• Qy::Any: array containing $y$-gradient of PV due to $β$, $U$, and topographic PV in each fluid layer

• S::Any: array containing coeffients for getting PV from streamfunction

• S⁻¹::Any: array containing coeffients for inverting PV to streamfunction

• rfftplan::Any: rfft plan for FFTs

struct SingleLayerParams{T, Aphys3D, Aphys2D, Trfft} <: AbstractParams

The parameters for the a single-layer MultiLayerQG problem.

• β::Any: planetary vorticity $y$-gradient

• U::Any: array with imposed constant zonal flow $U(y)$

• eta::Any: array containing the periodic component of the topographic PV

• topographic_pv_gradient::Tuple{T, T} where T: tuple containing the $(x, y)$ components of topographic PV large-scale gradient

• μ::Any: linear drag coefficient

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• calcFq!::Function: function that calculates the Fourier transform of the forcing, $F̂$

• Qx::Any: array containing $x$-gradient of PV due to topographic PV

• Qy::Any: array containing $y$-gradient of PV due to $β$, $U$, and topographic PV

• rfftplan::Any: rfft plan for FFTs

struct TwoLayerParams{T, Aphys3D, Aphys2D, Trfft} <: AbstractParams

The parameters for the a two-layer MultiLayerQG problem.

• f₀::Any: constant planetary vorticity

• β::Any: planetary vorticity $y$-gradient

• b::Tuple: array with Boussinesq buoyancy of each fluid layer

• H::Tuple: tuple with rest height of each fluid layer

• U::Any: array with imposed constant zonal flow $U(y)$ in each fluid layer

• eta::Any: array containing periodic component of the topographic PV

• topographic_pv_gradient::Tuple{T, T} where T: tuple containing the $(x, y)$ components of topographic PV large-scale gradient

• μ::Any: linear bottom drag coefficient

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• calcFq!::Function: function that calculates the Fourier transform of the forcing, $F̂$

• g′::Any: the reduced gravity constants for the fluid interface

• Qx::Any: array containing $x$-gradient of PV due to topographic PV in each fluid layer

• Qy::Any: array containing $y$-gradient of PV due to $β$, $U$, and topographic PV in each fluid layer

• rfftplan::Any: rfft plan for FFTs

struct Vars{Aphys, Atrans, F, P} <: AbstractVars

The variables for multi-layer QG problem.

• q: relative vorticity + vortex stretching

• ψ: streamfunction

• u: x-component of velocity

• v: y-component of velocity

• qh: Fourier transform of relative vorticity + vortex stretching

• ψh: Fourier transform of streamfunction

• uh: Fourier transform of $x$-component of velocity

• vh: Fourier transform of $y$-component of velocity

• Fqh: Fourier transform of forcing

• prevsol: sol at previous time-step

DecayingVars(grid, params)

Return the variables for an unforced multi-layer QG problem with grid and params.

ForcedVars(grid, params)

Return the variables for a forced multi-layer QG problem with grid and params.

StochasticForcedVars(grid, params)

Return the variables for a forced multi-layer QG problem with grid and params.

Params{T}(ν, nν, calcF!)

A struct containing the parameters for Surface QG dynamics. Included are:

• ν::Any: buoyancy (hyper)-viscosity coefficient

• nν::Int64: buoyancy (hyper)-viscosity order

• calcF!::Function: function that calculates the Fourier transform of the forcing, $F̂$

Vars{Aphys, Atrans, F, P}(b, u, v, bh, uh, vh, Fh, prevsol)

The variables for surface QG problem:

• b: buoyancy

• u: $x$-component of velocity

• v: $y$-component of velocity

• bh: Fourier transform of buoyancy

• uh: Fourier transform of $x$-component of velocity

• vh: Fourier transform of $y$-component of velocity

• Fh: Fourier transform of forcing

• prevsol: sol at previous time-step

DecayingVars(grid)

Return the variables for unforced surface QG dynamics on grid.

ForcedVars(grid)

Return the variables for forced surface QG dynamics on grid.

StochasticForcedVars(grid)

Return the variables for stochastically forced surface QG dynamics on grid.

Params{T, Aphys, Atrans}(β, eta, etah, μ, ν, nν, calcF!)

A struct containing the parameters for a barotropic QL QG problem. Included are:

• β::Any: planetary vorticity $y$-gradient

• eta::Any: topographic potential vorticity

• etah::Any: Fourier transform of topographic potential vorticity

• μ::Any: linear drag coefficient

• ν::Any: small-scale (hyper)-viscosity coefficient

• nν::Int64: (hyper)-viscosity order, nν$≥ 1$

• calcF!::Function: function that calculates the Fourier transform of the forcing, $F̂$

Vars{Aphys, Atrans, F, P}(u, v, U, uzeta, vzeta, zeta, Zeta, psi, Psi, N, NZ, uh, vh, Uh, zetah, Zetah, psih, Psih, Fh, prevsol)

The variables for barotropic QL QG:

• u: $x$-component of small-scale velocity

• v: $y$-component of small-scale velocity

• U: $x$-component of large-scale velocity

• uzeta: small-scale $u′ζ′$

• vzeta: small-scale $v′ζ′$

• zeta: small-scale relative vorticity

• Zeta: large-scale relative vorticity

• psi: small-scale streamfunction

• Psi: large-scale streamfunction

• Nz: small-scale nonlinear term

• NZ: large-scale nonlinear term

• uh: Fourier transform of $x$-component of small-scale velocity

• vh: Fourier transform of $y$-component of small-scale velocity

• Uh: Fourier transform of $x$-component of large-scale velocity

• zetah: Fourier transform of small-scale relative vorticity

• Zetah: Fourier transform of large-scale relative vorticity

• psih: Fourier transform of small-scale relative vorticity

• Psih: Fourier transform of large-scale relative vorticity

• Fh: Fourier transform of forcing

• prevsol: sol at previous time-step

DecayingVars(grid)

Return the variables for unforced two-dimensional quasi-linear barotropic QG problem on grid.

ForcedVars(grid)

Return the variables for forced two-dimensional quasi-linear barotropic QG problem on grid.

StochasticForcedVars(grid)

Return the variables for stochastically forced two-dimensional quasi-linear barotropic QG problem on grid.