Problems

struct BackgroundFlow{T}

The balanced background gradients. The background flow is in thermal wind balance and therefore assumed to be steady.

Fields

• f::Any: Coriolis frequency $f$

• Vx::Matrix: Lateral shear $\partial V/\partial x$

• Bx::Matrix: Horizontal buoyancy gradient $\partial B/\partial x = f\partial V/\partial z$

• Bz::Matrix: Vertical buoyancy gradient $\partial B/\partial z$

BackgroundFlow(grid::Grid{T}) -> BackgroundFlow

BackgroundFlow(grid::Grid{T}, f) -> BackgroundFlow

Create a new BackgroundFlow given a Grid and Coriolis frequency $f$ which defaults to 1. Background gradients are initialised to 0.

Examples

grid = Grid(256,128,2000.0,1.0)
bg = BackgroundFlow(grid)

# output
BackgroundFlow:
  ├─── f: 1
  ├── Vx: 256×128 Matrix{Float64}
  │       [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]
  ├── Bx: 256×128 Matrix{Float64}
  │       [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]
  └── Bz: 256×128 Matrix{Float64}
          [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]

mutable struct Clock{T}

Current simulation time and iteration.

• t::Any

• iteration::Int64

Default initialiser for Clock

struct Problem{T, F, G, H}

A struct representing a Sawyer-Eliassen problem.

Fields

• domain::Domain{T} where T

• background::BackgroundFlow

• ζ_forcing::Any

• v_forcing::Union{NoForcing{T}, GlobalPhysicalForcing{T}, PointwisePhysicalForcing{T}} where T

• b_forcing::Union{NoForcing{T}, GlobalPhysicalForcing{T}, PointwisePhysicalForcing{T}} where T

• state::State

• scratch::Scratch

struct Scratch{T}

Scratch space for temporary variables used in the Sawyer-Eliassen problem. These variables have two primary uses in the code:

1) intermediate terms in the computation of the Sawyer-Eliassen operator 𝓛
2) intermediate terms in the advection of the background flow

Between timesteps these variables are available for other purposes e.g. setting the initial conditions, computing output.

Fields

• FS_tmp::FSVariable

• FC_tmp::FCVariable

• XS_tmp::XSVariable

• XC_tmp::XCVariable

• XZ_tmp::XZVariable

• XZ_tmp2::XZVariable

struct State{T}

State variables of the problem.

• ζ::FSVariable

• ζₜ::FSVariable

• v::XZVariable

• b::XZVariable

• clock::Clock

compute_ζₜ!(problem::Problem)

Compute and set ζₜ by projecting b onto sine space, v onto cosine space and using ζₜ = fvz - bx

get_Bx(bg::BackgroundFlow) -> Matrix

get_Bx(problem::Problem) -> Matrix

get_Bz(bg::BackgroundFlow) -> Matrix

get_Bz(problem::Problem) -> Matrix

get_Vx(bg::BackgroundFlow) -> Matrix

get_Vx(problem::Problem) -> Matrix

get_f(bg::BackgroundFlow) -> Any

get_f(problem::Problem) -> Any

get_iteration(problem::Problem) -> Int64

get_iteration(state::State) -> Int64

Get current iteration.

get_problem(problem::Problem) -> Problem

get_scratch(problem::Problem) -> Scratch

get_time(problem::Problem) -> Any

get_time(state::State) -> Any

Get current simulation time.

get_ζ_forcing(problem::Problem) -> Any

set_b!(problem::Problem, b)

set_b!(state::State, func::Function)

Set b from a function b(x,z).

set_b!(state::State, b::XZVariable)

Set b from a variable.

set_v!(problem::Problem, v)

set_v!(state::State, func::Function)

Set v from a function v(x,z).

set_v!(state::State, v::XZVariable)

Set v from a variable.

set_vb!(problem::Problem; v, b)

Set v and / or b and then compute and set ζₜ

set_ζ!(problem::Problem, ζ) -> Any

set_ζ!(problem::Problem; u, w)

set_ζ!(state::State, ζ::FSVariable)

Set ζ from a variable in spectral space.

set_ζ!(state::State, func::Function)

Set ζ from a function. func should specify ζ = func(x,z) pointwise.

set_ζ!(state::State, ζ::XSVariable)

Set ζ from a variable in XS space.

set_ζ!(state::State, ζ::XZVariable)

Set ζ from a variable in physical space.

set_ζ!(state::State; u, w)

Set ζ from u and w. u and w may be a XZVariable, XCVariable/ XSVariable, FCVariable / FSVariable or a function specifying u(x,z) / w(x,z) pointwise. If not specified u and w default to 0.