Library

Documenting the user interface.

Radiative transfer models

Walrus.RadiativeTransfer — Module

RadiativeTransfer

Includes models for ratiative transfer through water which can induce body heating

Walrus.RadiativeTransfer.HomogeneousBodyHeating — Type

HomogeneousBodyHeating

A model for single band light attenuation which heats the water in the form:

\[I(x, y, z) = I_0(x, y) * \exp\left(-\alpha z\right),\]

where $I$ is the radiation intensity and $\alpha$ is the attenuation coefficient. This heats the water like $\frac{\partial T(x, y, z)}{\partial t} = \frac{I(x, y, z)A}{c^p\rho}$ where $A$ is the area of the cell, $c^p$ is the specific heat capacity and $\rho$ is the water density.

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Walrus.RadiativeTransfer.HomogeneousBodyHeating — Method

HomogeneousBodyHeating(; surface_flux,
                         water_attenuation_coefficient = 1.8,
                         water_heat_capacity = 3991.0, # J K⁻¹ kg⁻¹
                         water_density = 1026.0) # kg m⁻³

Creates a model in which a surface_flux (W / m²) is attenuated by and heats the water. This interacts with Oceananigans as a body forcing.

Keyword Arguments

surface_flux (required): a function returning the surface radiaiton flux in the form surface_flux(x, y, t) or single value
water_attenuation_coefficient: the radiation attenuation coefficient of the water
water_heat_capacity: the specific heat capacity of the water
water_density: density of the water

Example

julia> using Walrus: HomogeneousBodyHeating

julia> using Oceananigans

julia> grid = RectilinearGrid(size = (128, 128, 128), extent = (1000, 1000, 1000))
128×128×128 RectilinearGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.Periodic, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 3×3×3 halo
├── Periodic x ∈ [0.0, 1000.0)  regularly spaced with Δx=7.8125
├── Periodic y ∈ [0.0, 1000.0)  regularly spaced with Δy=7.8125
└── Bounded  z ∈ [-1000.0, 0.0] regularly spaced with Δz=7.8125
julia> body_heating = HomogeneousBodyHeating(; surface_flux = (x, y, t) -> 100)
(::HomogeneousBodyHeating{Float64, var"#1#2"}) (generic function with 1 method)

julia> model = NonhydrostaticModel(; grid, forcing = (; T = Forcing(body_heating, discrete_form=true)), tracers = :T)
NonhydrostaticModel{CPU, RectilinearGrid}(time = 0 seconds, iteration = 0)
├── grid: 128×128×128 RectilinearGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.Periodic, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 3×3×3 halo
├── timestepper: QuasiAdamsBashforth2TimeStepper
├── advection scheme: Centered reconstruction order 2
├── tracers: T
├── closure: Nothing
├── buoyancy: Nothing
└── coriolis: Nothing

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Tidal forcing models

Walrus.TidalForcings — Module

TidalForcing

Provides quick setup of tidal forcing

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Walrus.TidalForcings.Tide — Type

Tide(; x_amplitude, 
       y_amplitude, 
       period = 12.3782216453hours,
       nodal_time = 0., 
       x_lag = 0., 
       y_lag = 0.,
       coriolis = nothing)

Sets up a model of tidal forcing with default parameters of an M2 tide.

Keyword Arguments

x_amplitude: the tidal amplitude in the x direction
y_amplitude: the tidal amplitude in the x direction
period: the tidal period (defaults to that of an M2 tide)
nodal_time: the time at which peak flow occurs
x_lag: the phase lag for the tidal component in the x direction
y_lag: the phase lag for the tidal component in the y direction
coriolis: a model for the coriolis parameter

Example

julia> using Walrus: Tide

julia> using Oceananigans

julia> tide = Tide(x_amplitude = 0.1, y_amplitude = 0.)
(::Tide{Float64, Nothing}) (generic function with 2 methods)
julia> forcing = (u = Forcing(tide, parameters = Val(:x), discrete_form = true),
                  v = Forcing(tide, parameters = Val(:y), discrete_form = true))
(u = DiscreteForcing{Val{:x}}
├── func: (::Tide{Float64, Nothing}) (generic function with 2 methods)
└── parameters: Val{:x}(), v = DiscreteForcing{Val{:y}}
├── func: (::Tide{Float64, Nothing}) (generic function with 2 methods)
└── parameters: Val{:y}())

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Walrus.TidalForcings.TidalForcing — Method

TidalForcing(; x_amplitude,
               y_amplitude,
               period = 12.3782216453hours,
               nodal_time = 0.,
               x_lag = 0.,
               y_lag = 0.,
               coriolis = nothing)

A convenience constructor for Tide which returns the forcings pre wrapped.

Keyword Arguments

x_amplitude: the tidal amplitude in the x direction
y_amplitude: the tidal amplitude in the x direction
period: the tidal period (defaults to that of an M2 tide)
nodal_time: the time at which peak flow occurs
x_lag: the phase lag for the tidal component in the x direction
y_lag: the phase lag for the tidal component in the y direction
coriolis: a model for the coriolis parameter

Example

julia> using Walrus: TidalForcing

julia> tidal_forcing = TidalForcing(x_amplitude = 0.1, y_amplitude = 0.)
(u = DiscreteForcing{Val{:x}}
├── func: (::Tide{Float64, Nothing}) (generic function with 2 methods)
└── parameters: Val{:x}(), v = DiscreteForcing{Val{:y}}
├── func: (::Tide{Float64, Nothing}) (generic function with 2 methods)
└── parameters: Val{:y}())

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Wind stress model

Walrus.WindStressModel.LogarithmicNeutralWind — Method

LogarithmicNeutralWind(; monin_obukhov_stability_length = 0.4
                         charnock_coefficient = 0.014
                         air_kinematic_viscosity = 1.488e-5
                         gravity_wave_coefficient = 0.11
                         gravity = g_Earth,

                         precomputed_roughness_length = false,
                         precompute_wind_speeds = [0:25/100000:25;],
                         arch = CPU())

Returns a LogarithmicNeutralWind parameterisation for the surface drag coefficient

$C_d$ is parameterised as,

\[C_d = \left(\frac{\kappa}{\log{\frac{10}{z_0}}}\right)^2,\]

where $\kappa$ is the Monin‐Obukhov stability length and $z_0$ is the velocity roughness length. This is the roughness length scale which logarithmically brings the relative velocity to zero at the surface, i.e.

\[U=\frac{u\star}{\kappa}\log\frac{z}{z_0},\]

where $u\star$ is the friction velocity. Additionally $z_0$ is given as,

\[z_0=b\frac{\nu}{u\star} + \frac{a_c}{g}u\star^2,\]

where $\nu$ is the kinematic viscosity of air and g is the acceleration of gravity.

This model itterativly solves these equations to find $z_0$. Alternativly, if the flag precomputed_roughness_length is set to they are pre computed at precompute_wind_speeds between which $z_0$ is then interpolated during run time. Precomputed velocities are converted to appropriate types for arch (i.e. CPU() or GPU())

This parameterisaion is described in Smith (1988)

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Walrus.WindStressModel.WindStress — Method

WindStress(; reference_wind_speed, 
             reference_wind_direction,
             drag_coefficient = LogarithmicNeutralWind(), 
             air_density = 1.225, 
             water_density = 1026.)

Returns a wind stress model where the stress is given by,

\[\frac{\tau}{\rho_o} = \rho_aC_dSU_{x/y},\]

where $\rho_o$ is the water density, $\rho_a$ is the air density, $C_d$ is the drag coefficient, $U_{x/y}$ are the x and y components of relative wind speed, and $S=\sqrt{U_x^2+U_y^2}$.

$C_d$ is calculated from a parameterisation, by default this is a "log neutral" wind parameterisation with velocity roughness length parameterisaion like Smith (1988).

In the default configuration this is the same as described in Fairall et al. (2011).

Keyword Arguments

reference_wind_speed (required): a function returning the (10m neutral) wind speed in the form reference_wind_speed(x, y, t) or single value
reference_wind_direction (required): a function returning the (10m neutral) wind direction in the form reference_wind_direction(x, y, t) or single value
drag_coefficient: the drag coefficient parameterisation
air_density: air density in kg/m³
water_density: water density in kg/m³

Example

julia> using Walrus: WindStress

julia> using Oceananigans

julia> reference_wind_speed = 0.1
0.1

julia> reference_wind_direction = 0.
0.0

julia> wind_stress = WindStress(; reference_wind_speed, reference_wind_direction)
(::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) (generic function with 2 methods)

julia> boundary_conditions = (u = FieldBoundaryConditions(top = FluxBoundaryCondition(wind_stress, parameters = Val(:x))),
                              v = FieldBoundaryConditions(top = FluxBoundaryCondition(wind_stress, parameters = Val(:y))))
(u = Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: ContinuousBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) at (Nothing, Nothing, Nothing)
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing), v = Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: ContinuousBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) at (Nothing, Nothing, Nothing)
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing))

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Walrus.WindStressModel.WindStressBoundaryConditions — Method

WindStressBoundaryConditions(; reference_wind_speed, 
                               reference_wind_direction,
                               drag_coefficient = LogarithmicNeutralWind(), 
                               air_density = 1.225, 
                               water_density = 1026.)

Convenience constructor to setup WindStress boundary conditions.

Keyword Arguments

reference_wind_speed (required): a function returning the (10m neutral) wind speed in the form reference_wind_speed(x, y, t) or single value
reference_wind_direction (required): a function returning the (10m neutral) wind direction in the form reference_wind_direction(x, y, t) or single value
drag_coefficient: the drag coefficient parameterisation
air_density: air density in kg/m³
water_density: water density in kg/m³

Example

julia> using Walrus: WindStressBoundaryConditions

julia> using Oceananigans

julia> wind_stress_boundary_conditions = WindStressBoundaryConditions(; reference_wind_speed = 0.1, reference_wind_direction = 90.)
(u = FluxBoundaryCondition: DiscreteBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) with parameters Val{:x}, v = FluxBoundaryCondition: DiscreteBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) with parameters Val{:y})

julia> boundary_conditions = (u = FieldBoundaryConditions(top = wind_stress_boundary_conditions.u),
                              v = FieldBoundaryConditions(top = wind_stress_boundary_conditions.v))
(u = Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: DiscreteBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) with parameters Val{:x}
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing), v = Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: DiscreteBoundaryFunction (::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) with parameters Val{:y}
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing))

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Walrus.WindStressModel.find_velocity_roughness_length — Method

find_velocity_roughness_length(wind_speed, reference_height, params)

A function that finds the velocity roughness length for the LogarithmicNeutralWind drag coefficient model.

This will sometimes fail as the function is not well behaved at either low reference heights (it has been tuned for 10m wind), or high (⪆ 20 m/s).

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Surface heat exchange model

Walrus.SurfaceHeatingModel.SurfaceHeatExchange — Method

SurfaceHeatExchange(; wind_stress,
                      air_temperature = 18, # °C
                      latent_heat_vaporisation = EmpiricalLatentHeatVaporisation(),
                      vapour_pressure = AugustRocheMagnusVapourPressure(),
                      water_specific_heat_capacity = 3991., # J / K / kg
                      water_density = 1026., # kg / m³
                      air_specific_heat_capacity = 1003.5, # J / K / kg
                      air_density = 1.204, # kg
                      air_water_mixing_ratio = 0.001, # kg / kg
                      stephan_boltzman_constant = 5.670374419e-8) # W / K⁴

Specifies surface heat exhange in the form:

\[Q = Qᵢᵣ + Qₛ + Qₗ,\]

where $Qᵢᵣ$ is the heat flux due to long wave (infra red) radiation, $Qₛ$ is the sensible heat flux, and $Qₗ$ is the latent heat flux. Notably the short wave radiation flux is neglegted here as it is assumed to penatrate far enough into the water that it is treated separately by HomogeneousBodyHeating (we therefore are also assuming that the short wave penitration is suitably short that it is neglected).

The short wave term is given by the Stephan-Boltzman equation so:

\[Qᵢᵣ = σ(T⁴ - Tₐ⁴),\]

where $σ$ is the Stephan-Boltzman constant, $T$ is the ocean temperature, and $Tₐ$ is the 2m air temperature.

The sensible and latent heat flux's are given by the bluk parameterisations described in Fairall et al. (2011) and are given by:

\[Qₛ = ρₐcₚₐCₕS(T - Tₐ),\]

and $Qₗ = ρₐLₑCₕS(q(T) - qₐ)$, where $ρₐ$ is the density of the air, $cₚₐ$ is the specific heat capacity of air, $Cₕ$ is the heat transfer coefficient, $S$ is the wind speed, $Lₑ$ is the latent heat of vaporizaion parameterised by latent_heat_vaporisation, $q(T)$ is the saturation vapour pressure of water and is parameterised by vapour_pressure.

The heat transfer coefficients are given by the same parameterisation as the WindStress. For example for the LogarithmicNeutralWind the transfer coefficient is given as: $C_h = \frac{\kappa}{\log{\frac{2}{z_0}}}\frac{\kappa}{\log{\frac{2}{z_{ot}}}}$, where $z_{ot}$ is the sclar roughness parameter given by: $z_{ot} = \min\left(1.15\cdot10^{-4}, 5.5\cdot10^{-5}R_r^{-0.6}\right)$, where $R_r$ is the roughness reynolds number given as $R_r = \frac{u\star z_0}{\nu}$ where $\nu$ is the kinematic viscosity of air.

The heat flux is then given by:

\[F = \frac{Q}{\rho_oc_{po}},\]

where $\rho_o$ and $c_{po}$ are the density and specific heat capacity of water.

(Note: we will retain the Oceananigans convention that negative heat flux at a top boundary increases temeprature).

Keyword Arguments

wind_stress: wind stress model
air_temperature: the air temperature in °C as a function with signature (x, y, t) or a constant
latent_heat_vaporisation: latent heat of vaporisation in J / kg
vapour_pressure: parameterisation for saturation vapour pressure in water
water_specific_heat_capacity: the specific heat capacity of water in J / K / kg
water_density: water density in kg / m³
air_specific_heat_capacit: the specific heat capacity of air in J / K / kg
air_density: air density in kg / m³
air_water_mixing_ratio: water content of air in kg / kg
stephan_boltzman_constant: the Stephan-Boltzman constant in W / K⁴

Example

julia> using Walrus

julia> using Oceananigans

julia> wind_stress = WindStress(; reference_wind_speed = 0., reference_wind_direction = 90.)
(::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) (generic function with 2 methods)

julia> surface_heat_exchange = SurfaceHeatExchange(; wind_stress)
(::SurfaceHeatExchange{WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}, Int64, Walrus.SurfaceHeatingModel.EmpiricalLatentHeatVaporisation{Float64}, Walrus.SurfaceHeatingModel.AugustRocheMagnusVapourPressure{Float64}, Float64}) (generic function with 1 method)

julia> boundary_conditions = (; T = FieldBoundaryConditions(top = FluxBoundaryCondition(surface_heat_exchange, field_dependencies = (:T, :u, :v))))
(T = Oceananigans.FieldBoundaryConditions, with boundary conditions
├── west: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── east: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── south: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── north: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── bottom: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing)
├── top: FluxBoundaryCondition: ContinuousBoundaryFunction (::SurfaceHeatExchange{WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}, Int64, Walrus.SurfaceHeatingModel.EmpiricalLatentHeatVaporisation{Float64}, Walrus.SurfaceHeatingModel.AugustRocheMagnusVapourPressure{Float64}, Float64}) at (Nothing, Nothing, Nothing)
└── immersed: DefaultBoundaryCondition (FluxBoundaryCondition: Nothing),)

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Walrus.SurfaceHeatingModel.SurfaceHeatExchangeBoundaryCondition — Method

SurfaceHeatExchange(; wind_stress,
                      air_temperature = 18, # °C
                      latent_heat_vaporisation = EmpiricalLatentHeatVaporisation(),
                      vapour_pressure = AugustRocheMagnusVapourPressure(),
                      water_specific_heat_capacity = 3991., # J / K / kg
                      water_density = 1026., # kg / m³
                      air_specific_heat_capacity = 1003.5, # J / K / kg
                      air_density = 1.204, # kg
                      air_water_mixing_ratio = 0.001, # kg / kg
                      stephan_boltzman_constant = 5.670374419e-8) # W / K⁴

A convenience constructor returning SurfaceHeatExchange as a boundary condition

Keyword Arguments

wind_stress: wind stress model
air_temperature: the air temperature in °C as a function with signature (x, y, t) or a constant
latent_heat_vaporisation: latent heat of vaporisation in J / kg
vapour_pressure: parameterisation for saturation vapour pressure in water
water_specific_heat_capacity: the specific heat capacity of water in J / K / kg
water_density: water density in kg / m³
air_specific_heat_capacit: the specific heat capacity of air in J / K / kg
air_density: air density in kg / m³
air_water_mixing_ratio: water content of air in kg / kg
stephan_boltzman_constant: the Stephan-Boltzman constant in W / K⁴

Example

julia> using Walrus

julia> wind_stress = WindStress(; reference_wind_speed = 0., reference_wind_direction = 90.)
(::WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}) (generic function with 2 methods)

julia> surface_heat_exchange = SurfaceHeatExchangeBoundaryCondition(; wind_stress)
FluxBoundaryCondition: DiscreteBoundaryFunction with (::SurfaceHeatExchange{WindStress{Float64, Float64, LogarithmicNeutralWind{Float64, Nothing}, Float64}, Int64, Walrus.SurfaceHeatingModel.EmpiricalLatentHeatVaporisation{Float64}, Walrus.SurfaceHeatingModel.AugustRocheMagnusVapourPressure{Float64}, Float64})

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Library

Wall stress model

Radiative transfer models

Tidal forcing models

Wind stress model

Surface heat exchange model