Coriolis

The Coriolis option determines whether the fluid experiences the effect of the Coriolis force, or rotation. Currently three options are available: no rotation, $f$-plane, and $\beta$-plane.

No rotation

By default there is no rotation. This can be made explicit by passing coriolis = nothing to a model constructor.

Traditional $f$-plane

To set up an $f$-plane with, for example, Coriolis parameter $f = 10^{-4} \text{s}^{-1}$

julia> coriolis = FPlane(f=1e-4)
FPlane{Float64}: f = 1.00e-04

An $f$-plane can also be specified at some latitude on a spherical planet with a planetary rotation rate. For example, to specify an $f$-plane at a latitude of $\varphi = 45°\text{N}$ on Earth which has a rotation rate of $\Omega = 7.292115 \times 10^{-5} \text{s}^{-1}$

julia> coriolis = FPlane(rotation_rate=7.292115e-5, latitude=45)
FPlane{Float64}: f = 1.03e-04

in which case the value of $f$ is given by $2\Omega\sin\varphi$.

Non-traditional $f$-plane

To set up an $f$-plane with non-traditional Coriolis terms, for example, with $\bm{f} = (0, f_y, f_z) = (0, 2, 1) \times 10^{-4} \text{s}^{-1}$,

julia> coriolis = NonTraditionalFPlane(fz=1e-4, fy=2e-4)
NonTraditionalFPlane{Float64}: fz = 1.00e-04, fy = 2.00e-04

An $f$-plane with non-traditional Coriolis terms can also be specified at some latitude on a spherical planet with a planetary rotation rate. For example, to specify an $f$-plane at a latitude of $\varphi = 45°\text{N}$ on Earth which has a rotation rate of $\Omega = 7.292115 \times 10^{-5} \text{s}^{-1}$

julia> coriolis = NonTraditionalFPlane(rotation_rate=7.292115e-5, latitude=45)
NonTraditionalFPlane{Float64}: fz = 1.03e-04, fy = 1.03e-04

in which case $f_z = 2\Omega\sin\varphi$ and $f_y = 2\Omega\cos\varphi$.

Traditional $\beta$-plane

To set up a $\beta$-plane the background rotation rate $f_0$ and the $\beta$ parameter must be specified. For example, a $\beta$-plane with $f_0 = 10^{-4} \text{s}^{-1}$ and $\beta = 1.5 \times 10^{-11} \text{s}^{-1}\text{m}^{-1}$ can be set up with

julia> coriolis = BetaPlane(f₀=1e-4, β=1.5e-11)
BetaPlane{Float64}: f₀ = 1.00e-04, β = 1.50e-11

Alternatively, a $\beta$-plane can also be set up at some latitude on a spherical planet with a planetary rotation rate and planetary radius. For example, to specify a $\beta$-plane at a latitude of $\varphi = 10\degree{S}$ on Earth which has a rotation rate of $\Omega = 7.292115 \times 10^{-5} \text{s}^{-1}$ and a radius of $R = 6,371 \text{km}$

julia> coriolis = BetaPlane(rotation_rate=7.292115e-5, latitude=-10, radius=6371e3)
BetaPlane{Float64}: f₀ = -2.53e-05, β = 2.25e-11

in which case $f_0 = 2\Omega\sin\varphi$ and $\beta = 2\Omega\cos\varphi / R$.

Non-traditional $\beta$-plane

A non-traditional $\beta$-plane requires either 5 parameters (by default Earth's radius and rotation rate are used):

julia> NonTraditionalBetaPlane(fz=1e-4, fy=2e-4, β=4e-11, γ=-8e-11)
NonTraditionalBetaPlane{Float64}: fz = 1.00e-04, fy = 2.00e-04, β = 4.00e-11, γ = -8.00e-11, R = 6.37e+06

or the rotation rate, radius, and latitude:

julia> NonTraditionalBetaPlane(rotation_rate=5.31e-5, radius=252.1e3, latitude=10)
NonTraditionalBetaPlane{Float64}: fz = 1.84e-05, fy = 1.05e-04, β = 4.15e-10, γ = -1.46e-10, R = 2.52e+05