Rotating System

Rotating System

Considering a system rotating at the angular velocity Ω₀ in the polar coordinates, one has to take the Coriolis and centrifugal forces and the energy source from the centrifugal force into account.

In cylindrical coordinates, the rotation direction is the x2 direction. The extra forces are described as F₁ = 2 Ω₀ v_φ + R Ω₀² in the x1 direction and F₂ = -2 Ω₀ v_R in the x2 direction. The extra energy source is described as S = ρ R Ω₀² v_R.

In spherical polar coordinates, the rotation direction is the x3 direction. The extra forces are described as F₁ = 2 Ω₀ sin(θ) v_φ + r (Ω₀ sin(θ))² in the x1 direction, F₂ = cot(θ) (2 Ω₀ sin(θ) v_φ + r (Ω₀ sin(θ))²) in the x2 direction, and F₃ = -2 sin(θ) Ω₀ (v_r + cot(θ) v_θ) in the x3 direction. The extra energy source is described as S = ρ r (Ω₀ sin(θ)² (v_r + cot(θ) v_θ).

Configuration

Nothing to do at the configuration for the rotating system.

Input File

The angular velocity of the rotating system is set at Omega0 in the cylindrical or spherical polar coordinates. In order to activate the rotating system, one has to change the <orbital_advection> block as follows:

    <orbital_advection>
    Omega0     = 1.0             # angular velocity of the rotating system