Tornado-like flows

Abstract

Simple exact solutions for horizontal flows, with a stagnant funnel consisting of a lighter fluid and narrowing toward the ground, exhibit the main features of real tornadoes. The two-fluid model is quite robust, as it can be adapted to any vorticity distribution, any vertical stratification, and the effects of compressibility.

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

“…The 2-magnet configuration clearly enhances the temperature fluctuations along the centreline. This is a consequence of the cold fluid stream that is carried by the strong swirling tornado-like motion (similar to that analysed in Yih [47]) that creates a vertically elongated thermal plume. It is noted that the 3-magnet configuration significantly reduces the level of temperature fluctuations along the centreline.…”

Mathematical Modeling of Structure and Dynamics of Concentrated Tornado-like Vortices: A Review

“…The simplest model of a tornado is a vortex flow with a vertical axis of symmetry and a fixed core (or funnel) [26]. Figure 1 shows a diagram of the vortex under consideration.…”

“…where Y(x, y) = ∂x ∂r ∂y ∂z − ∂x ∂z ∂y ∂ r is the Jacobian. Transformations of the original system of equations to the system of Equations ( 24)- (26) were made using known relations: ω φ = ∂U r /∂z − ∂U z /∂r, Γ = rU φ , U r = r −1 ∂Ψ/∂z, and U z = −r −1 ∂Ψ/∂r. Equations ( 24)-( 26) make up a system of three equations with three variables: the stream function Ψ, circulation Γ, and the azimuthal component of the vorticity ω φ .…”

“…Equations ( 24)-( 26) make up a system of three equations with three variables: the stream function Ψ, circulation Γ, and the azimuthal component of the vorticity ω φ . The boundary and initial conditions for solving the system of Equations ( 24)- (26) were selected in accordance with the conditions of the experiments [14]. The boundary conditions were as follows: (1) on the axis of symmetry (U r = 0, Γ = 0, and ω φ = 0), (2) on the lower wall of the chamber (U r = 0, U z = 0, and Γ = 0), (3) on the upper wall of the chamber (U r = 0, ∂Γ/∂z = 0, and ∂ω φ /∂z = 0), (4) on the side wall of the chamber (U r = 0, ω φ = 0, and ∂(Γ/r 2 )/∂r = 0), and (5) in the entrance section (U r = U r0 , Γ = Γ 0 , and ω φ = 0).…”

“…The boundary conditions were as follows: (1) on the axis of symmetry (U r = 0, Γ = 0, and ω φ = 0), (2) on the lower wall of the chamber (U r = 0, U z = 0, and Γ = 0), (3) on the upper wall of the chamber (U r = 0, ∂Γ/∂z = 0, and ∂ω φ /∂z = 0), (4) on the side wall of the chamber (U r = 0, ω φ = 0, and ∂(Γ/r 2 )/∂r = 0), and (5) in the entrance section (U r = U r0 , Γ = Γ 0 , and ω φ = 0). The following are the initial conditions (τ = 0): ω φ (r, z) = 0 and Ψ = Ψ(r, z), being solution (26) at ω φ = 0 and Γ(r, z) = 0 for all r and z except r = r 1 and 0 ≤ z ≤ h, where the circulation is given (Γ = Γ 0 ).…”