The Fluid Dynamics of Tornadoes Richard Rotunno NCAR NCAR is funded by the National Science Foundation Lecture 3: Numerical Simulations & Dynamics of The.

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Presentation transcript:

The Fluid Dynamics of Tornadoes Richard Rotunno NCAR NCAR is funded by the National Science Foundation Lecture 3: Numerical Simulations & Dynamics of The Two-Celled Vortex

Numerical Model of Ward Vortex Chamber …inadequate top boundary condition…  …difficult to model top boundary condition… Ward (1972, JAS)

Numerical Model of Ward Vortex Chamber …inadequate top boundary condition…  …difficult to model top boundary condition… Rotunno (1977, JAS)

Numerical Simulations of Ward Chamber S = 0.1S = 0.4S =1.0 Rotunno (1979, JAS)

Fiedler Chamber Fiedler (1994, Atmos-Ocn) Swirl RatioReynolds # Boundary condition

Nondimensional Governing Equations in Cylindrical Polar Coordinates velocity scale length scale buoyancy scale

Fiedler Chamber Fiedler (1994, Atmos-Ocn) Boundary condition Buoyancy force

Imposed Buoyancy Force and Grid r

r

Steady Solution v. Swirl Ratio

Two-Celled Vortex End-Wall Vortex End-Wall Boundary Layer Corner Flow Outer Flow

The Two-Celled Vortex

Fiedler Chamber Fiedler (1994, Atmos-Ocn) Boundary condition Boundary Eliminate lower boundary layer / zero-stress condition 

z=0 Two-Celled Vortex Steady Solution v. Swirl Ratio

z=0 Two-Celled Vortex Steady Solution v. Swirl Ratio

z=0 Two-Celled Vortex Steady Solution v. Swirl Ratio

z=0 Two-Celled Vortex Steady Solution v. Swirl Ratio

z=0 Two-Celled Vortex Steady Solution v. Swirl Ratio

r z Circulation Around the Domain Two-Celled Vortex At steady state and applying boundary conditions 

r z Conservation of Angular Momentum Thermodynamic Speed Core size Increases with Swirl Ratio Two-Celled Vortex: Balance of Buoyancy and Centrifugal Tendencies (Rankine Vortex)

Core Size and Max Velocity from Free-Slip Two-Celled Vortex Experiments

Imposed Buoyancy Force and Grid r

Two-Celled Vortex End-Wall Vortex End-Wall Boundary Layer Corner Flow Outer Flow

Summary 1.Fiedler Chamber also produces a realistic range of vortex structures 2.Free-slip conditions eliminate the surface boundary layer and corner flow  3.Two-celled vortex has its own distinct dynamics, essentially the classic mechanism of conservation of angular momentum