Richard Rotunno NCAR NCAR is funded by the National Science Foundation Lecture 3 Numerical Simulations amp Dynamics of The Two Celled Vortex Numerical Model of Ward Vortex Chamber ID: 417903
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Slide1
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 VortexSlide2
Numerical Model of Ward Vortex Chamber
…
inadequate top boundary condition
…
…
difficult to model top boundary condition
…
Ward (1972,
JAS
)Slide3
Numerical Model of Ward Vortex Chamber
…
inadequate top boundary condition
…
…
difficult to model top boundary condition
…
Rotunno
(1977,
JAS
)Slide4
Numerical Simulations of Ward Chamber
S = 0.1
S = 0.4
S =1.0
Rotunno
(1979,
JAS
)Slide5
Fiedler Chamber
Fiedler (1994,
Atmos-Ocn
)
Swirl Ratio
Reynolds #
Boundary conditionSlide6
Nondimensional Governing Equations in
Cylindrical Polar Coordinates
velocity scale
length scale
buoyancy scaleSlide7
Fiedler Chamber
Fiedler (1994,
Atmos-Ocn
)
Boundary condition
Buoyancy forceSlide8
Imposed Buoyancy Force and Grid
rSlide9
Imposed Buoyancy Force and Grid
rSlide10
Steady Solution
v. Swirl RatioSlide11
Steady Solution
v. Swirl RatioSlide12
Steady Solution
v
. Swirl RatioSlide13
Steady Solution
v. Swirl RatioSlide14
Steady Solution
v
. Swirl RatioSlide15
Two-Celled Vortex
End-Wall Vortex
End-Wall Boundary Layer
Corner Flow
Outer FlowSlide16
The Two-Celled VortexSlide17
Fiedler Chamber
Fiedler (1994,
Atmos-Ocn
)
Boundary condition
Boundary condition @
Eliminate lower boundary layer
/ zero-stress condition
Slide18
Free-Slip @
z
=0
Two-Celled Vortex
Steady Solution v. Swirl RatioSlide19
Free-Slip @
z=0
Two-Celled Vortex
Steady Solution v. Swirl RatioSlide20
Free-Slip @
z
=0
Two-Celled Vortex
Steady Solution
v
. Swirl RatioSlide21
Free-Slip @
z
=0
Two-Celled Vortex
Steady Solution
v
. Swirl RatioSlide22
Free-Slip @
z=0
Two-Celled Vortex
Steady Solution v. Swirl RatioSlide23
r
z
Circulation Around the Domain
Two-Celled Vortex
At steady state and applying boundary conditions
Slide24
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)Slide25
Core Size and Max Velocity from
Free-Slip Two-Celled Vortex ExperimentsSlide26
Imposed Buoyancy Force and Grid
rSlide27
Two-Celled Vortex
End-Wall Vortex
End-Wall Boundary Layer
Corner Flow
Outer FlowSlide28
Summary
Fiedler Chamber also produces a realistic range of vortex structures
Free-slip conditions eliminate the surface boundary layer and corner flow
Two-celled vortex has its own distinct dynamics, essentially the classic mechanism of conservation of angular momentum