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Tornado

ISBN:
978-1-56700-283-6 (Print)
978-1-56700-293-5 (Online)

Tornado

Aleksey Yur'evich Varaksin
Joint Institute for High Temperatures (JIHT) of the Russian Academy of Sciences, Izhorskaya Street, 13, Building 2, 125412, Moscow, Russia

M.E. Romash
Joint Institute for High Temperatures, Moscow, Russia

V.N. Kopeitsev
Joint Institute for High Temperatures, Moscow, Russia

Description

This book is devoted to the fundamental problems of investigation of free concentrated vortices. The possibilities of mathematical modeling of whirlwinds (tornadoes) are discussed; it states and solves, for the first time in domestic and global practice, the problem of physical (laboratory) modeling of whirlwinds without using mechanical whirling devices. The issues of generation and stability of free vortices and methods for controlling their characteristics are analyzed. The possibilities for affecting atmospheric whirling formations of various scales are described. The book is designed for scientists investigating hydrodynamics and heat and mass transfer of vortex flows, as well as for university teachers, students and post-graduate students.

Table of Contents:

FOREWORD
NOMENCLATURE
CHAPTER 1 INTRODUCTORY CHAPTER
1.1. Preliminary Remarks
1.2 Basic Defi nitions
1.3 Winds
1.3.1 The Beaufort wind force scale
1.4 Hurricanes
1.4.1 Saffi r–Simpson hurricane wind scale
1.4.2 The 2005 hurricane season
1.4.3 Hurricane Katrina
1.4.4 Hurricane whirlwinds (tornados)
1.5 Whirlwinds (tornados)
1.5.1 Fujita tornado scale
1.5.2 The enhanced tornado scale
1.6 Some Conclusions
CHAPTER 2 BRIEF DATA ON CYCLONES (ANTICYCLONES)
2.1 Preliminary Remarks
2.2 The Earth Atmosphere
2.2.1 The atmosphere composition and structure
2.2.2 The atmospheric pressure fi eld
2.2.3 Vertical atmospheric balance
2.2.4 Frontal zones
2.2.5 Weather fronts
2.2.6 Weather in the passing fronts
2.3 Properties of Cyclones (Anticyclones)
2.3.1 Development stages
2.3.2 Specifi c features of air movement
2.3.3 Frequency and sites of generation
2.3.4 Typical pressure values
2.4 Natural Phenomena Accompanying Cyclones (Anticyclones)
2.4.1 Atmospheric precipitations in the system of cyclones
2.4.2 Hurricane winds in the system of cyclones (anticyclones)
2.5 Heat (Cold) Transfer by Extratropical Cyclones
2.5.1 Main mechanisms of heat (cold) transfer
2.5.2 Effects of vortices on heat transfer by ocean currents
2.6 Tropical Cyclones
CHAPTER 3 BRIEF DATA ON WHIRLWINDS
3.1 Preliminary Remarks
3.2 Whirlwind Clouds
3.2.1 General characterization
3.2.2 Shapes and dimensions
3.2.3 The internal structure
3.2.4 Horizontal whirlwind clouds
3.2.5 Towering whirlwind clouds
3.3 The Whirlwind Structure
3.3.1 Funnel
3.3.2 The cascade
3.4 Whirlwind Shapes
3.4.1 Dense whirlwinds
3.4.2 Blurred whirlwinds
3.4.3 Groups of whirlwinds
3.5 Properties of Whirlwinds
3.5.1 Stages of development
3.5.2 The speed of movement, lifetime, and path length
3.5.3 Sizes and weight
3.5.4 Frequency and places of generation
3.6. Types of Whirlwinds and Vortices
3.6.1 Invisible whirlwinds and vortices
3.6.2 Dust whirlwinds and vortices
3.6.3 Waterspouts and vortices
3.6.4 Fire whirlwinds and vortices
3.6.5 Snow whirlwinds and vortices
3.7 Brief Description of the Most Known Whirlwinds
3.7.1 Russia
3.7.2 Western Europe
3.7.3 United States of America
3.8 Study of Tornados and Possibilities for Protection
3.8.1 Study and forecasting of tornados
3.8.2 Damage from tornados
3.8.3 Protection against tornados
CHAPTER 4 BASES OF THE THEORY OF VORTEX MOTION
4.1 Preliminary Remarks
4.2 Systems of Coordinates
4.3 Some Defi nitions
4.3.1 Streamline
4.3.2 Filament. Stream tube
4.3.3 Vortex line
4.3.4 Vortex rope. Vortex tube
4.4 Characteristics of Vortex Flows
4.4.1 Azimuthal (tangential) velocity
4.4.2 Twisting parameter
4.4.3 Vorticity. Angular velocity
4.4.4 Circulation
4.4.5 The Rossby number
4.5 Elementary Data on Vortices
4.5.1 Free (potential) vortex
4.5.2 Forced vortex (solid-state rotation)
4.5.3 A combined (Rankine) vortex
4.6 Basic Equations
4.6.1 The continuity equation
4.6.2 The Navier–Stokes equation
4.6.3 The vorticity equation
4.7 Elements of Hydrostatics
4.7.1 Dropping liquid equilibrium in a rotating vessel
4.7.2 Equilibrium of gases. Dry-adiabatic gradient
4.8 Coriolis Force and Its Impact on the Motion of the Material Point
4.8.1 The cause of the Coriolis force
4.8.2 Impact of the Coriolis force on vertical motion
4.8.3 Impact of the Coriolis force on motion in the horizontal plane
CHAPTER 5 MATHEMATICAL MODELING OF WHIRLWINDS
5.1 Preliminary Remarks
5.2 A Simple Analytical Model
5.2.1 A very simple solution for tornados
5.2.2 Exact solution for tornados
5.2.3 Stratifi ed tornados
5.3 Analysis of Vortex Instability
5.3.1 Derivation of the vorticity equation
5.3.2 Analysis of the vorticity equation
5.3.3 Calculation results
5.4 Analytical Solution of the Navier–Stokes Equations
5.4.1 Generalized solution for vortex sink
5.4.2 Using the solution for analysis of tornados
5.5 Modeling the Ascending Twisted Flow
5.5.1 Formation of an ascending twisted fl ow
5.5.2 The system of equations with account for the Coriolis force
5.5.3 Development of twisting in the bottom part of an ascending fl ow
5.5.4 Steady-state fl ow in the bottom part of an ascending fl ow
5.6 Numerical Simulation of Tornados
CHAPTER 6 PHYSICAL MODELING OF TORNADOS
6.1 Preliminary Remarks
6.2 Experimental Unit
6.2.1 Description of the unit
6.2.2 Thermal conditions
6.3 Results
6.3.1 The underlying surface (temperature distribution)
6.3.2 Air (temperature distribution)
6.3.3 Generalization of data (Rayleigh number)
6.3.4 Integrated parameters of vortex structures
6.3.5 Dynamics of vortex structures
6.3.6 Traces of vortex structures
6.3.7 Visualization of the vortex funnel
6.3.8 The parameter of twisting. Rossby number
6.3.9 Instantaneous velocity field
CHAPTER 7 A NEW METHOD FOR TORNADO CONTROL
7.1 Preliminary Remarks
7.2 Brief Information on Control Methods
7.3 Experimental Unit
7.4 Vortex-Mesh Interaction: Basic Ideas
7.5 Vortex Interaction with Single-Mesh Structures
7.6 Vortex Interaction with Two-Mesh Structures
7.7 The New Passive-Active Protection Method: Physical Principles and Advantages
7.7.1 Non-use of a solid barrier
7.7.2 Generation of small-scale turbulence
7.7.3 Effect of aerodynamic increase of the 'working' surface
7.7.4 Long-distance interaction
7.7.5 Effect of enhanced impact at smaller distances
7.7.6 Small height of the mesh structure
7.7.7 Effect of increasing the relative size of the mesh protective structure at smaller distances
7.7.8 Effect of rapid and seasonal installation
7.7.9 Effect of protection against debris
CONCLUSIONS
REFERENCES
ANNEX 1
ANNEX 2
ANNEX 3
INDEX