Offers an introduction to the physics of fast secondary or induced nonlinear instabilities in wave-sustaining media, integrating a full general theory with results from across several subject areas. Concepts are presented along with specific calculations and detailed descriptions of mathematics involved. Some phenomena explained are wave-turbulent instabilities, vortex dynamics, beam-plasma interactions, plasma confinement, and magnetic fields in galaxies.

Preface

ix

Direct nonlinear instabilities

1

(19)

Parametric decay instability

1

(1)

Decay instabilities in media with wave-modulated phase velocity; qualitative theory and principal features of PDI

2

(5)

PDI of magnetohydrodynamic waves (quantitative theory)

7

(7)

Modulation instability

14

(1)

Explosive instability of negative-energy waves

15

(5)

Induced instabilities, the symmetry and the evolution of non-equilibrium systems

20

(16)

Systems with multiparametric non-equilibrium

20

(2)

Group methods of analyzing secondary quasi-stationary states

22

(8)

Introduction

22

(1)

Scaling transformation group

23

(3)

Supersymmetry group

26

(4)

Effective collision frequencies in turbulent media

30

(2)

Induced drift instabilities

32

(4)

External noise and stability of plasmas

36

(21)

Introduction

36

(2)

Fluctutional chaos

38

(3)

Universal noise-induced plasma instability and accelerated fluctuational dynamics in the vicinity of a point of instability

41

(10)

Anomalous diffusion of particles

51

(3)

Fluctuations of transfer coefficients in the plasma and in hydrodynamics

54

(3)

Non-standard evolution of turbulent media

57

(26)

Introduction

57

(1)

Drift instability cascade and energy transfer in ionospheric turbulence

58

(9)

Wave-turbulent instability

67

(16)

The helical mechanism of large-scale structure generation in continuous media

83

(78)

Introduction

83

(1)

Helical structures and helical mechanisms of generation in hydrodynamics

84

(9)

On the role of helicity, on the similarity and differences between the magnetic and vortex dynamo in turbulent media

84

(3)

Generation of large-scale helical vortices in convective media

87

(3)

Helical mechanism of generation of large-scale structures in non-convective hydrodynamic media

90

(3)

Hydrodynamic α-effect in compressible media

93

(12)

Introduction

93

(1)

Qualitative discussion

94

(4)

Closure of averaged equation

98

(2)

α as a function of compressibility coefficient: limiting cases

100

(2)

Large-scale instability

102

(1)

Discussion

103

(2)

Large-scale vortical instability and convection: further progress

105

(12)

Equation of vortical instability due to convective turbulence and Coriolis force

105

(7)

Rayleigh-Benar convection in turbulent fluid at very large Reynolds numbers

112

(5)

Reverse energy cascade in uniform turbulent shear flow

117

(12)

Introduction

117

(1)

Formulation of the problem. Basic equations. Homogeneous helical anisotropic flow

118

(2)

Closing the equations for perturbations of turbulent shear flow in the second-order correlation approximation

120

(4)

Interval instability of turbulent Couette flow

124

(5)

Helicity as a possible physical mechanism for the amplification of typhoon-type vortical perturbations in the atmosphere and of the modulation of rotation frequency of the Earth

129

(15)

Introductory remarks

129

(1)

Qualitative analysis of the role played by helicity in typhoon generation

130

(4)

On typhoon precursors

134

(2)

On the mechanism of modulation of the number of strong earthquakes and of the Earth's rotation frequency

136

(8)

The importance and prospects of further research into nonlinear instabilities in helicoidal media (concluding remarks)

144

(17)

Two-dimensional or helical turbulence?

144

(3)

Vortical processes in the Jovian atmosphere induced by the collision with the Shoemaker-Levy 9 comet

147

(9)

Some yet unsolved problems

156

(5)

Index

161

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