Shtern Vladimir. Counterflows: Paradoxical Fluid Mechanics Phenomena

Cambridge University Press, 2012. — 470 p.Counterflows play important roles in nature and technology. A natural example is the Gulf Stream and the opposite flow in the ocean depths. Technological applications include hydrocyclones, vortex tubes, and vortex combustors. These elongated counterflows are wildly turbulent but survive intense mixing, a seeming paradox. Local counterflows, whose spatial extent is small compared with that of surrounding flows, occur behind bluff bodies and in swirling streams. The latter are often referred to as vortex breakdown bubbles, which occur in tornadoes and above delta wings. Most scale counterflows are cosmic bipolar jets. Most miniature counterflows occur in capillary menisci of electrosprays and fuel atomizers. This book discusses the physical mechanisms that drive counterflows, examining how they emerge, develop, become double and multiple counterflows, and comprise both global and local circulationsNatural and Technological Counterflows
Physical Mechanisms of Counterflows
Counterflow Applications, Control, and Stability
Approach
Accumulation Counterflows
Conical Similarity Flows
Conical Jets
Super-Collimated Jet
Capillary Jet
Bifurcation of Swirl in Conical Counterflows
Observations of Spontaneous Swirl Appearance
Bifurcation of Swirl as Symmetry Breaking
Swirl Appearance in Capillary Flows
Swirl Appearance in Electro-Vortex Flows
Mechanism of Swirl Appearance in Conical Flows
Bifurcation of Counter-Swirl
Outline of Stability and Bifurcation Features
Parallel Jetlike Flows
Secondary Flows
The Lyapunov-Schmidt Method
Bifurcations in the Jetlike Flows
MHD Flow in an Annular Pipe
Solving Stability Problems for Large Re
Bifurcations in the Annular-Pipe Flows
Conical Counterflows Driven by Swirl
Swirling Jet Above a Plane
A Half-Line Vortex in a Free Space
Swirling Jets in Conical Regions
Super-Collimation in Swirling Counterflows
Jetlike Swirling Counterflows
Power-Law Jets
Analytical Modeling of Multiple Counterflows
Swirling Counterflows in a Capillary Meniscus
Swirling Counterflows in Cylindrical Devices
Swirl-Decay Mechanism
Modeling Counterflows in Vortex Separators
Numerical Study of Vortex Breakdown and Double Counterflow
Double Counterflow in a Vortex Trap
Separation Counterflows
Counterflows in a Plane Diverging Channel
Counterflows Due to Bifurcations of Vortex Source Flow
Stability of Plane Counterflows
Transition Flows
Summary of Plane Counterflow Features
Counterflows Due to Internal Separation in Spatial Conical Flows
Temperature Distribution in Swirling Counterflows
Temperature Distribution in Conical Similarity Jets
Temperature Distribution in Generalized Vortex-Sink
Temperature Distribution in a Cylindrical Counterflow
Onset of Buoyancy Similarity Counterflows
Development of Conical Buoyancy Bipolar Jets
Onset of Keplerian Buoyancy Flows
Thermal Convection Counterflows
Model of a Free Convection Near a Black Smoker
Model of a Free Convection Near a Volcano
Centrifugal Convection
Centrifugal Convection of a Perfect Gas
Control of Vortex BreakdownExperimental Study of VB Control
Numerical Study of VB Control by Temperature Gradients
VB Control by Adding Near-Axis Swirl and Temperature Gradients
Magnetic Counterflows
Problem Formulation
Magnetic Field Bifurcation in the Bipolar Accretion Flow
Magnetic Field Bifurcation in the Bipolar Vortex-Sink Accretion Flow
Magnetic Field Bifurcation Near a Point Source of Heat and Gravity
Instability Nature of MHD Bifurcation
Bifurcation of Magnetic Field in an Electro-Vortex Flow
Stability of Conical Flows
Formulation of the Stability Problem
Stability of the Fluid at Rest
Instability Nature of Folds and Hysteresis in Swirl-Free Jets
Deceleration Instability of Jets
Instability of Swirling Jets
Instability Nature of Swirl Bifurcation
Instability of Flows Diverging Near a Surface
Concluding Remarks