Instabilities of Flows and Transition to Turbulence: 1st Edition (Paperback) book cover

Instabilities of Flows and Transition to Turbulence

1st Edition

By Tapan K. Sengupta

CRC Press

528 pages | 234 B/W Illus.

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Addressing classical material as well as new perspectives, Instabilities of Flows and Transition to Turbulence presents a concise, up-to-date treatment of theory and applications of viscous flow instability. It covers materials from classical instability to contemporary research areas including bluff body flow instability, mixed convection flows, and application areas of aerospace and other branches of engineering. Transforms and perturbation techniques are used to link linear instability with receptivity of flows, as developed by the author.

The book:

  • Provides complete coverage of transition concepts, including receptivity and flow instability
  • Introduces linear receptivity using bi-lateral Fourier-Laplace transform techniques
  • Presents natural laminar flow (NLF) airfoil analysis and design as a practical application of classical and bypass transition
  • Distinguishes strictly between instability and receptivity, which leads to identification of wall- and free stream-modes
  • Describes energy-based receptivity theory for the description of bypass transitions

Instabilities of Flows and Transition to Turbulence has evolved into an account of the personal research interests of the author over the years. A conscious effort has been made to keep the treatment at an elementary level requiring rudimentary knowledge of calculus, the Fourier-Laplace transform, and complex analysis. The book is equally amenable to undergraduate students, as well as researchers in the field.


"The monograph contains the following topics of hydrodynamics: 1. Classic linear hydrodynamic instability; 2. Receptivity and instability of different types; 3. Vortex-induced instability and bypass transition; 4. Transient growth and spatio-temporal instability; 5. Bifurcation and dynamical system theory of nonlinear instabilities for different flows; 6. Instability of mixed convection flows by restricted heat transfer; 7. Instability of three-dimensional flows; 8. Applications of instability and transition for flows past airfoils. These linear and nonlinear aspects of flow instabilities are studied by using analytic and computational (numerical simulation) means. … "

––Boris V. Loginov, Zentralblatt MATH

Table of Contents

Introduction to Instability and Transition


What Is Instability?

Temporal and Spatial Instability

Some Instability Mechanisms

Computing Transitional and Turbulent Flows

Fluid Dynamical Equations

Some Equilibrium Solutions of the Basic Equation

Boundary Layer Theory

Control Volume Analysis of Boundary Layers

Numerical Solution of the Thin Shear Layer (TSL) Equation

Laminar Mixing Layer

Plane Laminar Jet

Issues of Computing Space-Time Dependent Flows

Wave Interaction: Group Velocity and Energy Flux

Issues of Space-Time Scale Resolution of Flows

Temporal Scales in Turbulent Flows

Computing Time-Averaged and Unsteady Flows

Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods

DRP Schemes: Parameter Ranges for Creating q-Waves

Instability and Transition in Flows


Parallel Flow Approximation and Inviscid Instability Theorems

Viscous Instability of Parallel Flows

Properties of the Orr-Sommerfeld Equation and Boundary Conditions

Instability Analysis from the Solution of the Orr-Sommerfeld Equation

Receptivity Analysis of the Shear Layer

Direct Simulation of Receptivity to Free Stream Excitation

Nonparallel and Nonlinear Effects on Instability and Receptivity

Bypass Transition: Theory, Computations and Experiments


Transition via Growing Waves and Bypass Transition

Visualization Study of Vortex-Induced Instability as Bypass Transition

Computations of Vortex-Induced Instability as a Precursor to Bypass Transition

The Instability Mechanism in Vortex-Induced Instability

Instability at the Attachment Line of Swept Wings

Spatio-Temporal Wave Front and Transition


Transient Energy Growth

Bromwich Contour Integral Method and Energy-Based Receptivity Analysis

Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Method

Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and

Bypass Route

Calculation of the N Factor

Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition


Receptivity of Bluff-Body Flows to Background Disturbances

Multiple Hopf Bifurcations, Landau Equation and Flow Instability

Instability of Flow Past a Cylinder

Role of FST on Critical Reynolds Number for a Cylinder

POD Modes and Nonlinear Stability

The Landau-Stuart-Eckhaus Equation

Universality of POD Modes

Stability and Transition of Mixed Convection Flows


The Governing Equations

Equilibrium Boundary Layer Flow Equations

Linear Spatial Stability Analysis of the Boundary Layer over a Heated Plate

Nonlinear Receptivity of Mixed Convection Flow over a Heated Plate

Concluding Remarks

Instabilities of Three-Dimensional Flows


Three-Dimensional Flows

Infinite Swept Wing Flow

Attachment Line Flow

Boundary Layer Equations in the Transformed Plane

Simplification of Boundary Layer Equations in the Transformed Plane

Instability of Three-Dimensional Flows

Linear Stability Theory for Three-Dimensional Flows

Experimental Evidence of Instability on Swept Wings

Infinite Swept Wing Boundary Layer

Stability of the Falkner-Skan-Cooke Profile

Stationary Waves over Swept Geometries

Traveling Waves over Swept Geometries

Attachment Line Problem

Empirical Transition Prediction Method for Three-Dimensional Flows

Analysis and Design of Natural Laminar Flow Airfoils


Airfoil Nomenclature and Basic Aerodynamic Properties

Pressure Distribution and Pressure Recovery of Some Low Drag Airfoils

Flapping of Airfoils

Effects of Roughness and Fixing Transition

Effects of Vortex Generator or Boundary Layer Re-energizer

Section Characteristics of Various Profiles

High Speed NLF Airfoils

Direct Simulation of Bypass Transitional Flow Past an Airfoil



Relevance of Two-Dimensional Turbulence

Role of Formulation in the Numerical Solution in Two-dimensional DNS

Dynamical System Representation of Turbulent Flows

Role of the Computational Domain

Free and Forced Turbulence

Selected Problems

Bibliography and Index

About the Author

About the author: Professor Tapan K. Sengupta is affiliated with the High Performance Computing Laboratory in the Department of Aerospace Engineering at the Indian Institute of Technology, Kanpur, India.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics