Stability and Transition in Shear Flows

1. Front Matter

   Pages i-xiii

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2. Introduction and General Results

   1. Introduction and General Results

      • Peter J. Schmid, Dan S. Henningson

      Pages 1-10

3. Temporal Stability of Parallel Shear Flows

   1. Front Matter

      Pages 11-13

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   2. Linear Inviscid Analysis

      • Peter J. Schmid, Dan S. Henningson

      Pages 15-53

   3. Eigensolutions to the Viscous Problem

      • Peter J. Schmid, Dan S. Henningson

      Pages 55-98

   4. The Viscous Initial Value Problem

      • Peter J. Schmid, Dan S. Henningson

      Pages 99-151

   5. Nonlinear Stability

      • Peter J. Schmid, Dan S. Henningson

      Pages 153-193

4. Stability of Complex Flows and Transition

   1. Front Matter

      Pages 195-196

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   2. Temporal Stability of Complex Flows

      • Peter J. Schmid, Dan S. Henningson

      Pages 197-252

   3. Growth of Disturbances in Space

      • Peter J. Schmid, Dan S. Henningson

      Pages 253-371

   4. Secondary Instability

      • Peter J. Schmid, Dan S. Henningson

      Pages 373-399

   5. Transition to Turbulence

      • Peter J. Schmid, Dan S. Henningson

      Pages 401-475

5. Back Matter

   Pages 477-558

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The field of hydrodynamic stability has a long history, going back to Rey­ nolds and Lord Rayleigh in the late 19th century. Because of its central role in many research efforts involving fluid flow, stability theory has grown into a mature discipline, firmly based on a large body of knowledge and a vast body of literature. The sheer size of this field has made it difficult for young researchers to access this exciting area of fluid dynamics. For this reason, writing a book on the subject of hydrodynamic stability theory and transition is a daunting endeavor, especially as any book on stability theory will have to follow into the footsteps of the classical treatises by Lin (1955), Betchov & Criminale (1967), Joseph (1971), and Drazin & Reid (1981). Each of these books has marked an important development in stability theory and has laid the foundation for many researchers to advance our understanding of stability and transition in shear flows.

• Analysis
• Fluid Mechanics
• Hydrodynamic Stability
• Shear Flows
• Stability Theory
• Turbulence
• fluid dynamics
• model
• numerical methods
• simulation
• fluid- and aerodynamics

From the reviews:

SIAM REVIEW

"This book presents a modern treatment of stability in shear flows. Stability theory has seen a number of classic treatments over the years…Schmid and Henningson’s book builds on these and offers much new material relevant to stability in shear flows…The MATLAB codes included in the appendix and a discussion of the effects of rounding error and resolution on the computations of eigenvalues of linear stability operators will be particularly helpful for students and researchers as they get started with stability computations…As the basis for a course, the first part of the book would permit students to build a solid foundation in classical and modern stability theory, while a selection of advanced topics from the second half of the book could be treated later in the course or through projects and independent study by students."

ZENTRALBLATT MATH

"The book addresses to graduate students as well as to a broad community of researchers with a basic knowledge of fundamental fluid dynamics…The topics are treated with mathematical rigor while the physical motivation and usefulness of mathematical concepts is kept close at hand. The work is elegantly structured, and the graphical material is very suggestive."

• Applied Mathematics Department, University of Washington, Seattle, USA

  Peter J. Schmid

• Department of Mechanics, Royal Institute of Technology (KTH), Stockholm, Sweden

  Dan S. Henningson