Research Catalog

Title

Gravity-capillary free-surface flows / Jean-Marc Vanden-Broeck.

Author

Vanden-Broeck, J.-M. (Jean-Marc)

Publication

New York : Cambridge University Press, 2010.

Items in the Library & Off-site

Details

Description

xi, 318 p. : ill.; 26 cm.

Summary

"Free-surface problems occur in many aspects of science and of everyday life, for example in the waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a container and sails billowing in the wind. Consequently, the theory of gravity£capillary free-surface flows continues to be a fertile field of research in applied mathematics and engineering." "Concentrating on applications arising from fluid dynamics, Vanden-Broeck draws upon his years of experience in the field to address the many challenges involved in attempting to describe such flows mathematically. Whilst careful numerical techniques are implemented to solve the basic equations, an emphasis is placed upon the reader developing a deep understanding of the structure of the resulting solutions. The author also reviews relevant concepts in fluid mechanics to enable readers from other scientific fields to develop a working knowledge of free-boundary problems." "This series was established in 1952 as a medium for the publication of major new works of scholarship on all aspects of theoretical and applied mechanics. From its inception it has maintained a reputation for the publication of outstanding monographs, many of which have later been re-issued in paperback. The series covers such areas as wave propagation, fluid dynamics, theoretical geophysics, combustion and the mechanics of solids. Authors are encouraged to write for a wide audience and to balance mathematical analysis with physical interpretation and experimental data where appropriate. Although the research literature is expected to be a major source for the content of the books, authors should aim to synthesise new results rather than just survey them."--BOOK JACKET.

Series Statement

Cambridge monographs on mechanics

Uniform Title

Cambridge monographs on mechanics.

Subjects

• Nonlinear waves > Mathematical models
• Surface waves (Oceanography) > Mathematical models
• Fluid mechanics

Bibliography (note)

• Includes bibliographical references and index.

Contents

1. Introduction -- 2. Basic concepts -- 2.1. The equations of fluid mechanics -- 2.2. Free-surface flows -- 2.3. Two-dimensional flows -- 2.4. Linear waves -- 2.4.1. The water-wave equations -- 2.4.2. Linear solutions for water waves -- 2.4.3. Superposition of linear waves -- 3. Free-surface flows that intersect walls -- 3.1. Free streamline solutions -- 3.1.1. Forced separation -- 3.1.2. Free separation -- 3.2. The effects of surface tension -- 3.2.1. Forced separation -- 3.2.2. Free separation -- 3.3. The effects of gravity -- 3.3.1. Solutions with β1 = 0 (funnels) -- 3.3.2. Solutions with β1 = 0 (nozzles and bubbles) -- 3.3.3. Solutions with β1 = π/2 (flow under a gate with gravity) -- 3.4. The combined effects of gravity and surface tension -- 3.4.1. Rising bubbles in a tube -- 3.4.2. Fingering in a Hele Shaw cell -- 3.4.3. Further examples involving rising bubbles -- 3.4.4. Exponential asymptotics -- 4. Linear free-surface flows generated by moving disturbances -- 4.1. The exact nonlinear equations -- 4.2. Linear theory -- 4.2.1. Solutions in water of finite depth -- 4.2.2. Solutions in water of infinite depth -- 4.2.3. discussion of the solution -- 5. Nonlinear waves-asymptotic solutions -- 5.1. Periodic waves -- 5.1.1. Solutions when condition (5.55) is satisfied -- 5.1.2. Solutions when condition (55.5) is not satisfied -- 5.2. The Korteweg-de Vries equation -- 6. Numerical computations of nonlinear water waves -- 6.1. Formulation -- 6.2. Series truncation method -- 6.3. Boundary integral equation method -- 6.4. Numerical methods for solitary waves -- 6.4.1. Boundary integral equation methods -- 6.5. Numerical results for periodic waves -- 6.5.1. Pure capillary waves (g = 0, T is not = 0) -- 6.5.2. Pure gravity waves (g is not = 0, T = O) -- 6.5.3. Gravity capillary waves (g is not = 0, T is not =0) -- 6.6. Numerical results for solitary waves -- 6.6.1. Pure gravity solitary waves -- 6.6.2. Gravity capillary solitary waves -- 7. Nonlinear free-surface flows generated by nioving disturbances -- 7.1. Pure gravity free-surface flows in water of finite depth -- 7.1.1. Supercritical flows -- 7.1.2. Subcritical flows -- 7.2. Gravity capillary free-surface flows -- 7.2.1. Results in finite depth -- 7.2.2. Results in infinite depth (removal of the nonuniformity) -- 7.3. Gravity capillary free-surface flows with Wilton ripples -- 8. Free-surface flows with waves and intersections with rigid walls -- 8.1. Free-surface flow past, a flat plate -- 8.1.1. Numerical results -- 8.1.2. Analytical results -- 8.2. Free-surface flow past a surface-piercing object -- 8.2.1. Numerical results -- 8.2.2. Analytical results -- 8.3. Flow under a sluice gate -- 8.3.1. Formulation -- 8.3.2. Numerical procedure -- 8.3.3. Discussion of the results -- 8.4. Pure capillary free-surface flows -- 8.4.1. Numerical results -- 8.4.2. Analytical results -- 9. Waves with constant vorticity -- 9.1. Solitary waves with constant vorticity -- 9.1.1. Mathematical formulation -- 9.1.2. Numerical procedure -- 9.1.3. Discussion of the results -- 9.2. Periodic waves with constant vorticity -- 9.2.1. Mathematical formulation -- 9.2.2. Numerical procedure -- 9.2.3. Numerical results -- 9.2.4. Discussion -- 10. Three-dimensional free-surface flows -- 10.1. Green's function formulation for two-dimensional problems -- 10.1.1. Pressure distribution -- 10.1.2. Two-dimensional surface-piercing object -- 10.2. Extension to three-dimensional free-surface flows -- 10.2.1. Gravity flows generated by moving disturbances in water of infinite depth -- 10.2.2. Three-dimensional gravity-capillary free-surface flows in water of infinite depth -- 10.3. Further extensions -- 11. Time-dependent free-surface flows -- 11.1. Introduction -- 11.2. Nonlinear gravity-capillary standing waves.

ISBN

• 9780521811903 (hardback)
• 0521811902 (hardback)

LCCN

• 2010000473
• 40018273855

OCLC

• ocn501510339
• 501510339
• SCSB-5544537

Owning Institutions

Columbia University Libraries