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Gravity-Capillary Free-Surface Flows

ISBN-10: 0521811902

ISBN-13: 9780521811903

Edition: 2005

Authors: Jean-Marc Vanden-Broeck

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Gravity-capillary flows, in which the effects of pipe flow, gravity flow, and surface tension combine to produce a singular flow pattern, are utilised in many practical applications. The effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering. Concentrating on applications arising from fluid dynamics, Professor Vanden-Broeck's volume draws from his own results, collected from years of experience in the subject, and places this knowledge within the context of recent developments. 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. Surface flows are treated for cases where there may, or may not, exist intersections between the flow and rigid bodies; other examples include free bubbles rising in a fluid and solitary waves.
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Book details

List price: $149.00
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 7/15/2010
Binding: Hardcover
Pages: 330
Size: 6.75" wide x 9.75" long x 1.00" tall
Weight: 1.210
Language: English

Jean-Marc Vanden-Broeck is Professor in the Department of Mathematics at University College London.

Basic concepts
The equations of fluid mechanics
Free-surface flows
Two-dimensional flows
Linear waves
The water-wave equations
Linear solutions for water waves
Superposition of linear waves
Free-surface flows that intersect walls
Free streamline solutions
Forced separation
Free separation
The effects of surface tension
Forced separation
Free separation
The effects of gravity
Solutions with �<sub>1</sub> = 0 (funnels)
Solutions with �<sub>1</sub> = 0 (nozzles and bubbles)
Solutions with �<sub>1</sub> = �/2 (flow under a gate with gravity)
The combined effects of gravity and surface tension
Rising bubbles in a tube
Fingering in a Hele Shaw cell
Further examples involving rising bubbles
Exponential asymptotics
Linear free-surface flows generated by moving disturbances
The exact nonlinear equations
Linear theory
Solutions in water of finite depth
Solutions in water of infinite depth
Discussion of the solutions
Nonlinear waves - asymptotic solutions
Periodic waves
Solutions when condition (5.55) is satisfied
Solutions when condition (5.55) is not satisfied
The Korteweg-de Vries equation
Numerical computations of nonlinear water waves
Series truncation method
Boundary integral equation method
Numerical methods for solitary waves
Boundary integral equation methods
Numerical results for periodic waves
Pure capillary waves (g = 0, T &#8800; 0)
Pure gravity waves (g &#8800; 0, T = 0)
Gravity-capillary waves (g &#8800; 0, T &#8800; 0)
Numerical results for solitary waves
Pure gravity solitary waves
Gravity-capillary solitary waves
Nonlinear free-surface flows generated by moving disturbances
Pure gravity free-surface flows in water of finite depth
Supercritical flows
Subcritical flows
Gravity-capillary free-surface flows
Results in finite depth
Results in infinite depth (removal of the nonuniformity)
Gravity-capillary free-surface flows with Wilton ripples
Free-surface flows with waves and intersections with rigid walls
Free-surface flow past a flat plate
Numerical results
Analytical results
Free-surface flow past a surface-piercing object
Numerical results
Analytical results
Flow under a sluice gate
Numerical procedure
Discussion of the results
Pure capillary free-surface flows
Numerical results
Analytical results
Waves with constant vorticity
Solitary waves with constant vorticity
Mathematical formulation
Numerical procedure
Discussion of the results
Periodic waves with constant vorticity
Mathematical formulation
Numerical procedure
Numerical results
Three-dimensional free-surface flows
Green's function formulation for two-dimensional problems
Pressure distribution
Two-dimensional surface-piercing object
Extension to three-dimensional free-surface flows
Gravity flows generated by moving disturbances in water of infinite depth
Three-dimensional gravity-capillary free-surface flows in water of infinite depth
Further extensions
Time-dependent free-surface flows
Nonlinear gravity-capillary standing waves