The Resource A modern introduction to the mathematical theory of water waves, R.S. Johnson
A modern introduction to the mathematical theory of water waves, R.S. Johnson
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The item A modern introduction to the mathematical theory of water waves, R.S. Johnson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 2 library branches.
Resource Information
The item A modern introduction to the mathematical theory of water waves, R.S. Johnson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 2 library branches.
 Summary
 Beginning with the introduction of the appropriate equations of fluid mechanics, Johnson considers classical problems in linear and nonlinear waterwave theory, goes on to look at soliton type equations and closes with an introduction to viscosity
 Language
 eng
 Extent
 xiv, 445 pages
 Contents

 Mathematical preliminaries
 The governing equations of fluid mechanics: The equation of mass conservation; The equation of motion: Euler's equation; Vorticity, streamlines and irrotational flow
 The boundary conditions for water waves: The kinematic condition; The dynamic condition; The bottom condition; An integrated mass conservation condition; An energy equation and its integral
 Nondimensionalisation and scaling: Nondimensionalisation; Scaling of the variables; Approximate equations
 Some classical problems in waterwave theory
 Linear problems
 Wave propagation for arbitrary depth and wavelength: Particle paths
 Group velocity and the propagation of energy; Concentric waves on deep water
 Wave propagation over variable depth: Linearised gravity waves of any wave number moving over a constant slope; Edge waves over a constant slope
 Ray theory for a slowly varying environment: Steady, oblique plane waves over variable depth; Ray theory in cylindrical geometry; Steady plane waves on a current
 The shipwave pattern: Kelvin's theory; Ray theory
 Nonlinear problems
 The Stokes wave
 Nonlinear long waves: The method of characteristics; The hodograph transformation
 Hydraulic jump and bore
 Nonlinear waves on a sloping beach
 The solitary wave: The sech2 solitary wave; Integral relations for the solitary wave
 Weakly nonlinear dispersive waves
 Introduction
 The Kortewegde Vries family of equations: Kortewegde Vries (KdV) equation; Twodimensional Kortewegde Vries (2D KdV) equation; Concentric Kortewegde Vries (cKdV) equation; Nearly concentric Kortewegde Vries (ncKdV) equation; Boussinesq equation; Transformations between these equations; Matching to the nearfield
 Completely integrable equations: some results from soliton theory: Solution of the Kortewegde Vries equation; Soliton theory for other equations; Hirota's bilinear method; Conservation laws
 Waves in a nonuniform environment: Waves over a shear flow; The Burns condition; Ring waves over a shear flow; The Kortewegde Vries equation for variable depth; Oblique interaction of waves
 Slow modulation of dispersive waves
 The evolution of wave packets: Nonlinear Schrodïnger (NLS) equation; DaveyStewartson (DS) equations; Matching between the NLS and KdV equations
 NLS and DS equations: some results from soliton theory: Solution of the Nonlinear Schrodïnger equation; Bilinear method for the NLS equation; Bilinear form of the DS equations for long waves; Conservation laws for the NLS and DS equations
 Applications of the NLS and DS equations: Stability of the Stokes wave; Modulation of waves over a shear flow; Modulation of waves over variable depth
 Epilogue
 The governing equations with viscosity
 Application to the propagation of gravity waves: Small amplitude harmonic waves; Attenuation of the solitary wave; Undular boremodel I; Undular boremodel II
 Isbn
 9780521598323
 Label
 A modern introduction to the mathematical theory of water waves
 Title
 A modern introduction to the mathematical theory of water waves
 Statement of responsibility
 R.S. Johnson
 Language
 eng
 Summary
 Beginning with the introduction of the appropriate equations of fluid mechanics, Johnson considers classical problems in linear and nonlinear waterwave theory, goes on to look at soliton type equations and closes with an introduction to viscosity
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1944
 http://library.link/vocab/creatorName
 Johnson, R. S.
 Dewey number
 532/.593/0151
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA927
 LC item number
 .J65 1997
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Cambridge texts in applied mathematics
 http://library.link/vocab/subjectName

 Wavemotion, Theory of
 Water waves
 Label
 A modern introduction to the mathematical theory of water waves, R.S. Johnson
 Bibliography note
 Includes bibliographical references (pages 429435) and indexes
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Mathematical preliminaries  The governing equations of fluid mechanics: The equation of mass conservation; The equation of motion: Euler's equation; Vorticity, streamlines and irrotational flow  The boundary conditions for water waves: The kinematic condition; The dynamic condition; The bottom condition; An integrated mass conservation condition; An energy equation and its integral  Nondimensionalisation and scaling: Nondimensionalisation; Scaling of the variables; Approximate equations  Some classical problems in waterwave theory  Linear problems  Wave propagation for arbitrary depth and wavelength: Particle paths  Group velocity and the propagation of energy; Concentric waves on deep water  Wave propagation over variable depth: Linearised gravity waves of any wave number moving over a constant slope; Edge waves over a constant slope  Ray theory for a slowly varying environment: Steady, oblique plane waves over variable depth; Ray theory in cylindrical geometry; Steady plane waves on a current  The shipwave pattern: Kelvin's theory; Ray theory  Nonlinear problems  The Stokes wave  Nonlinear long waves: The method of characteristics; The hodograph transformation  Hydraulic jump and bore  Nonlinear waves on a sloping beach  The solitary wave: The sech2 solitary wave; Integral relations for the solitary wave  Weakly nonlinear dispersive waves  Introduction  The Kortewegde Vries family of equations: Kortewegde Vries (KdV) equation; Twodimensional Kortewegde Vries (2D KdV) equation; Concentric Kortewegde Vries (cKdV) equation; Nearly concentric Kortewegde Vries (ncKdV) equation; Boussinesq equation; Transformations between these equations; Matching to the nearfield  Completely integrable equations: some results from soliton theory: Solution of the Kortewegde Vries equation; Soliton theory for other equations; Hirota's bilinear method; Conservation laws  Waves in a nonuniform environment: Waves over a shear flow; The Burns condition; Ring waves over a shear flow; The Kortewegde Vries equation for variable depth; Oblique interaction of waves  Slow modulation of dispersive waves  The evolution of wave packets: Nonlinear Schrodïnger (NLS) equation; DaveyStewartson (DS) equations; Matching between the NLS and KdV equations  NLS and DS equations: some results from soliton theory: Solution of the Nonlinear Schrodïnger equation; Bilinear method for the NLS equation; Bilinear form of the DS equations for long waves; Conservation laws for the NLS and DS equations  Applications of the NLS and DS equations: Stability of the Stokes wave; Modulation of waves over a shear flow; Modulation of waves over variable depth  Epilogue  The governing equations with viscosity  Application to the propagation of gravity waves: Small amplitude harmonic waves; Attenuation of the solitary wave; Undular boremodel I; Undular boremodel II
 Control code
 36423414
 Dimensions
 24 cm
 Extent
 xiv, 445 pages
 Isbn
 9780521598323
 Isbn Type
 (pbk.)
 Lccn
 97005742
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
 Label
 A modern introduction to the mathematical theory of water waves, R.S. Johnson
 Bibliography note
 Includes bibliographical references (pages 429435) and indexes
 Carrier category
 volume
 Carrier category code
 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Mathematical preliminaries  The governing equations of fluid mechanics: The equation of mass conservation; The equation of motion: Euler's equation; Vorticity, streamlines and irrotational flow  The boundary conditions for water waves: The kinematic condition; The dynamic condition; The bottom condition; An integrated mass conservation condition; An energy equation and its integral  Nondimensionalisation and scaling: Nondimensionalisation; Scaling of the variables; Approximate equations  Some classical problems in waterwave theory  Linear problems  Wave propagation for arbitrary depth and wavelength: Particle paths  Group velocity and the propagation of energy; Concentric waves on deep water  Wave propagation over variable depth: Linearised gravity waves of any wave number moving over a constant slope; Edge waves over a constant slope  Ray theory for a slowly varying environment: Steady, oblique plane waves over variable depth; Ray theory in cylindrical geometry; Steady plane waves on a current  The shipwave pattern: Kelvin's theory; Ray theory  Nonlinear problems  The Stokes wave  Nonlinear long waves: The method of characteristics; The hodograph transformation  Hydraulic jump and bore  Nonlinear waves on a sloping beach  The solitary wave: The sech2 solitary wave; Integral relations for the solitary wave  Weakly nonlinear dispersive waves  Introduction  The Kortewegde Vries family of equations: Kortewegde Vries (KdV) equation; Twodimensional Kortewegde Vries (2D KdV) equation; Concentric Kortewegde Vries (cKdV) equation; Nearly concentric Kortewegde Vries (ncKdV) equation; Boussinesq equation; Transformations between these equations; Matching to the nearfield  Completely integrable equations: some results from soliton theory: Solution of the Kortewegde Vries equation; Soliton theory for other equations; Hirota's bilinear method; Conservation laws  Waves in a nonuniform environment: Waves over a shear flow; The Burns condition; Ring waves over a shear flow; The Kortewegde Vries equation for variable depth; Oblique interaction of waves  Slow modulation of dispersive waves  The evolution of wave packets: Nonlinear Schrodïnger (NLS) equation; DaveyStewartson (DS) equations; Matching between the NLS and KdV equations  NLS and DS equations: some results from soliton theory: Solution of the Nonlinear Schrodïnger equation; Bilinear method for the NLS equation; Bilinear form of the DS equations for long waves; Conservation laws for the NLS and DS equations  Applications of the NLS and DS equations: Stability of the Stokes wave; Modulation of waves over a shear flow; Modulation of waves over variable depth  Epilogue  The governing equations with viscosity  Application to the propagation of gravity waves: Small amplitude harmonic waves; Attenuation of the solitary wave; Undular boremodel I; Undular boremodel II
 Control code
 36423414
 Dimensions
 24 cm
 Extent
 xiv, 445 pages
 Isbn
 9780521598323
 Isbn Type
 (pbk.)
 Lccn
 97005742
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code
 n
 Other physical details
 illustrations
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