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<TABLE CELLSPACING=0 CELLPADDING=0><TR><TD>Preface</TD><TD WIDTH=40></TD><TD VALIGN=TOP>xi</TD><TD></TD></TR><TR><TD>Introduction: Basic Theory of Surface Waves</TD><TD WIDTH=40></TD><TD VALIGN=TOP>1</TD><TD VALIGN=TOP>(1)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Mathematical Formulation</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>1</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Linearized Unsteady Problem</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>5</TD><TD VALIGN=TOP>(5)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Linear Time-Harmonic Waves (the Water-Wave Problem)</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>10</TD><TD VALIGN=TOP>(5)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Linear Ship Waves on Calm Water (the Neumann-Kelvin Problem)</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>15</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD>1. Time-Harmonic Waves</TD><TD WIDTH=40></TD><TD VALIGN=TOP>19</TD><TD VALIGN=TOP>(244)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Green's Functions</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>21</TD><TD VALIGN=TOP>(29)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Three-Dimensional Problems of Point Sources</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>21</TD><TD VALIGN=TOP>(16)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Two-Dimensional and Ring Green's Functions</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>37</TD><TD VALIGN=TOP>(5)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Green's Representation of a Velocity Potential</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>42</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>48</TD><TD VALIGN=TOP>(2)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Submerged Obstacles</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>50</TD><TD VALIGN=TOP>(49)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Method of Integral Equations and Kochin's Theorem</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>50</TD><TD VALIGN=TOP>(17)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Conditions of Uniqueness for All Frequencies</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>67</TD><TD VALIGN=TOP>(20)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Unique Solvability Theorems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>87</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>96</TD><TD VALIGN=TOP>(3)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Semisubmerged Bodies, I</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>99</TD><TD VALIGN=TOP>(43)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Integral Equations for Surface-Piercing Bodies</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>99</TD><TD VALIGN=TOP>(17)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>John's Theorem on the Unique Solvability and Other Related Theorems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>116</TD><TD VALIGN=TOP>(24)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>140</TD><TD VALIGN=TOP>(2)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Semisubmerged Bodies, II</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>142</TD><TD VALIGN=TOP>(72)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Trapped Waves</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>143</TD><TD VALIGN=TOP>(21)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Uniqueness Theorems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>164</TD><TD VALIGN=TOP>(48)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>212</TD><TD VALIGN=TOP>(2)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Horizontally Periodic Trapped Waves</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>214</TD><TD VALIGN=TOP>(49)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Two Types of Trapped Modes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>215</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Edge Waves</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>219</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Trapped Modes Above Submerged Obstacles</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>229</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Waves in the Presence of Surface-Piercing Structures</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>237</TD><TD VALIGN=TOP>(17)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Vertical Cylinders in Channels</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>254</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD>2. Ship Waves on Calm Water</TD><TD WIDTH=40></TD><TD VALIGN=TOP>263</TD><TD VALIGN=TOP>(156)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Green's Functions</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>265</TD><TD VALIGN=TOP>(53)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Three-Dimensional Problem of a Point Source in Deep Water</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>265</TD><TD VALIGN=TOP>(18)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Far-Field Behavior of the Three-Dimensional Green's Function</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>283</TD><TD VALIGN=TOP>(22)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Two-Dimensional Problems of Line Sources</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>305</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>315</TD><TD VALIGN=TOP>(3)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>The Neumann-Kelvin Problem for a Submerged Body</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>318</TD><TD VALIGN=TOP>(43)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Cylinder in Deep Water</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>319</TD><TD VALIGN=TOP>(22)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Cylinder in Shallow Water</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>341</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Wave Resistance</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>349</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Three-Dimensional Body in Deep Water</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>353</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>359</TD><TD VALIGN=TOP>(2)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Two-Dimensional Problem for a Surface-Piercing Body</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>361</TD><TD VALIGN=TOP>(58)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>General Linear Supplementary Conditions at the Bow and Stern Points</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>362</TD><TD VALIGN=TOP>(31)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Total Resistance to the Forward Motion</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>393</TD><TD VALIGN=TOP>(3)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Other Supplementary Conditions</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>396</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Trapped Modes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>405</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Cylinder in the Supercritical Stream</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>411</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>415</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD>3. Unsteady Waves</TD><TD WIDTH=40></TD><TD VALIGN=TOP>419</TD><TD VALIGN=TOP>(66)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Submerged Obstacles: Existence and Properties of Velocity Potentials</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>421</TD><TD VALIGN=TOP>(14)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>The Initial-Boundary Value Problem and an Auxiliary Steady-State Problem</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>421</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Operator Equation for the Unsteady Problem</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>425</TD><TD VALIGN=TOP>(2)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Main Results</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>427</TD><TD VALIGN=TOP>(5)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>432</TD><TD VALIGN=TOP>(3)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Waves Caused by Rapidly Stabilizing and High-Frequency Disturbances</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>435</TD><TD VALIGN=TOP>(50)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Rapidly Stabilizing Surface Disturbances</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>435</TD><TD VALIGN=TOP>(18)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Rapidly Stabilizing Underwater Disturbances</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>453</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>High-Frequency Surface Pressure</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>460</TD><TD VALIGN=TOP>(14)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>High-Frequency Underwater Disturbances</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>474</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=40></TD><TD>Bibliographical Notes</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>484</TD><TD VALIGN=TOP>(1)</TD></TR><TR><TD>Bibliography</TD><TD WIDTH=40></TD><TD VALIGN=TOP>485</TD><TD VALIGN=TOP>(20)</TD></TR><TR><TD>Name Index</TD><TD WIDTH=40></TD><TD VALIGN=TOP>505</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD>Subject Index</TD><TD WIDTH=40></TD><TD VALIGN=TOP>509</TD><TD></TD></TR></TABLE>

1 online resource (xvii, 513 pages) : illustrations

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. Linear Water Waves will serve as an ideal reference for those working in fluid mechanics, applied mathematics, and engineering

Linear water waves : a mathematical approach