## Wave AsymptoticsThe occasion of Professor Fritz Ursell's retirement was marked by a two-day meeting consisting of invited talks by some of the most distinguished researchers in the various topics of fluid mechanics and asymptotics studied by Professor Ursell throughout his long and distinguished career. The papers collected here outline the development of fluid dynamical topics from asymptotic methods in anisotropic wave systems, surface wave theory, biological models, and differential equations, through to slender body theory, water wave theory propellor-generated wakes. |

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### Contents

Uniform asymp | 24 |

Converging factors | 54 |

Matched asymptotic methods in surface | 69 |

Approximation of freesurface | 107 |

On farfield approximations to the wave pattern | 136 |

An analytical theory of propeller generated | 160 |

Analytical aspects of slender body theory | 184 |

bodies | 202 |

Some unsolved and unfinished problems in | 220 |

### Common terms and phrases

amplitude analysis analytic application approximation asymptotic expansion axis behaviour Bessel functions boundary condition calculation coalescing saddle points coefficients complex computational confluent hypergeometric function Connor constant contribution converging factors curve defined derived differential equations Dingle disc domain economized polynomials effective wake eigenvalues evaluation example exponential integral expression Figure finite free surface free-surface Green functions frequency Fritz Ursell given Green function group velocity hyperbolic umbilic infinite infinite-depth inner integral equation integral representation integrand Kelvin Leppington Liapunov function Lighthill limit linear theory Math mathematical method numerical obtained Olver oscillating parameters Phil plane polynomial problem Proc propeller region result rigorous saddle points Sequel shear flow ship waves shown singularity slender body theory solution spheroid submerged circular cylinder surface waves theorem three-dimensional tion transform trapped modes two-dimensional uniform asymptotic valid values variable vector velocity potential vertical water waves wave pattern wave resistance wavemaking wavenumber zero

### Popular passages

Page 227 - Ursell, F.: The effect of a fixed vertical barrier on surface waves in deep water.

Page 246 - INTEGRALS WITH A LARGE PARAMETER AND SEVERAL NEARLY COINCIDENT SADDLE POINTS THE CONTINUATION OF UNIFORMLY ASYMPTOTIC EXPANSIONS. PROC. CAMBRIDGE PHILOS. SOC. 76. 211-231 (1974) 282.41011 — 291.92082