scholarly journals Michael Selwyn Longuet-Higgins. 8 December 1925—26 February 2016

2018 ◽  
Vol 65 ◽  
pp. 249-265
Author(s):  
Shahrdad G. Sajjadi ◽  
Julian C. R. Hunt
Keyword(s):  
Water Waves ◽  
Ocean Waves ◽  
Breaking Waves ◽  
Finite Amplitude ◽  
Nonlinear Phenomena ◽  
Physical Oceanography ◽  
Applied Mathematician ◽  
Geometrical Character ◽  
Tidal Streams ◽  
Quasi Crystals

Michael Longuet-Higgins was a geometer and applied mathematician who made notable contributions to geophysics and physical oceanography, particularly to the theory of oceanic microseism and to the dynamics of finite amplitude, sharp-crested wind-generated surface waves. The latter led to his pioneering studies on breaking waves. On a much larger scale, he showed how ocean waves produce currents around islands in the ocean. He considered wider aspects of the physics of waves, including wave-driven transport of sand along beaches, and the electrical effects of tidal streams. He also contributed to subjects of a geometrical character such as the growth of quasi-crystals, the assembly of protein sheaths in viruses, to chains of circle themes and to a wide variety of other topics. He was an extraordinary applied mathematician, using the simplest forms of mathematics to demonstrate and discover highly complex nonlinear phenomena. In particular, he often thought of problems involving water waves using his unique knowledge of geometry and then tested his theories by experiment. Along with Brooke Benjamin FRS, Sir James Lighthill FRS, Walter Munk FRS, John Miles and Andrei Monin, Michael Longuet-Higgins stands out as one of the towering figures of theoretical fluid dynamics in the twentieth century. His contributions will have a continuing influence on our attempts to understand better the processes that influence the oceans.

A Study on Predictions of Fully Nonlinear Motion Aircushion Type Floating Structures Using 2D MPS Method

2008 ◽  
Author(s):  
Mitsuhiro Masuda ◽  
Tomoki Ikoma ◽  
Koichi Masuda ◽  
Hisaaki Maeda
Keyword(s):  
Water Waves ◽  
Theoretical Calculations ◽  
Numerical Technique ◽  
Ocean Waves ◽  
Nonlinear Phenomena ◽  
Linear Potential ◽  
Floating Structure ◽  
Fully Nonlinear ◽  
Floating Structures ◽  
Mps Method

Very large floating structures (VLFSs) have been proposed for new ocean space utilization and many researches have been carried out. VLFSs are elastically deformed due to ocean waves because the rigidity of the structure decreases relatively. The authors examine the aircushion type floating structure in order to reduce hydroelastic motion. An aircushion type floating structure to which air-chambers are installed can reduce the wave drifting force and hydroelastic motion at the same time. Most theoretical calculations of motion of aircushion type floating structures in water waves have been done based on a linear potential theory so far. As a result, the utility of the aircushion has been proved. However fully nonlinear phenomena such as deck wetness, slamming and air-leakage cannot be investigated by using existing calculations based on the linear theory. In this study, a computer program code of the two-dimensional MPS method that can consider fully nonlinear influence is developed and then the air layer inside an aircushion is expressed with particles of the MPS. Moreover, the numerical technique for introducing directly the mooring force into the motion equation of the particle is developed. Motion response of aircushion type floating structures in a billow is computed. As a result, the usefulness of this numerical calculation method is confirmed.

scholarly journals Breather Turbulence: Exact Spectral and Stochastic Solutions of the Nonlinear Schrödinger Equation

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 72 ◽  
Author(s):  
Osborne
Keyword(s):  
Fourier Series ◽  
Fourier Analysis ◽  
Water Waves ◽  
Ocean Waves ◽  
Airborne Lidar ◽  
Ocean Dynamics ◽  
Theoretical Interpretation ◽  
Maximum Height ◽  
Nonlinear Phenomena ◽  
Nonlinear Schrödinger

I address the problem of breather turbulence in ocean waves from the point of view of the exact spectral solutions of the nonlinear Schrödinger (NLS) equation using two tools of mathematical physics: (1) the inverse scattering transform (IST) for periodic/quasiperiodic boundary conditions (also referred to as finite gap theory (FGT) in the Russian literature) and (2) quasiperiodic Fourier series, both of which enhance the physical and mathematical understanding of complicated nonlinear phenomena in water waves. The basic approach I refer to is nonlinear Fourier analysis (NLFA). The formulation describes wave motion with spectral components consisting of sine waves, Stokes waves and breather packets that nonlinearly interact pair-wise with one another. This contrasts to the simpler picture of standard Fourier analysis in which one linearly superposes sine waves. Breather trains are coherent wave packets that “breath” up and down during their lifetime “cycle” as they propagate, a phenomenon related to Fermi-Pasta-Ulam (FPU) recurrence. The central wave of a breather, when the packet is at its maximum height of the FPU cycle, is often treated as a kind of rogue wave. Breather turbulence occurs when the number of breathers in a measured time series is large, typically several hundred per hour. Because of the prevalence of rogue waves in breather turbulence, I call this exceptional type of sea state a breather sea or rogue sea. Here I provide theoretical tools for a physical and dynamical understanding of the recent results of Osborne et al. (Ocean Dynamics, 2019, 69, pp. 187–219) in which dense breather turbulence was found in experimental surface wave data in Currituck Sound, North Carolina. Quasiperiodic Fourier series are important in the study of ocean waves because they provide a simpler theoretical interpretation and faster numerical implementation of the NLFA, with respect to the IST, particularly with regard to determination of the breather spectrum and their associated phases that are here treated in the so-called nonlinear random phase approximation. The actual material developed here focuses on results necessary for the analysis and interpretation of shipboard/offshore platform radar scans and for airborne lidar and synthetic aperture radar (SAR) measurements.

scholarly journals GPU-ACCELERATED SPH MODEL FOR WATER WAVES AND FREE SURFACE FLOWS

2011 ◽  
Vol 1 (32) ◽  
pp. 9 ◽  
Author(s):  
Robert Anthony Dalrymple ◽  
Alexis Herault ◽  
Giuseppe Bilotta ◽  
Rozita Jalali Farahani
Keyword(s):  
Water Waves ◽  
Graphics Processing Unit ◽  
Low Cost ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Nonlinear Phenomena ◽  
Processing Unit ◽  
Rip Currents ◽  
Nearshore Circulation ◽  
Sph Model

This paper discusses the meshless numerical method Smoothed Particle Hydrodynamics and its application to water waves and nearshore circulation. In particularly we focus on an implementation of the model on the graphics processing unit (GPU) of computers, which permits low-cost supercomputing capabilities for certain types of computational problems. The implementation here runs on Nvidia graphics cards, from off-the-shelf laptops to the top-of-line Tesla cards for workstations with their current 480 massively parallel streaming processors. Here we apply the model to breaking waves and nearshore circulation, demonstrating that SPH can model changes in wave properties due to shoaling, refraction, and diffraction and wave-current interaction; as well as nonlinear phenomena such as harmonic generation, and, by using wave-period averaged quantities, such aspects of nearshore circulation as wave set-up, longshore currents, rip currents, and nearshore circulation gyres.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

A Coupled-Mode Technique for the Run-Up of Non-Breaking Dispersive Waves on Plane Beaches

2006 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Breaking Waves ◽  
Numerical Results ◽  
Coupled Mode Theory ◽  
Mode Theory ◽  
Coupled Mode ◽  
Run Up

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).

A computer study of finite-amplitude water waves

1970 ◽  
Vol 6 (1) ◽  
pp. 68-94 ◽  
Author(s):  
Robert K.-C Chan ◽  
Robert L Street
Keyword(s):  
Water Waves ◽  
Finite Amplitude ◽  
Computer Study

scholarly journals ESTIMATION OF WATER PARTICLE VELOCITIES OF SHALLOW WATER WAVES BY A MODIFIED TRANSFER FUNCTION METHOD

1986 ◽  
Vol 1 (20) ◽  
pp. 33 ◽  
Author(s):  
Hirofumi Koyama ◽  
Koichiro Iwata
Keyword(s):  
Transfer Function ◽  
Shallow Water ◽  
Approximate Method ◽  
Stream Function ◽  
Water Waves ◽  
Function Method ◽  
Finite Amplitude ◽  
Water Particle ◽  
Irregular Wave ◽  
Particle Velocities

This paper Is intended to propose a simple, yet highly reliable approximate method which uses a modified transfer function in order to evaluate the water particle velocity of finite amplitude waves at shallow water depth in regular and irregular wave environments. Using Dean's stream function theory, the linear function is modified so as to include the nonlinear effect of finite amplitude wave. The approximate method proposed here employs the modified transfer function. Laboratory experiments have been carried out to examine the validity of the proposed method. The approximate method is shown to estimate well the experimental values, as accurately as Dean's stream function method, although its calculation procedure is much simpler than that of Dean's method.

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