Author:
Lake Bruce M.,Yuen Henry C.
Abstract
The problem of the instability of a uniform, nonlinear, deep-water wave train to infinitesimal long-wave perturbations, first studied by Benjamin ' Feir (1967) and Benjamin (1967), is re-examined. It is found that the apparent discrepancy between the experimental and theoretical growth rates of the instability is associated with the experimental generation of waves which do not have the Stokes wave profiles assumed in the theory. Experimental and theoretical results relating the initial wave steepness and the most unstable long-wave perturbation are used to obtain a correction factor, which is found to account for the mismatch in wave forms and which resolves the discrepancy in growth rates. The results illustrate that, when theory is compared with experiments in which the values of certain higher-order (nonlinear) quantities must be deduced from measurements of first-order quantities, great care must be taken to ascertain that the experimental conditions and the theoretical assumptions are indeed compatible to the required order.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference8 articles.
1. Chu, V. H. & Mei, C. C. 1971 The nonlinear evolution of Stokes waves in deep water.J. Fluid Mech. 47,337.
2. Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid.Sov. Phys. J. Appl. Mech. Tech. Phys. 4,86.
3. Lake, B. M. , Yuen, H. C. , Rungaldier, H. & Ferguson, W. E. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train.J. Fluid Mech. 83,49.
4. Chu, V. H. & Mei, C. C. 1970 On slowly-varying Stokes waves.J. Fluid Mech. 41,873.
5. Benjamin, T. B. 1967 Instability of periodic wavetrains in nonlinear dispersive systems.Proc. Roy. Soc. A 299,59.
Cited by
43 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献