Introduction. Experimental nonlinear dynamics of fluids

Abstract

Nearly six decades ago, Stoker, in the introduction to his seminal book on nonlinear vibrations (Stoker 1950), pointed out 'It is perhaps worth while to consider for a moment the reasons why one should be interested particularly in the nonlinear problems in mechanics. Basically the reason is, of course, that all of the problems in mechanics are nonlinear from the outset, and the linearizations commonly practiced are an approximating device which is often a confession of defeat in the challenge presented by nonlinear problems as such'. This powerful statement is echoed in the celebrated book on nonlinear oscillators (Andronov et al. 1966), which provides a very comprehensive source of the theoretical foundations and applications in the area of nonlinear oscillations. The concepts of slow and fast oscillations, small and large terms in solutions, and periodicity have been clearly introduced in this book by solving various dynamical problems. In more recent works (e.g. Guckenheimer & Holmes 1983;Thompson & Stewart 1986), one can find a systematic approach to model and analyse nonlinear systems exhibiting chaos.Since the invention of digital computers, the interest in the area of nonlinear mechanics, and nonlinear dynamics in particular, has grown nearly in an exponential manner. Currently we have in excess of 40 journals that publish nonlinear dynamics results. However, there is a huge disproportion between numbers of theoretical and experimental papers. A very conservative estimate would account for approximately 5% of experimental articles. Experiments are vital to confirm new theories, make viable predictions and ultimately to establish firm foundations for developments in science and technology.The main aim of arranging and compiling this theme is to perhaps address in a small but powerful way the misbalance mentioned above. The theme comprising a total 12 papers has two issues 'Experimental nonlinear dynamics I. Solids' and 'Experimental nonlinear dynamics II. Fluids'.This second part of the theme is formed from five papers written by world experts in the areas of fluid-structure interactions and fluids. The first two articles by Benaroya & Gabbai (2008) and Modarres-Sadeghi et al. (2008) form a bridge between solids and fluids as they consider fluid-structure interactions. The following three contributions are focused on the nonlinear effects originating mainly from fluids.