Self-organization of ultrasound in viscous fluids

Abstract

We report the theoretical and experimental demonstration of pattern formation in acoustics. The system is an acoustic resonator containing a viscous fluid. When the system is driven by an external periodic force, the ultrasonic field inside the cavity experiences different pattern-forming instabilities leading to the emergence of periodic structures. The system is also shown to possess bistable regimes, in which localized states of the ultrasonic field develop. The thermal nonlinearity in the viscous fluid, together with the far-from-equilibrium conditions, are is the responsible of the observed effects.Spontaneous pattern formation is a universal behavior observed in a diverse class of far from equilibrium systems in chemistry, biology, fluid mechanics, and nonlinear optics [1,2]. The latter has recently received great attention, owing to the potential applications in all-optical signal processing devices [2]. One noticeable exception in the list of disciplines where pattern formation has been demonstrated is acoustics. Although several nonlinear dynamic phenomena have been reported in acoustics, there not exists up to now a clear evidence of self-organization of sound, in spite of the strong similarities between the behaviour of light and sound waves. On one side, the observation of patterns requires systems with a large aspect ratio or Fresnel number, a situation which is not commonly considered in acoustics. On the other side, nonlinearity in typical fluids is quadratic and of elastic nature. This circumstance, together with the absence of dispersion of sound (but not optical) waves, results in higher harmonics generation with a complicated spectrum which makes difficult the observation and analysis of spatial instabilities. We present here what we believe to be the first experimental observation of spontaneous pattern formation of a confined ultrasonic field, propagating in a viscous medium and driven far from equilibrium.The physical model we consider is an acoustic resonator or interferometer, formed by two flat, parallel and highly reflecting walls which contain a viscous fluid. One of the walls vibrates at ultrasonic frequencies f with a given amplitude. For high enough driving amplitudes, the system behaviour is nonlinear, the main source of nonlinearity being of thermal (not elastic) origin. In a viscous medium the sound velocity c depends significantly on temperature, c = c 0 (1 -σT′), where c 0 is the velocity of sound at some equilibrium (ambient) temperature, T′ denotes the variation of the medium temperature from that equilibrium due to the intense acoustic wave, and σ is the parameter of thermal nonlinearity. The propagation of sound in such a medium has been shown to be described in terms of two coupled equations for pressure, p′, and temperature, T′, deviations [5]. A previous theoretical and experimental study in this system [6] evidenced the existence of nontrivial temporal dynamics (self-pulsations and chaos). All these studies were performed in the framework of the plane wave approximation...