Ray chaos and ray clustering in an ocean waveguide

Abstract

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a rangedependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a random-like sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincaré maps, plots of variations of the action per a ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a random-like multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.

Advanced Applications for Underwater Acoustic Modeling

“…Chaotic and stochastic nonlinear ray dynamics can occur in underwater-acoustic waveguides with longitudinal variations in the sound speed caused by internal waves [152]. This situation was investigated using a model of a "frozen" medium in which the temporal variations in the environment were neglected and only the spatial variations due to the comparatively small propagation time of sound in the ocean were considered.…”

Chaotic Diffusion at Sound Propagation in a Range-Dependent Underwater Sound Channel

“…В настоящей работе мы будем рассматривать модель волновода, в которой функции ∆c(z) и δc(z, x) задаются выражениями [10] …”

“…Поэтому методы теории квантового хаоса нашли широкое применение, например, в исследовании свойств микро-волновых оптических резонаторов (эта проблема широко освещена в книге [2]), а сравнительно недавно предметом пристального внимания стала проблема волнового хаоса при дальнем рас-пространении звука в океане [6][7][8][9][10][11][12].…”

Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

“…Then we can treat V (x, t) as a deterministic function and refer to (9) as the system of ordinary differential equations. As V (x, t) is an oscillating function of time, the domains of finite-time stability may involve components which transform to themselves without mixing in course of evolution from t = 0 to t = τ .…”

“…Such trajectories form bundles like branched flows in quantum point contacts [5][6][7][8], or coherent ray clusters in ocean acoustics [9]. One shouldn't confuse this kind of coherent phenomena with the domains of particle clusterization in random fields [10].…”