کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1899746 1534062 2010 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Pulse dynamics in low-Reynolds-number interfacial hydrodynamics: Experiments and theory
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Pulse dynamics in low-Reynolds-number interfacial hydrodynamics: Experiments and theory
چکیده انگلیسی

We analyze interaction of nonlinear pulses in active–dispersive–dissipative nonlinear media. A particular example of such media is a viscous thin film coating a vertical fibre. Experiments for this system reveal that the interface evolves into a train of droplike solitary pulses in which numerous inelastic coalescence events take place. In such events, larger pulses catch up with smaller ones and annihilate them. However, for certain flow conditions and after a certain distance from the inlet, no more coalescence is observed and the flow is described by quasi-equilibrium solitary pulses interacting continuously with each other through attractions and repulsions, and, eventually they form bound states of groups of pulses in which the pulses travel with the same velocities as a whole. This experimental study represents the first evidence of formation of bound states in low-Reynolds-number interfacial hydrodynamics. To gain theoretical insight into the interaction of the pulses and formation of bound states, we derive a weakly nonlinear model for the flow, the generalized Kuramoto–Sivashinsky (gKS) equation, that retains the fundamental mechanisms of the wave evolution, namely, dominant nonlinearity, instability, stability and dispersion. Much like in the experiments, the spatio-temporal evolution of the gKS equation is dominated by quasi-stationary solitary pulses which continuously interact with each other through coalescence events or attractions/repulsions. To understand the latter case, we utilize a weak-interaction theory for the solitary pulses of the gKS equation. The theory is based on representing the solution of the equation as a superposition of the pulses and an overlap function and leads to a coupled system of ordinary differential equations describing the evolution of the locations of the pulses, or, alternatively, the evolution of the separation distances. By analyzing the fixed points of this system, we obtain bound states of interacting pulses. For two pulses, we provide a criterion for the existence of a countable infinite or finite number of bound states, depending on the strength of the dispersive term in the equation. The interaction theory and resulting bound states are corroborated by computations of the full equation. We also find qualitative agreement between the theory and the experiments.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 239, Issues 20–22, 15 October 2010, Pages 2000–2010
نویسندگان
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