Notes on the two main routes of period doubling and 1/2 order subharmonic oscillations in a bubble oscillator

A. J. Sojahrood; R. E. Earl; M. C. Kolios; R. Karshafian

Home/Archive/arXiv

arXiv · 1909.02694

Notes on the two main routes of period doubling and 1/2 order subharmonic oscillations in a bubble oscillator

A. J. Sojahrood·R. E. Earl·M. C. Kolios·R. Karshafian

View original source ↗Read source document ↗Export metadata ↓

Abstract

Period doubling route to chaos is one of the well-known characteristics of nonlinear oscillators. A bubble is a highly nonlinear oscillator that exists in various phenomena and applications ranging from material science and underwater acoustics to medical ultrasound. The occurrence of period doubling (PD) in the oscillations of the bubbles is concomitant with the generation of 1/2 order subharmonics (SHs). SH oscillations are used to monitor the bubble activity and are employed as a measure of stable cavitation. As bubbles are intravascular contrast agents, SH oscillations are used in diagnostic ultrasound to increase the contrast of the blood vessels to the tissue. Despite the importance of PD in a bubble oscillator, the dynamical behavior of the bubble during stable SH and ultra-harmonic (UH) oscillations have not thoroughly studied yet. In this work, through applying a comprehensive bifurcation method, we study the nonlinear radial oscillations of the bubble oscillator as a function of ultrasound driving pressure. The frequency of the driving force is chosen as the linear resonance frequency (fr) and linear SH resonance frequency (fsh=2fr) of the bubble. Results show that, when the bubble is sonicated with 2fr, PD doubling occurrence is more likely to result in non-destructive oscillations. The evolution of the bubble stable P2 dynamics forms the shape of a bow-tie for bubbles with an initial diameter of 740nm and above. When f=2fr, the phase portrait of the P2 attractor is distinctly different from a P2 attractor when f=fr, and SH component of the backscattered pressure is maximum. When sonicated by 2fr, due to lower oscillation amplitude and gentler bubble collapse, the bubble can sustain stable P2 oscillations for a longer duration and over a broader range of applied acoustic pressure.

Explore related subjects

physics.flu-dyn

Keep this discovery

BibTeX RIS

A. J. Sojahrood, R. E. Earl, M. C. Kolios, R. Karshafian. 2019-09-06. Notes on the two main routes of period doubling and 1/2 order subharmonic oscillations in a bubble oscillator. https://arxiv.org/abs/1909.02694

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Correlative effects of induced magnetic field-buoyancy on reactive solute dispersion dynamics in couple-stress fluids

We investigate the dispersion of a reactive solute in a couple-stress fluid flowing between two parallel plates under the combined effects of pressure-driven flow, buoyancy, and an induced magnetic field. The model incorporates first-order heterogeneous reactions at both channel walls alongside a bulk reaction. Using Mei's multiscale homogenization technique accurate to third order, we develop a higher-order asymptotic formulation to determine the effective longitudinal dispersion coefficient and concentration field. Analytical predictions are complemented by Brownian dynamics simulations and finite-difference solutions, while the Aris method of moments quantifies transient mean displacement, spatial variance, and effective dispersivity. The hydrodynamic analysis reveals a singular branch in the velocity solution when the Hartmann number equals half the couple-stress parameter and identifies a characteristic quarter-power scaling between the Hartmann number and couple-stress parameter, separating couple-stress- and magnetically dominated regimes. The model recovers classical Taylor-dispersion behavior in the non-reactive Newtonian limit and agrees well with experimental measurements. Couple-stress rheology and magnetic damping suppress shear-induced dispersion, whereas buoyancy enhances dispersion through additional transverse velocity gradients. A distinct saturation regime of the dispersion coefficient emerges with an increasing couple-stress parameter, while unequal wall absorption induces persistent transverse asymmetry, and stronger absorption enhances solute removal near the source. Numerical and stochastic results validate the analytical framework while resolving higher-order concentration structures and particle-scale wall adsorption.

physics.flu-dyn↗

arXiv2026

DiffSWE2d: a differentiable Shallow Water Equations solver for end-to-end flood and tsunami modelling

Solving inverse and optimisation problems with traditional shallow water equations (SWE) solvers can be computationally expensive, particularly when gradients with respect to model inputs or parameters must be estimated through repeated forward simulations. In this paper, we introduce DiffSWE2d, an open-source differentiable shallow water equations solver for end-to-end flood and tsunami modelling implemented in PyTorch. By leveraging automatic differentiation, DiffSWE2d represents the time-marching physics as a differentiable computational graph, enabling gradients to be propagated directly through the numerical solver. We validate the solver against two established benchmark cases and demonstrate its application to tsunami waveform inversion, showing its ability to infer model inputs through gradient-based optimisation. DiffSWE2d provides a flexible framework for integrating physics-based hydrodynamic modelling with modern optimisation and machine learning methods. The source code and reproducible examples are publicly available at: https://github.com/ZhonghouXu/DiffSWE2d

physics.flu-dyn↗

arXiv2026

Low inertia limit of elasto-inertial turbulence

Pipe and channel flows of viscoelastic fluids display chaotic dynamics at unusually low speeds, a phenomenon referred to as elasto-inertial turbulence, EIT. First reported in experiments a century ago, recent theoretical studies and model computations predict a variety of scenarios for the phenomenon's origin, ranging from hoop stress modes to center modes and to Tollmien-Schlichting waves. Lacking experimental confirmation, the relevant scenario in actual flows of polymer solutions remains unknown. We here determine the transition threshold of EIT in pipe experiments, covering three decades in elasticity number. Across this entire parameter range, the transition features center mode structures at onset. Eventually the instability diverges at a lower inertia (upper elasticity) limit, which is a robust signature of this center mode scenario. Finally, we report the first experimental observation of a traveling wave in viscoelastic pipe flow, and the sequences of localized structures found, are in excellent agreement with a center mode traveling wave, the "arrowhead" solution, discovered in model simulations.

physics.flu-dyn↗