Density Oscillators

Kano, Takeshi

doi:10.1016/b978-0-12-397014-5.00004-3

Pattern Formations and Oscillatory Phenomena 2013

DOI: 10.1016/b978-0-12-397014-5.00004-3

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Density Oscillators

Takeshi Kano¹

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2020

2024

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Cited by 3 publications

(1 citation statement)

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“…From Martin's first report in 1970, there have been experimental and theoretical papers on the density oscillators. Some are on the theoretical analysis on the mechanism of oscillation [8][9][10][11][12][13][14][15] and others are on the coupling between two or more oscillators [16][17][18][19][20][21]. For the bifurcation phenomenon, some theoretical studies have been performed based on the reduced ordinary differential equations, which have predicted various types of bifurcations according to various bifurcation parameters [10,11].…”

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confidence: 99%

Experimental study on the bifurcation of a density oscillator depending on density difference

Ito

Itasaka

Takeda

et al. 2020

EPL

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Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is triggered by the increase in the density difference of the two fluids. Our results show that the oscillation amplitude increases from zero and the period decreases above a critical density difference. The detailed data close to the bifurcation point provide a critical exponent consistent with the supercritical Hopf bifurcation.

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mentioning

confidence: 99%

Experimental study on the bifurcation of a density oscillator depending on density difference

Ito

Itasaka

Takeda

et al. 2020

EPL

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Transport-driven chemical oscillations: a review

Budroni,

Rossi

2024

Phys. Chem. Chem. Phys.

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Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow

Burmasheva

Prosviryakov

2022

Dynamics

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The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.

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Density Oscillators

Cited by 3 publications

References 55 publications

Experimental study on the bifurcation of a density oscillator depending on density difference

Experimental study on the bifurcation of a density oscillator depending on density difference

Transport-driven chemical oscillations: a review

Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow

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