Acoustic microstreaming produced by two interacting gas bubbles undergoing axisymmetric shape oscillations

2021 ◽  
Vol 931 ◽  
Author(s):  
Alexander A. Doinikov ◽  
Gabriel Regnault ◽  
Cyril Mauger ◽  
Philippe Blanc-Benon ◽  
Claude Inserra
Keyword(s):  
Velocity Field ◽  
Penetration Depth ◽  
Analytical Solutions ◽  
Input Data ◽  
Gas Bubbles ◽  
Linear Velocity ◽  
Analytical Theory ◽  
Oscillation Modes ◽  
Linear Velocity Field ◽  
Axisymmetric Shape

An analytical theory is developed that describes acoustic microstreaming produced by two interacting bubbles. The bubbles are assumed to undergo axisymmetric oscillation modes, which can include radial oscillations, translation and shape modes. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the modal amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radii to the viscous penetration depth and the distance between the bubbles. The interaction between the bubbles is considered both when the linear velocity field is calculated and when the second-order velocity field of acoustic microstreaming is calculated. Capabilities of the analytical theory are illustrated by computational examples.

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Light subsystem with a linear velocity field inside a gravitating sphere

Astrophysics ◽  
1995 ◽  
Vol 38 (1) ◽  
pp. 27-38
Author(s):  
M. G. Abramian ◽  
Kh. G. Kokobelian
Keyword(s):  
Velocity Field ◽  
Linear Velocity ◽  
Linear Velocity Field

scholarly journals New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 123
Author(s):  
Renata Nikonorova ◽  
Dilara Siraeva ◽  
Yulia Yulmukhametova
Keyword(s):  
Velocity Field ◽  
Exact Solutions ◽  
Gas Dynamics ◽  
Three Dimensional ◽  
State Equation ◽  
Linear Velocity ◽  
State Equations ◽  
Gas Dynamics Equations ◽  
Linear Velocity Field ◽  
Monatomic Gas

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

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