Acoustic-drift equation

Vladimir A. Vladimirov

Acoustic-drift equation

Mathematics

Research output: Working paper › Preprint

Abstract

The aim of this paper is to derive a new equation (the \emph{acoustic-drift equation} (ADE)) describing the generation of a flow by an acoustic wave. We consider acoustic waves of perfect barotropic gas as the zero-order solution and derive the equation for the averaged flow of the first order. The used small parameter of our asymptotic study is dimensionless inverse frequency, and the leading term for a velocity field is chosen to be a purely oscillating acoustic field. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equation is similar to the original vorticity equation, where the Reynolds stresses has been transformed to an additional advection with the drift velocity. Hence ADE can be seen as a compressible version of the Craik-Leibovich equation. In particular, ADE shows that if the averaged vorticity is absent in the initial data, then it will always be equal to zero. This property confirms that the acoustic streaming is of viscous nature. At the same time ADE can be useful for the description of secondary motions which take place for `strong' acoustic streaming flow.

Original language	English
Number of pages	12
Publication status	In preparation - 6 Jun 2012

Access to Document

http://arxiv.org/abs/1206.1297

Cite this

@techreport{103e8964b2904527bbb0b2afbc0c10e1,

title = "Acoustic-drift equation",

abstract = "The aim of this paper is to derive a new equation (the \emph{acoustic-drift equation} (ADE)) describing the generation of a flow by an acoustic wave. We consider acoustic waves of perfect barotropic gas as the zero-order solution and derive the equation for the averaged flow of the first order. The used small parameter of our asymptotic study is dimensionless inverse frequency, and the leading term for a velocity field is chosen to be a purely oscillating acoustic field. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equation is similar to the original vorticity equation, where the Reynolds stresses has been transformed to an additional advection with the drift velocity. Hence ADE can be seen as a compressible version of the Craik-Leibovich equation. In particular, ADE shows that if the averaged vorticity is absent in the initial data, then it will always be equal to zero. This property confirms that the acoustic streaming is of viscous nature. At the same time ADE can be useful for the description of secondary motions which take place for `strong' acoustic streaming flow.",

author = "{A. Vladimirov}, Vladimir",

year = "2012",

month = jun,

day = "6",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Acoustic-drift equation

AU - A. Vladimirov, Vladimir

PY - 2012/6/6

Y1 - 2012/6/6

N2 - The aim of this paper is to derive a new equation (the \emph{acoustic-drift equation} (ADE)) describing the generation of a flow by an acoustic wave. We consider acoustic waves of perfect barotropic gas as the zero-order solution and derive the equation for the averaged flow of the first order. The used small parameter of our asymptotic study is dimensionless inverse frequency, and the leading term for a velocity field is chosen to be a purely oscillating acoustic field. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equation is similar to the original vorticity equation, where the Reynolds stresses has been transformed to an additional advection with the drift velocity. Hence ADE can be seen as a compressible version of the Craik-Leibovich equation. In particular, ADE shows that if the averaged vorticity is absent in the initial data, then it will always be equal to zero. This property confirms that the acoustic streaming is of viscous nature. At the same time ADE can be useful for the description of secondary motions which take place for `strong' acoustic streaming flow.

AB - The aim of this paper is to derive a new equation (the \emph{acoustic-drift equation} (ADE)) describing the generation of a flow by an acoustic wave. We consider acoustic waves of perfect barotropic gas as the zero-order solution and derive the equation for the averaged flow of the first order. The used small parameter of our asymptotic study is dimensionless inverse frequency, and the leading term for a velocity field is chosen to be a purely oscillating acoustic field. The employed mathematical approach combines the two-timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equation is similar to the original vorticity equation, where the Reynolds stresses has been transformed to an additional advection with the drift velocity. Hence ADE can be seen as a compressible version of the Craik-Leibovich equation. In particular, ADE shows that if the averaged vorticity is absent in the initial data, then it will always be equal to zero. This property confirms that the acoustic streaming is of viscous nature. At the same time ADE can be useful for the description of secondary motions which take place for `strong' acoustic streaming flow.

M3 - Preprint

BT - Acoustic-drift equation

ER -