A generalized acoustic analogy

The purpose of this article is to show that the Navier–Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear-stress and energy-flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the ‘base flow’ about which the linearization is carried out.

[1]  Sébastien Candel,et al.  Computation of jet mixing noise due to coherent structures: the plane jet case , 1997, Journal of Fluid Mechanics.

[2]  Charles G. Speziale,et al.  ANALYTICAL METHODS FOR THE DEVELOPMENT OF REYNOLDS-STRESS CLOSURES IN TURBULENCE , 1990 .

[3]  Reda R. Mankbadi,et al.  Sound generated aerodynamically revisited: large-scale structures in a turbulent jet as a source of sound , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[4]  G. M. Lilley,et al.  THE RADIATED NOISE FROM ISOTROPIC TURBULENCE WITH APPLICATIONS TO THE THEORY OF JET NOISE , 1996 .

[5]  N. Marcuvitz,et al.  Electron-stream interaction with plasmas , 1965 .

[6]  M. E. Goldstein,et al.  Sound production in a moving stream , 1978, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  Emerson,et al.  STABILITY OF PARALLEL FLOWS , 2019 .

[8]  D. Pridmore‐Brown,et al.  Sound Propagation in a Fluid Flowing through an Attenuating Duct , 1958 .

[9]  A. Hussain Coherent structures—reality and myth , 1983 .

[10]  J. Seiner,et al.  On the Two Components of Turbulent Mixing Noise from Supersonic Jets , 1996 .

[11]  E J Stringas,et al.  High Velocity Jet Noise Source Location and Reduction. Task 4. Development/Evaluation of Techniques for 'Inflight' Investigation. , 1977 .

[12]  Sanjiva K. Lele,et al.  Compressibility Effects on Turbulence , 1994 .

[13]  Eliezer Kit,et al.  Large-scale structures in a forced turbulent mixing layer , 1985, Journal of Fluid Mechanics.

[14]  Nicolas Reau,et al.  On harmonic perturbations in a turbulent mixing layer , 2002 .

[15]  S. Crow,et al.  Aerodynamic Sound Emission as a Singular Perturbation Problem , 1970 .

[16]  S. Crow,et al.  Orderly structure in jet turbulence , 1971, Journal of Fluid Mechanics.

[17]  M. Lighthill On sound generated aerodynamically II. Turbulence as a source of sound , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  Jonathan B. Freund,et al.  Ray Traces through Unsteady Jet Turbulence , 2002 .

[19]  M. C. O L O N I U S,et al.  Sound generation in a mixing layer , 2022 .

[20]  C. Bogey,et al.  Computation of Flow Noise Using Source Terms in Linearized Euler's Equations , 2000 .

[21]  M. Lighthill On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[22]  P. C. Jain A theory of homogeneous isotropic turbulence , 1959 .

[23]  D. G. Crighton,et al.  Computational Aeroacoustics for Low Mach Number Flows , 1993 .

[24]  M. E. Goldstein,et al.  A Unified Approach to Some Recent Developments in Jet Noise Theory , 2002 .

[25]  O. M. Phillips,et al.  On the generation of sound by supersonic turbulent shear layers , 1960, Journal of Fluid Mechanics.

[26]  Nicolas Reau,et al.  On harmonic perturbations in turbulent wakes , 2000 .

[27]  梶島 岳夫 乱流の数値シミュレーション = Numerical simulation of turbulent flows , 2003 .

[28]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[29]  Luc Mongeau,et al.  Effects of Spatial Filtering on Sound Radiation from a Subsonic Axisymmetric Jet , 2000 .

[30]  A. Hussain,et al.  The mechanics of an organized wave in turbulent shear flow , 1970, Journal of Fluid Mechanics.

[31]  C. Tam,et al.  Jet Mixing Noise from Fine-Scale Turbulence , 1998 .

[32]  J. Freund Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9 , 2001, Journal of Fluid Mechanics.

[33]  Alexander J. Smits,et al.  Turbulent Shear Layers in Supersonic Flow , 1996 .

[34]  S. Lele,et al.  Spatial Scale Decomposition of Shear Layer Turbulence and the Sound Sources Associated with the Missing Scales in a Large-Eddy Simulation , 2002 .

[35]  Christopher K. W. Tam,et al.  Jet Noise: Since 1952 , 1998 .

[36]  T. Balsa,et al.  High Velocity Jet Noise Source Location and Reduction. Task 2. Theoretical Developments and Basic Experiments. , 1978 .

[37]  J. Liu Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows , 1988 .

[38]  Sébastien Candel,et al.  Stochastic approach to noise modeling for free turbulent flows , 1994 .