Journal of Computational Acoustics

Lighthill's Acoustic Analogy has been the dominant theory of aeroacoustics, especially jet aeroacoustics for almost fifty years. As yet, except for the u⁸ scaling law, which was derived by dimensional analysis, jet noise prediction based on the Acoustic Analogy approach has not been particularly successful. This paper examines some of the weaknesses and ambiguities in the formulation of the Acoustic Analogy theories. It is concluded that if the analogy is carried out completely, in the sense that the full wave propagation terms are retained in the propagation part of the equations of the analogy, then the theory offers no sensible noise source terms. To demonstrate that the Acoustic Analogy can fail to identify the correct noise sources, four examples are considered. They include an initial value problem, a boundary problem, the problem of weak solution and the problem of sound generation by instability waves in jets and mixing layers. These examples show clearly how, in each case, the Acoustic Analogy theory identifies the wrong noise source. Indeed, the Acoustic Analogy could provide, if not careful, misleading interpretation of the physics of sound generation.

This paper is dedicated to Professor David G. Crighton, outstanding applied mathematician, world famous acoustician and a much respected friend.

The stabilities of an elastic plate clamped on an infinite, rigid baffle subject to any time dependent force excitation in the presence of mean flow are examined. The mechanisms that can cause plate flexural vibrations to be absolute unstable when the mean flow speed exceeds a critical value are revealed. Results show that the instabilities of an elastic plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. This added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of the plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibrium positions. When the mean flow speed exceeds the critical values, the plate may be unstable and jump from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic.

A coupled three-dimensional fluid-elastic wave propagation mathematical model has been developed to handle environmental interactions in the ocean between a fluid medium and an elastic bottom. The existing model combines three-dimensional fluid and elastic wave propagation models with the incorporation of a set of horizontal fluid-elastic interface conditions. This paper extends the above model to consider an irregular fluid-elastic interface. The theoretical development of the irregular fluid-elastic interface equations is presented. Comparison of the fluid-elastic irregular interface to the horizontal case is one of the major objectives of this paper. Another major objective of this paper is the construction of a complete set of three-dimensional fluid-elastic wave equations, including the irregular interface, in a form suitable for stable numerical solution.

The sound from a light aircraft in flight is generated primarily by the propeller, which produces a sequence of harmonics in the frequency band between about 80 Hz and 1 kHz. Such an airborne sound source has potential in underwater acoustics applications, including inversion procedures for determining the wave properties of marine sediments. A series of experiments has recently been performed off the coast of La Jolla, California, in which a light aircraft was flown over a sensor station located in a shallow (approximately 15 m deep) ocean channel. The sound from the aircraft was monitored with a microphone above the sea surface, a vertical array of eight hydrophones in the water column, and two sensors, a hydrophone and a bender intended for detecting shear waves, buried 75 cm deep in the very-fine-sand sediment. The propeller harmonics were detected on all the sensors, although the s-wave was masked by the p-wave on the buried bender. Significant Doppler shifts of the order of 17%, were observed on the microphone as the aircraft approached and departed from the sensor station. Doppler shifting was also evident in the hydrophone data from the water column and the sediment, but to a lesser extent than in the atmosphere. The magnitude of the Doppler shift depends on the local speed of sound in the medium in which the sensor is located. A technique is described in which the Doppler difference frequency between aircraft approach and departure is used to determine the speed of sound at low-frequencies (80 Hz to 1 kHz) in each of the three environments, the atmosphere, the ocean and the sediment. Several experimental results are presented, including the speed of sound in the very fine sand sediment at a nominal frequency of 600 Hz, which was found from the Doppler difference frequency of the seventh propeller harmonic to be 1617 m/s.