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Distortion and harmonic generation in the nearfield of a finite amplitude sound beam are considered, assuming time-periodic but otherwise arbitrary on-source conditions. The basic equations of motion for a lossy fluid are simplified by utilizing the parabolic approximation, and the solution is derived by seeking a Fourier series expansion for the sound pressure. The harmonics are governed by an infinite set of coupled differential equations in the amplitudes, which are truncated and solved numerically. Amplitude and phase of the fundamental and the first few harmonics are calculated along the beam axis, and across the beam at various ranges from the source. Two cases for the source are considered and compared: one with a uniformly excited circular piston, and one with a Gaussian distribution. Various source levels are used, and the calculations are carried out into the shock region. The on-axis results for the fundamental amplitude are compared with results derived using the linearized solution modified with various taper functions. Apart from a nonlinear tapering of the amplitude along and near the axis, the results are found to be very close to the linearized solution for the fundamental, and for the second harmonic close to what is obtained from a quasilinear theory. The wave profile is calculated at various ranges. An energy equation for each harmonic is obtained, and shown to be equivalent within our approximation to the three-dimensional version of Westervelt’s energy equation. Recent works on one-dimensional propagation are reviewed and compared.

This paper deals with nonlinear streaming effects associated with oscillatory motion in a viscous fluid. A previous theory by Holtsmarket al.(1954) for the streaming near a circular cylinder in an incompressible fluid of infinite extent is reconsidered and used to obtain new numerical results, which are compared with earlier observations. The regime of validity of this theory is considered. The condition to be satisfied by the Reynolds number is found to be less stringent than was previously supposed.The more recent theory by Wang (1968) based on the outer–inner expansion technique is discussed and corrected with the Stokes drift.The case of an incompressible fluid enclosed between two coaxial cylinders, one of which is oscillating, is considered in detail. New theoretical and experimental results are given for various values of the parameters involved (Reynolds number, amplitude and cylinder radii).

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