## Selected Publications

**Abstract:**The skewness of the first time derivative of a pressure waveform, or derivative skewness, has been used previously to describe the presence of shock-like content in jet and rocket noise. Despite its use, a quantitative understanding of derivative skewness values has been lacking. In this paper, the derivative skewness for nonlinearly propagating waves is investigated using analytical, numerical, and experimental methods. Analytical expressions for the derivative skewness of an initially sinusoidal plane wave are developed and, along with numerical data, are used to describe its behavior in the preshock, sawtooth, and old-age regions. Analyses of common measurement issues show that the derivative skewness is relatively sensitive to the effects of a smaller sampling rate, but less sensitive to the presence of additive noise. In addition, the derivative skewness of nonlinearly propagating noise is found to reach greater values over a shorter length scale relative to sinusoidal signals. A minimum sampling rate is recommended for sinusoidal signals to accurately estimate derivative skewness values up to five, which serves as an approximate threshold indicating significant shock formation.

**Abstract:**In this study, two different acoustic measurements (acoustic intensity vector measurement and visualization movie analysis) are carried out to measure the near-field acoustic phenomena of a correctly expanded supersonic free jet. Both of these measurements consistently reveal the features of the acoustic wave of near field, which are not observed by the conventional sound pressure level measurement. Each measurement has an advantage: the acoustic intensity vector measurement shows not only the wave propagation direction but also the intensity level of the acoustic wave, whereas the visualization movie can capture the acoustic phenomenon in a close region to the flow or around a boundary of regions with different propagation features. Therefore, it is concluded that the combination of these measurements is effective to discuss the near-field characteristics of the acoustic wave.

**Abstract:**A new method for the calculation of vector acoustic intensity from pressure microphone measurements has been applied to the aeroacoustic source characterization of an unheated, Mach 1.8 laboratory-scale jet. Because of the ability to unwrap the phase of the transfer functions between microphone pairs in the measurement of a broadband source, physically meaningful near-field intensity vectors are calculated up to the maximum analysis frequency of 32 kHz. This result improves upon the bandwidth of the traditional crossspectral intensity calculation method by nearly an order of magnitude. The new intensity method is used to obtain a detailed description of the sound energy flow near the jet. The resulting intensity vectors have been used in a ray-tracing technique to identify the dominant source region over a broad range of frequencies. Additional aeroacoustics analyses provide insight into the frequency-dependent characteristics of jet noise radiation, including the nature of the hydrodynamic field and the sharp transition between the Mach wave and sideline radiation.

**Abstract:**Cross beamforming methods improve upon traditional beamforming in that they relax the assumption of multiple-source incoherence. This paper compares the abilities of three cross beamforming methods to reproduce source and field characteristics for an extended, partially correlated source that mimics supersonic jet noise radiation. Standard cross beamforming and two related methods that involve regularization—the hybrid method and improved generalized inverse beamforming—are applied to a numerically generated dataset along a near-field line. Estimated levels and coherence lengths are compared with benchmarks at the source as well as near and far-field locations. All three methods are successful in reproducing the field and source properties in high-amplitude regions. Although regularization generally helps to improve both source and field reconstructions, results are sensitive to regularization parameters, particularly for the generalized inverse method. The successful application of the three methods demonstrate the utility of crossbeamforming in formulating equivalent source models for accurate field prediction of complex sources, including jet noise.

**Abstract:**Crackle, the impulsive quality sometimes present in supersonic jet noise, has traditionally been defined in terms of the pressure waveform skewness. However, recent work has shown that the pressure waveform time derivative is a better quantifier of the acoustic shocks believed to be responsible for crackle perception. This paper discusses two definitions of crackle: waveform asymmetry versus shock content and crackle as a source or propagation-related phenomenon. Data from two static military jet aircraft tests are used to demonstrate that the skewed waveforms radiated from the jet undergo significant nonlinear steepening and shock formation, as evidenced by the skewness of the time derivative of the pressure waveforms. To the extent that crackle is caused by the presence of shock-like features in the waveform, crackle's perceived quality is likely to be heavily influenced by propagation through the geometric near field and into the far field.

**Abstract:**

An exact formulation for the evolution of the probability density function of the time derivative of a waveform (slope density) propagating according to the one-dimensional inviscid Burgers equation is given. The formulation relies on the implicit Earnshaw solution and therefore is only valid prior to shock formation. As explicit examples, the slope density evolution of an initially sinusoidal plane wave, initially Gaussian-distributed planar noise, and an initially triangular wave are presented. The triangular wave is used to examine weak-shock limits without violating the theoretical assumptions. It is also shown that the moments of the slope density function as a function of distance may be written as an expansion in terms of the moments of the source slope density function. From this expansion, approximate expressions are presented for the above cases as well as a specific non-Gaussian noise case intended to mimic features of jet noise. Finally, analytical predictions of the propagation of initially Gaussian-distributed noise are compared favorably with plane-wave tube measurements.