Lauren E. Falco

Application of a New Technique for Deriving Prominence Mass from SOHO EIT Fe XII (19.5 nm) Absorption Features

In a previous study we developed a new technique for deriving prominence mass by observing how much coronal radiation in the Fe XII (19.5 nm) spectral line is absorbed by prominence material. In the present work we apply this new method, which allows us to consider the effects of both foreground and background radiation in our calculations, to a sample of different types of prominences (eruptive, quiescent, and surging) observed during the period 1999 July through 2004 July. The masses of prominences involved in CMEs are not generally measured, but the accurate determination of such masses may help in assessing the dynamical importance of prominences in CME events. In the present study, we find the average mass of our sample of quiescent prominences to be 4.18 × 1014 g, while the average mass of the eruptive prominences is 9.09 × 1014 g, and that of surges is 1.53 × 1014 g.

Bicoherence analysis of model-scale jet noise

Bicoherence analysis has been used to characterize nonlinear effects in the propagation of noise from a model-scale, Mach-2.0, unheated jet. Nonlinear propagation effects are predominantly limited to regions near the peak directivity angle for this jet source and propagation range. The analysis also examines the practice of identifying nonlinear propagation by comparing spectra measured at two different distances and assuming far-field, linear propagation between them. This spectral comparison method can lead to erroneous conclusions regarding the role of nonlinearity when the observations are made in the geometric near field of an extended, directional radiator, such as a jet.

Identification of Nonlinear and Near-field Effects in Jet Noise Using Nonlinearity Indicators

In the collection and analysis of high-amplitude jet noise data for nonlinear acoustic propagation, both model-scale and full-scale measurements have limitations. Model-scale measurements performed in anechoic facilities are usually limited by transducer and data acquisition system bandwidths and maximum propagation distance. The accuracy of fullscale measurements performed outdoors is reduced by ground reflections and atmospheric effects. This paper describes the use of two nonlinearity indicators as complementary to ordinary spectral analysis of jet noise propagation data. The first indicator is based on an ensemble-averaged version of the generalized Burgers equation. The second indicator is the bicoherence, which is a normalized version of the bispectral density. These indicators are applied to Mach-0.85 and Mach-2.0 unheated jet noise data collected at the National Center for Physical Acoustics. Specifically, the indicators are used to separate geometric near-field effects from nonlinear propagation effects for the Mach-2.0 data, which cannot be done conclusively using comparisons of power spectral densities alone.

Bispectral Analysis of High-Amplitude Jet Noise

*† ‡ § ¶ The overall sound pressure levels of noise radiated by military jet aircraft along certain angles are such that nonlinearity is likely to influence the propagation. Bispectral analysis of noise data from the F/A-18E Super Hornet has been carried out in order to provide further evidence that nonlinear effects are indeed present. The bicoherence, which is a normalized form of the bispectral density, has been previously used in a variety of applications to detect quadratic phase coupling (QPC) in a signal. In this case, the results of the bicoherence calculations indicate that QPC is indeed present at high-thrust conditions along the peak radiation angles, which means that nonlinearity does play a role. However, additional investigations are still needed to more fully understand the physical interpretation of the bispectral results for a random noise signal, which will also help better quantify the role of nonlinearity in jet noise propagation.

Investigation of a Single-Point Nonlinearity Indicator in the Propagation of High-Amplitude Jet Noise

There is evidence to suggest that nonlinearity is important in the propagation of highamplitude jet noise [Gee et al., AIAA J. 43(6), 1398-1401 (2005)]. Typically, the power spectral density (PSD) is used to assess the impact of jet noise on the surrounding environment, but such an assessment requires multiple measurement locations to observe the nonlinear evolution of the PSD. The difference in the PSDs measured at different locations depends on a combination of source level, nozzle diameter, and propagation distance. As a result, full scale measurements have to be extended over large distances, and model scale measurements require high measurement bandwidths. These constraints complicate the measurement and make it difficult to observe nonlinear effects using the PSD. Here a different technique for determining the importance of nonlinearity is investigated. The imaginary part of the cross-spectral density of the pressure and the square of the pressure, also called the quadspectral density (QSD), is related to the rate of nonlinear change of the PSD. Thus, the extent to which the PSD is evolving nonlinearly can be determined at a single measurement location. In the absence of absorption, energy is conserved, and the integration of the product of the QSD with frequency over all frequencies must be zero; when nonlinearity is present, the value of the QSD can be nonzero for many frequencies. Because nonlinearity tends to transfer energy from low frequencies to high frequencies and the QSD is positive at frequency components that are losing energy, using the integral of the QSD over its positive values as a nonlinearity indicator eliminates the need for high bandwidth measurements. Experimental measurements were taken in a plane wave tube with a working length of 9.55 m in which boundary layer losses dominate over atmospheric absorption. Experimental and numerical results show that the ratio of the integral of the QSD over the frequencies for which it is positive (Qpos) to the integral over the frequencies for which it is negative (Qneg) is close to one. Also, because the QSD is thirdorder in pressure, normalizing its integral by the cube of the rms pressure yields a quantity that is easily compared across experimental conditions. Results for both periodic and broadband signals are presented and the practicality of using the QSD as a single-point indicator of nonlinearity addressed.

Investigation of a Single‐Point Nonlinearity Indicator in One‐Dimensional Propagation

The influence of nonlinear effects in jet noise propagation is typically characterized by examining changes in the power spectral density (PSD) of the noise as a function of propagation distance. The rate of change of the PSD is an indicator of the importance of nonlinearity. Morfey and Howell [AIAA J. 19, 986–992 (1981)] introduced an analysis technique that has the potential to extract this information from a measurement at a single location. They develop an ensemble‐averaged Burgers equation that relates the rate of change of the PSD with distance to the quantity Qpp2, which is the imaginary part of the cross‐spectral density of the pressure and the square of the pressure. With the proper normalization, spreading and attenuation effects can be removed, and the normalized quantity represents only spectral changes which are due to nonlinearity. Despite its potential applicability to jet noise analysis, the physical significance and utility of Qpp2 have not been thoroughly studied. This work examines a normalization of Qpp2 and its dependence on distance for the propagation of plane waves in a shock tube. The use of such a controlled environment allows for better understanding of the significance of Qpp2.The influence of nonlinear effects in jet noise propagation is typically characterized by examining changes in the power spectral density (PSD) of the noise as a function of propagation distance. The rate of change of the PSD is an indicator of the importance of nonlinearity. Morfey and Howell [AIAA J. 19, 986–992 (1981)] introduced an analysis technique that has the potential to extract this information from a measurement at a single location. They develop an ensemble‐averaged Burgers equation that relates the rate of change of the PSD with distance to the quantity Qpp2, which is the imaginary part of the cross‐spectral density of the pressure and the square of the pressure. With the proper normalization, spreading and attenuation effects can be removed, and the normalized quantity represents only spectral changes which are due to nonlinearity. Despite its potential applicability to jet noise analysis, the physical significance and utility of Qpp2 have not been thoroughly studied. This work examines a no...

Nonlinearity analysis of model-scale jet noise

This paper describes the use of a spectrally-based “nonlinearity indicator” to complement ordinary spectral analysis of jet noise propagation data. The indicator, which involves the cross spectrum between the temporal acoustic pressure and the square of the acoustic pressure, stems directly from ensemble averaging the generalized Burgers equation. The indicator is applied to unheated model-scale jet noise from subsonic and supersonic nozzles. The results demonstrate how the indicator can be used to interpret the evolution of power spectra in the transition from the geometric near to far field. Geometric near-field and nonlinear effects can be distinguished from one another, thus lending additional physical insight into the propagation.

Measurements of the rate of change of the power spectral density due to nonlinearity in one‐dimensional propagation

The influence of nonlinear effects in the propagation of jet noise is typically characterized by examining the change in the power spectral density (PSD) of the noise as a function of propagation distance. The rate of change of the PSD is an indicator of the importance of nonlinearity. Morfey and Howell [AIAA J. 19, 986–992 (1981)] introduced an analysis technique that has the potential to extract this information from a measurement at a single location. They develop an ensemble‐averaged Burgers equation that relates the rate of change of the PSD with distance to the quantity Qp2p, which is the imaginary part of the cross‐spectral density of the pressure and the square of the pressure. Despite its potential applicability to jet noise analysis, the physical significance and utility of Qp2p have not been thoroughly studied. This work examines Qp2p for the one‐dimensional propagation of plane waves in a shock tube. The use of such a simple, controlled environment allows for a better understanding of the sign...

Single‐point nonlinearity indicators for the propagation of high‐amplitude jet noise

Prediction schemes based on linear acoustics are often insufficient to describe the character of the noise radiated from a jet engine. Nonlinear evolution of jet noise is usually identified using linear extrapolation and spectral comparisons. Because it requires measurements at multiple locations, this method is susceptible to errors in the presence of ground reflections or meteorological effects, when the location of the source is uncertain, and in the near‐field of the jet. Thus, an indicator of nonlinearity that can be derived from a measurement at a single point is desirable. This work introduces one such indicator based on a quantity found in a spectral Burgers equation derived by Morfey and Howell [AIAA J. 19, 986–992 (1981)]. The quantity, denoted Qp2p and commonly referred to as the QSD, is related to the nonlinear evolution of the signal. The indicator discussed here is a normalization of the QSD that assesses the relative importance of nonlinear, absorption, and spreading effects. For this reaso...

Analysis of high‐amplitude jet noise using nonlinearity indicators

Nonlinear effects in high‐amplitude jet noise are often characterized by examining spectral changes over some propagation range. However, in the case of typical laboratory‐based measurements with model‐scale nozzles, the study of nonlinearity via spectral changes is made difficult by both limited measurement bandwidth and short propagation distances. One analysis technique that potentially can overcome these difficulties is a single‐point measurement of nonlinearity that has been studied most recently by Falco et al. [J. Acoust. Soc. Am. 117, 2596 (2005)]. Another potential solution is bispectral analysis, which has been used in the past as an indicator of nonlinearity for a wide variety of applications. Both of these analysis methods have been applied to data from recent laboratory measurements at the National Center for Physical Acoustics. Observed trends for a variety of source conditions, measurement angles, and propagation distances are discussed. [Work supported in part by the Office of Naval Research.]