
 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken. We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator. This generalizes DMD to a larger class of datasets, including nonsequential time series. We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively. We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples. Such computations are not considered in the existing literature, but can be understood using our more general framework. In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory. It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science. We show that under certain conditions, DMD is equivalent to LIM.

On Dynamic Mode Decomposition: Theory and Applications

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

We consider the frequency domain form of proper orthogonal decomposition (POD), called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space–time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic Tools in Turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time, while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg–Landau equation and a turbulent jet.

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Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

Several years of earlier research for the Air Force, relatedto the impact that war head induced damage had on the aeroelastic integrity of lifting surfaces and in turn the resulting upset of the complete aircraft, prompted a current look at similar aeroelastic events that might be triggered by damage of the aircraft due to icing. This possible aeroelastic impact, on the aircraft, due to icing damage is not a very commonly explored area of re- search. Although seldom studied, icing can also significantly impact the aircraft's aeroelastic stability and hence the overall aircraft stability and control. In this latter context, classical flutter events of the lifting surfaces and controls can occurdue to ice-induced mass unbal- ance or control force reversal. Also, a loss of control e!ectiveness or limit cycle oscillations of the controls and lifting surfaces may appear, due to significant time dependent drag forces introduced by separated flow conditions imposed by the ice accumulation. Two commonly observed aircraft icing induced stability upset scenarioswere selected to research. The first scenario involves an elevator limit cycle oscillation and aresulting loss of elevator control e!ectiveness. The second upset is related to a violent wing rock or unstable Dutch Roll event. A plausible failure mechanism is proposed for both types of upsets.

Wind tunnel studies employing higher order statistics to detect icing induced upsets

Measurements of the pressure waveforms along a grid in the far-field of an unheated Mach 3 jet were conducted in order to study crackle. A detection algorithm is introduced which isolates the shock-type structures in the temporal waveform that are responsible for crackle. Ensemble averages of the structures reveal symmetric shocks at shallow angles, while they appear to be asymmetric near the Mach wave angle. Spectral quantification is achieved through time–frequency analyses and shows that crackle causes the expected high-frequency energy gain. The increase in energy due to crackle is proposed as a more reliable metric for the perception of crackle, as opposed to the Skewness of the pressure or pressure derivative.

Temporal and Spectral Quantification of the ‘Crackle’ Component in Supersonic Jet Noise

Two-component PIV measurements of a turbulent boundary layer corresponding to momentum thickness Reynolds numbers of 3400 and 6200 were conducted in a water tunnel to study the effects of boundary layer suction on the mean and turbulence statistics of the flow. Previous studies at UT-Austin in collaboration with ARL-UT have shown how modest amounts of suction through a porous two-dimensional slit can significantly reduce the fluctuating wall pressure immediately downstream of the suction slit. This study focuses on understanding to what effect boundary layer suction has on the turbulence structure and its footprint at the fluid structure interface. The findings show a pronounced effect on the flow in three distinct regions. The first is located upstream of the slit where turbulence levels are shown to decay upon reaching the suction slit and in following the mean streamlines. The second occurs immediately after the suction slit where turbulence levels abruptly increase due to collisions of the higher momentum regions of the flow with the wall at the downstream edge of the suction slit. The third region of turbulence activity occurs further downstream where the near wall collisions eventually relax and the boundary layer undergoes redevelopment. This appears to be the case for even small rates of suction.

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Flowfield and wall pressure characteristics downstream of a boundary layer suction device.

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A combustion model for studying the effects of ideal gas properties on jet noise

A number of well established higher-order statistical metrics are used to evaluate the significance of acoustic waveform nonlinearities in the sound field of a coaxial, co-rotating rotor in hover. These comprise the magnitude-squared coherence, skewness and kurtosis of the pressure waveform and its time derivative, number of zero crossings per rotation, a wave steepening factor, and the quadrature spectral density and its integral. A unique feature of the coaxial, co-rotating rotor, as well as distributed rotor propulsion systems for that matter, is the constructive and destructive interference of sound waves produced by neighboring blades, which are incubators for signal distortion effects; these effects are not captured using traditional metrics like overall sound pressure level and the sound pressure spectrum level. Waveform distortions are evaluated here using higher-order metrics for changes to the index angle and separation distance between the upper and lower rotors, as well as changes to rotor speed for different observer positions. Significant sensitivities in the kurtosis of the pressure waveform and its time derivative, the number of zero crossings, and the integral of the quadrature spectral density are shown for changes in rotor index angle, observer position and rotor speed; stacking distance appears less important at effecting changes to these metrics. The trade space between these metrics and rotor figure of merit demonstrates how relatively small changes in rotor performance can effect large changes in acoustic waveform nonlinearities. A common obstacle to the development of a ‘quiet’ rotor is the establishment of a firm connection between the rotor’s aerodynamic performance and the level of annoyance or detection that is observed in the acoustic far-field. An improved understanding of these higher-order effects could prove useful in narrowing this gap. 

Charles E. Tinney

Papers

Wind tunnel studies employing higher order statistics to detect icing induced upsets

Temporal and Spectral Quantification of the ‘Crackle’ Component in Supersonic Jet Noise

Flowfield and wall pressure characteristics downstream of a boundary layer suction device.

A combustion model for studying the effects of ideal gas properties on jet noise

Higher-order Statistical Metrics for Characterizing Rotor Acoustics.