Spatial Decay Rate Research Articles

Effects of Convection and Decay of Turbulence on the Wall Pressure Wavenumber-Frequency Spectrum

Cross-spectral and cross-correlation data from experiments and numerical simulations have shown the turbulent wall pressure convection velocity to vary with the streamwise sensor spatial separation. This variation is due to the spatial decay rates of turbulent structures in the inner and outer regions of the boundary layer. Its effect is shown to have a significant impact on the distribution of energy in the wavenumber-frequency spectrum Φ (k1, ω). The standard Corcos model is known to over predict the wavenumber-frequency spectrum at low wavenumbers. This is shown to result from its constant convection velocity assumption. The spectral levels at sub convective and lower wavenumbers are shown to be directly influenced by the spatial variation in convection velocity. Convection velocity measurements from past investigations that cover the range 285 ≤ Rθ ≤ 29,000 are compared, and an outer variable scaling is shown to effectively collapse the data.

Dynamics of a spin-exchange model

We study a model on the non-negative half line Z + 0, {0, 1, 2, …} in which particles created at the origin at rate 1 jump to the right at rate 1. If a particle jumps onto an already occupied site the two particles annihilate each other. In addition, whenever a particle jumps its closest neighbor to the right jumps along with it. We find that the spatial decay rate of the particle density in the stationary state is of order 1 √x at distance x from the origin. This model provides an approximation to the dynamics of an anchored Toom interface which can be represented as a spin-exchange model.

THE EFFECT OF PERIOD ASYMMETRY ON WAVE PROPAGATION IN PERIODIC BEAMS

The h-pversion of the finite element method is used to study flexural wave motion in a periodic beam with identical, but non-symmetric, periods. The convergence behaviour of the h-pmethod is benchmark validated against an exact analysis provided by the dynamic stiffness method in obtaining solutions for the wave propagation constant as a function of frequency. It is shown that period asymmetry can have a beneficial effect on the dynamic characteristics of the structure from a vibration control viewpoint and could feasibly be exploited as an additional design variable. It is also demonstrated that, in the presence of asymmetry, the pass-band bounding frequencies no longer correspond to the natural frequencies of an isolated bay. A study of the group velocity of wave motion as a function of frequency in an asymmetric system is also included. The ability to compute this information is important because it enables a direct measure of the energy flow, the modal density of the system, and the rate of spatial decay which is caused by an added damping treatment, to be estimated within a given pass-band.

Large Amplitude Flow Anomalies in Northern Hemisphere Midlatitudes

Abstract The composite of large amplitude flow anomalies identified from extremely large amplitudes of the planetary-scale waves is examined in terms of the temporal and spatial evolution of both the large-scale flow and the storm tracks. The characteristic spatial patterns, growth and decay rates, and persistence characteristics that the individual large amplitude anomaly cases share come out naturally in the analysis. The composite anomaly's growth and decay are very rapid, taking an average of only 4 days to develop local anomalies of 200–300 m. The spatial evolution of the flow suggests a rapidly growing standing wave over the North Pacific Ocean and North America. After a persistence of random duration (averaging 8.4 days), the composite anomaly's decay is accompanied by simultaneous retrogression of the pattern from western North America to eastern Asia and eastward progression of the pattern over Europe and western Asia. Substantial disruption of the Pacific storm track and enhancement of the Atlan...

Lagrangian velocity profiles in the wake of a high speed vessel

Abstract A video imaging technique is employed in a towing basin to obtain high resolution surface Lagrangian velocity observations in the centerline wake region of a high speed, twin screw surface vessel. Approximately 30,000 surface velocity realizations within the wake region extending from the stern to approximately six model ship lengths aft are used for comparison with both recent full-scale and numerical model results. Analysis of this data set reveals spatial decay rates in the mean and fluctuating velocity components which serve to identify relevant scales of motion and define candidate mechanisms for the persistence of these wakes in remotely sensed ocean surface data.

Individual And Interactive Mechanisms For Localization And Dissipation In A Mono-Coupled Nearly-Periodic Structure

The effect of structural damping on the dynamics of periodic and disordered nearly periodic systems is investigated. A chain of single-degree-of-freedom oscillators coupled by springs is used as a basic model of a mono-coupled periodic system. The dynamic response of the system to a harmonic excitation at the leftmost oscillator is considered. For a system with damping but no disorder (i.e., identical oscillators), an exact expression for the rate of exponential spatial amplitude decay is retrieved. It is found that the decay rate due to damping in a periodic system has a frequency dependence similar to that of the decay rate due to disorder in an undamped nearly periodic system. The magnitudes of the decay rates due to only damping or disorder are compared, and the concept of equivalent damping due to disorder is introduced. For systems with both disorder and damping, perturbation methods are used to find approximate expressions for the decay rate in the cases of strong and weak coupling between oscillators. It is shown that if the coupling is strong, the decay rates due to damping and disorder simply add up to produce the overall decay rate, and the effect of damping dominates. If the coupling is weak, however, the effects of damping and disorder on the overall decay are comparable in magnitude, and they interact in a more complicated manner.

The Accommodation of Traveling Waves of Fisher’s Type to the Dynamics of the Leading Tail

Traveling wave solutions for equations of Fisher’s type are given by a connection from a saddle point to a node, and their velocity for large times is known to be determined by the spatial decay rate of the initial conditions far ahead of the wave. To understand this phenomenon in simple terms, initial conditions are considered that correspond to a traveling wave, but with an exponential decay rate far ahead of the wave that varies slowly in the region referred to as the leading tail. The wave that results is supersonic in the sense that the speed of the core of the traveling wave is greater than the velocity of the characteristics, or group velocity, in the leading tail. Consequently, the speed of the core adjusts to accommodate the slowly varying decay rate in the leading tail. A generalization is also considered that includes Fisher's equation, for which traveling waves with a stable exponential tail corresponding to a node are supersonic.

Vibration Confinement Phenomena in Disordered, Mono-Coupled, Multi-Span Beams

The effects of small, periodicity-destroying irregularities on the dynamics of multi-span beams are examined. It is shown that minute deviations of the span lengths from an ideal value alter qualitatively the dynamic response by localizing vibrations and waves to small geometric regions. These confinement phenomena are studied over a wide frequency range for beams resting on simple supports and with variable interspan coupling. Approximations of the localization factor (the average rate of spatial exponential decay of the vibration amplitude) are derived by statistical perturbation methods and validated by Monte Carlo simulations. If the interspan coupling is strong, localization effects are weak and of no practical significance for most engineering structures. On the other hand, localization is severe for small interspan coupling. Confinement is also generally stronger near the edges of frequency passbands and increases nearly linearly with frequency from passband to passband. This means that strong localization occurs at high frequencies, even for large static coupling between spans.

Wall pressure fluctuations associated with complex flows.

The relationship between wall pressure fluctuations and turbulent structures in a boundary layer has been the subject of research for well over three decades. In that time, the focus of attention was for the canonical case of an equilibrium boundary layer. These studies have identified the causalities between the near-wall flow structures and the high-frequency pressures, and the outer-flow structures and the low-frequency pressures. For complex flows, the characteristics of the turbulence activities within the boundary layer have unique structures that are distinct from the canonical case. Accordingly, the features of the wall pressure field are quite different. As an example of a complex flow, the fluctuating wall pressures and turbulence statistics measured downstream of a backward facing step will be presented and compared to an equilibrium flow. The data demonstrate that the elevated low-frequency pressures directly track coherent turbulence structures in the flow field that result from passage over the step. In addition, these elevated pressures exhibit a slower spatial decay rate than that for equilibrium flows. These results illustrate the high sensitivity of the wall pressure to organized flow structures associated with complex flows.

The Rate of Spatial Decay of Nonnegative Solutions of Nonlinear Parabolic Equations and Inequalities

The Rate of Spatial Decay of Nonnegative Solutions of Nonlinear Parabolic Equations and Inequalities

The rate of spatial decay of nonnegative solutions of nonlinear parabolic equations and inequalities

Let L L be a uniformly parabolic linear partial differential operator. We show that nonnegative solutions of the differential inequality L u ≤ c ( u + | ∇ u | ) Lu \leq c(u + |\nabla u|) on R n × ( 0 , T ) {{\mathbf {R}}^n} \times (0,T) for which u ( x , T ) = 0 ( exp ⁡ ( − δ | x | 2 ) ) u(x,T) = {\mathbf {0}}(\exp {\text {(}} - \delta |x{|^2})) must be identically zero if the constant δ \delta is sufficiently large. An analogous result is given for nonlinear systems.

High-frequencyPnattenuation in the Canadian shield

AbstractFrequency-dependent spatial attenuation of Pn waves, incorporating the combined effects of geometrical spreading and anelastic dissipation, is investigated in eastern Canada between 3 and 15 Hz. Measurement of this total attenuation, instead of the two separate effects, circumvents the usual need for making a priori assumptions regarding the Pn geometrical spreading rate. The data consist of 77 Pn spectra, all amplitude-normalized using a set of previously measured spectral ratios of eastern Canadian earthquake sources. The normalization procedure eliminates the need for explicit source spectral assumptions, another common source of error in Pn attenuation measurements. An unconventional technique is introduced to account for differences in observed Pn spectra, which arise from geological site effects and instrument response error, both of which are frequency-dependent phenomena. We conclude that, at each frequency, the Pn amplitude falls off with distance according to: Δ−n, where Δ is epicentral distance. The exponent n is weakly frequency-dependent and takes the form: 2.2 + 0.02f. A unique interpretation of the behavior of the Pn spectral amplitude decay is unattainable, owing to the difficulty in separating the effects due to anelastic dissipation and the velocity structure in the uppermost mantle. It is interesting to note, however, that the spatial decay of pure elastic head waves follows the classical Δ−1/2L−3/2 relation, where L is the distance the waves travel in the mantle refractor. For the distance range of our interest (260-1087 km), this amounts to Δ−2.2. This indicates that towards low frequencies our n approaches a value which is consistent with the spatial decay rate expected of pure elastic head waves.

Role of spectral derivatives of structure reactance in vibration problems

Energy density and energy flux of resonant vibration of fluid-loaded structures are expressed in terms of spectral derivatives (i.e., derivatives with respect to frequency ω and wavenumber k) of structure surface wave reactance X. Two methods of derivation are presented: (1) Whitham's variational method is used after time-averaged Lagrangian density is expressed in terms of the structure teacrance X; (2) Pole contributions to structure transfer line admittance are evaluated. For small dissipation, both methods yield identical formulas for spatial and temporal decay rates of resonant vibration. Both methods are also capable of extensions that enable consideration of instabilities resulting from the presence of a uniformly moving fluid adjacent to the structure. [Work supported by the Office of Naval Research.]

Determining the spatial decay rate of free waves in layered plates

We will show that the spatial decay rate of free bending waves in multilayered fluid‐loaded plates can be estimated very easily using only a knowledge of the input admittance of the plate as a function of the frequency ω and wavenumber k of the normal stress applied to the plate. If the admittance is written in the form of a magnitude and a phase θ, the spatial decay rate ασ for free waves is given approximately by the expression ασ(ω)≈ − 2⧸∂(ω,k)∂k|θ = 0. The evaluation of the partial derivative of θ is performed with respect to real values of k. The justification for the result is based on arguments by K. Chandiramani and G. B. Witham which identify a proportionality between the Lagrangian energy density and the derivative with respect to frequency of the imaginary part of the surface impedance of the plate.

Transport of radon in flowing boreholes at Stripa, Sweden

Granitic rock in an underground experimental waste storage site at Stripa, Sweden, is unusually high in natural radioelements (∼40 ppm uranium), with higher concentrations occurring locally in thin chloritic zones and fractures. Consequently, groundwater seeping through fractures into open boreholes is highly anomalous in its radon content, with activity as high as 1 μCi/1. When total count gamma‐ray logs are run in boreholes where groundwater inflow is appreciable, the result is quite unusual: the radon daughter activity in the water adds considerably to the gamma contribution from the rock, and in fact often dominates the log. The total gamma activity increases where radon‐charged groundwater enters a borehole and decays as the water flows along the hole in response to the hydraulic gradient. As a consequence the gamma log serves as a flow profile, locating zones of water entry (or loss) by an increase (or decrease) in the total gamma activity. If mixing within the borehole does not occur, the activity decreases exponentially along the hole away from the entry point because of the steady decay of radon and its daughter products as they migrate with the flow in the water column.This spatial decay rate can be converted to a linear flow rate since the 3.8‐day half‐life of radon governs the response time. For example, if the volumetric flow rate in a 76‐mm hole falls within the range 0.5–50 liters per day and if observations are available from a 10‐m length of hole, then the flow rate can be measured quantitatively. Proportionately higher rates can be measured if longer hole lengths are available for observation. A model for flow through a thin crack emanating radon at a rate E shows that the radon concentration of water entering a hole is E/λh, where λ is the radon decay rate and h the crack aperture, assuming that the flow rate and crack source area are such that an element of water resides within the source area for several radon half‐lives or more. Using this simple relationship, independent measurements of emanation and concentration produce reasonable estimates of fracture aperture. Although uranium concentration values at Stripa are unusually high, neither the emanation coefficients nor the fracture properties appear to be unusual for granitic rock. It therefore seems likely that many granitic sites must exist where the radon content in groundwater is higher than in other geological terranes, although perhaps not as high as the microcurie per liter concentrations found at the Stripa site.

The rate of spatial decay of non-negative solutions of linear parabolic equations

for all xelR", then u = 0 on IR"x [0, t0]. Here to>0, X = ( X 1 . . . . . X n ) ~ n and [Ixl[ = 1/(x~ + . . + x.~). This question was taken up by GUSAROV in [4] and [5; Theorem 6]. He established the truth of the conjecture, and in fact showed that if u(x,t) =O(exp (kllxII2)), then there is a constant C, depending upon to, such that if u(x, to)= O ( e x p ( C ]]xll2)), then u=0. We show below that if the growth condition u(x,t)=O(exp(kHxll2)) is replaced by the assumption that u > 0, then a result similar to that of GUSAROV can be established for a very general class of linear second order parabolic equations, with coefficients depending upon t as well as x. This change in the hypothesis on u parallels that made by BOCHER [3] when dealing with elliptic equations, and the results given below are very closely related to the analogues of B0CHER's theorem presented in [1] (as well as in some of the works cited therein). We are concerned here with non-negative (weak) solutions of linear parabolic equations on a strip IR" x ]0, to]. We require that each such solution u has a representation in the form

Numerical Study of Electron Localization in Anderson Model for Disordered Systems: Spatial Extension of Wavefunction

The electron localization is investigated numerically in the Anderson model of disordered two dimensional square lattices. The spatial behaviors of wavefunctions are examined for large systems composed of 10 4 sites. Computations are carried out to see the Anderson transition at the band center and to see the localization near the mobility edge. Sharp transition at the band center is recognized and the electron localization is clearly visualized. The spatial decay rate of localized wavefunction is evaluated in the localized region and its dependence on energy or the degree of disorder is determined.

The effect of spatial discretization on the steady-state and transient solutions of a dispersive wave equation

The effect of replacing the spatial derivatives in a dispersive wave equation with second-order centered finite differences is examined with the use of Fourier transform techniques. The discretization is shown to both decrease the rate of spatial decay of the steady-state solution, and to introduce additional new transients at least as persistent as those in the differential case.

Energetics of fluid loaded hull-like structures

The spatial decay rate of vibratory response and of surface pressure for locally excited fluid-loaded ribbed plates is predicted and physically interpreted from the viewpoint of statistical energy analysis. Several canonical problem solutions are combined to yield a first order energetic model of the propagation of acoustic power along fluid loaded hull-like structures below critical frequency. These canonical problems are (1) damping of free flexural waves due to radiation from rib supports for periodically supported plates and (2) the hull grazing pressure field due to local excitation of a homogeneous plate. Comparison is made between analytic results and limited experimental data.

The upward jets of Niagara

International standards ISO 3382-2 and ISO 3382-3 are increasingly applied to determine the room acoustic conditions in open-plan offices because attention to noise control in such workplaces has increased. The precision of those standards in open-plan offices has not been published. The purpose of this study was to determine the precision of ISO 3382-2:2008 and ISO 3382-3:2012 in an open-plan office following the instructions of ISO 5725 standard. Furthermore, the results were analyzed in the light of ISO CD 3382-3:2020 involving improvements related to uncertainty. An accuracy experiment (a.k.a Round-Robin test, inter-laboratory test, intercomparison test) was arranged where nine independent participants conducted the measurements in the same open-plan office. For ISO 3382-3:2012, the reproducibility standard deviations were 530.5 dB, 1.3 dB, 1.3 dB, and 18% for spatial decay rate of speech (D2,S), A-weighted SPL of speech at 4 m distance (Lp,A,S,4m), A-weighted SPL of background noise (Lp,A,B), and distraction distance (rD). The corresponding values for ISO CD 3382-3:2020 were 0.3 dB, 1.1 dB, 0.6 dB, and 16%, respectively. The reproducibility standard deviations for reverberation time were 4.5–16% within 1/1-octave bands 125–8000 Hz. The measurement uncertainty of ISO CD 3382-3:2020 is smaller than that of ISO 3382-3:2012. The values depended mainly on between-laboratory differences while within-laboratory differences had only a marginal impact. The results can be used in the development of the standards.