A kinematic subgrid scale model for large-eddy simulation of turbulence generated sound

In the hybrid approach of large-eddy simulation (LES) and Lighthill’s acoustic analogy for turbulence-generated sound, the turbulence source fields are obtained using an LES and the turbulence-generated sound at far fields is calculated from Lighthill’s acoustic analogy. As only the velocity fields at resolved scales are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill’s acoustic equation, has to be evaluated from the resolved velocity fields. As a result, the contribution from the unresolved velocity fields is missing in the conventional LES. The sound of missing scales is shown to be important and hence needs to be modeled. The present study proposes a kinematic subgrid-scale (SGS) model which recasts the unresolved velocity fields into Lighthill’s stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with the imposed temporal statistics, which is consistent with the random sweeping hypothesis. The kinematic SGS model is used to calculate sound power spectra from isotropic turbulence and yields an improved result: the missing portion of the sound power spectra is approximately recovered in the LES.

Locally resonant phononic woodpile: A wide band anomalous underwater acoustic absorbing material

To meet the demand of modern acoustic absorbing material for which acoustic absorbing frequency region can be readily tailored, we introduced woodpile structure into locally resonant phononic crystal (LRPC) and fabricated an underwater acoustic absorbing material, which is called locally resonant phononic woodpile (LRPW). Experimental results show that LRPW has a strong capability of absorbing sound in a wide frequency range. Further theoretical research revealed that LRPC units and woodpile structure in LRPW play an important role in realization of wide band underwater strong acoustic absorption.

Two new integral transforms and their applications

This thesis is in two parts. In Part I the independent variable θ in the trigonometric form of Legendre's equation is extended to the range ( -∞, ∞). The associated spectral representation is an infinite integral transform whose kernel is the analytic continuation of the associated Legendre function of the second kind into the complex θ-plane. This new transform is applied to the problems of waves on a spherical shell, heat flow on a spherical shell, and the gravitational potential of a sphere. In each case the resulting alternative representation of the solution is more suited to direct physical interpretation than the standard forms.

In Part II separation of variables is applied to the initial-value problem of the propagation of acoustic waves in an underwater sound channel. The Epstein symmetric profile is taken to describe the variation of sound with depth. The spectral representation associated with the separated depth equation is found to contain an integral and a series. A point source is assumed to be located in the channel. The nature of the disturbance at a point in the vicinity of the channel far removed from the source is investigated.

Policy analysis of shoreline restoration options on private shorelines of Puget Sound

Puget Sound shorelines have historically provided a diversity of habitats that support a variety of aquatic resources throughout the region. These valued natural resources are iconic to the region and remain central to both the economic vitality and community appreciation of Puget Sound. Deterioration of upland and nearshore shoreline habitats, have placed severe stress on many aquatic resources within the region (PSAT, 2007). Since a majority of Washington State shorelines are privately owned, regulatory authority to legislate restoration on private property is limited in scope and frequency. Washington States’ Shoreline Management Act (RCW 90.58) requires local jurisdictions to plan for appropriate future shoreline uses. Under the Act, future development can be regulated to protect existing ecological functions, but lost functions cannot be restored without purchase or compensation of restored areas. Therefore, questions remains as to the ecological resilience of the region when considering cumulative effect of existing/ongoing shoreline development constrained by limited shoreline restoration opportunities. In light of these questions, this analysis will explore opportunities to promote restoration on privately owned shorelines within Puget Sound. These efforts are intended to promote more efficient ecosystem management and improve ecosystem-wide ecological functions. From an economics perspective, results of past shoreline management can generally be characterized as both market and government failure in effectively protecting the publics’ interest in maintaining healthy shoreline resources. Therefore coastal development has proceeded in spite of negative externalities and market imbalances resulting in inefficient resource management driven by the individual ambitions of private shoreline property owners to develop their property to their highest and best use. Federally derived property rights will protect continuation of existing uses along privately owned shorelines; therefore, a fundamental challenge remains in sustainable management of existing shoreline resources while also restoring ecological functions lost to past mistakes in an effort to increase the ecologic resiliency within the region. (PDF contains 5 pages)

Physical circulation measurements in Pamlico Sound, used to locate new oyster sanctuaries

The population of eastern oyster, C. virginica, has declined over the last century on most areas of the east and gulf coasts. North Carolina’s restoration efforts depend on the construction of subtidal oyster reefs to be used as broodstock sanctuaries in Pamlico Sound, NC. Successful restoration of the oyster population requires several thriving reefs connected as a meta-population. C. virginica has a 2-3 week larval stage, during which it gradually settles through the water column. Larvae that can travel from one reef to another during that stage form the basis of a meta-population. (PDF contains 3 pages)

Near dipole-dipole effects on the propagation of few-cycle pulse in a dense two-level medium

The propagation behaviors, which include the carrier-envelope phase, the area evolution and the solitary pulse number of few-cycle pulses in a dense two-level medium, are investigated based on full-wave Maxwell-Bloch equations by taking Lorentz local field correction (LFC) into account. Several novel features are found: the difference of the carrier-envelope phase between the cases with and without LFC can go up to pi at some location; although the area of ultrashort solitary pulses is lager than 2 pi, the area of the effective Rabi frequency, which equals to that the Rabi frequency pluses the product of the strength of the near dipole-dipole (NDD) interaction and the polarization, is consistent with the standard area theorem and keeps 2 pi; the large area pulse penetrating into the medium produces several solitary pulses as usual, but the number of solitary pulses changes at certain condition. (C) 2005 Optical Society of America.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Influence of atomic densities on propagation property for ultrashort pulses in a two-level medium

The influence of atomic densities on the propagation property for ultrashort pulses in a two-level atom (TLA) medium is investigated. With higher atomic densities, the self-induced transparency (SIT) cannot be recovered even for 2π ultrashort pulses. New features such as pulse splitting, red-shift and blue-shift of the corresponding spectra arise, and the component of central frequency gradually disappears.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Effect of time-dependent ionization on the propagation of a few-cycle laser pulse in a two-level medium

We investigate the influence of ionization on the propagation and spectral effects of a few-cycle ultrashort laser pulse in a two-level medium. It is found that when the fractional ionization is weak, the production of higher spectral components makes no difference. However, when the two states are essentially depleted before the peak of the laser pulse, the impact of ionization on the higher spectral components is very significant.

Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation

Nonlinear propagation of fs laser pulses in liquids and the dynamic processes of filamentation such as self-focusing, intensity clamping, and evolution of white light production have been analyzed by using one- and two-photon fluorescence. The energy losses of laser pulses caused by multiphoton absorption and conical emission have been measured respectively by z-scan technique. Numerical simulations of fs laser propagation in water have been made to explain the evolution of white light production as well as the small-scale filaments in liquids we have observed by a nonlinear fluorescence technique. (c) 2005 Optical Society of America.

Eliciting and using stakeholder input to guide Puget Sound nearshore restoration decisionmaking

The goal of the Puget Sound Nearshore Ecosystem Restoration Project (PSNERP) is to improve system-wide functionality of nearshorei ecosystem processes. To achieve that goal, PSNERP plans to strategically restore nearshore sites throughout Puget Sound. PSNERP scientists are assessing changes to the nearshore, and will recommend an environmentally strategic restoration portfolio. Yet, PSNERP also needs stakeholder input to design a socially strategic portfolio. This research investigates the values and preferences of stakeholders in the Whidbey Sub-Basin of Puget Sound to help PSNERP be both socially and environmentally strategic. This investigation may be repeated in the six other Puget Sound Sub-Basins. The results will guide restoration portfolio design and future stakeholder involvement activities. This study examines four areas of stakeholder values and preferences: 1) beliefs about the causes, solutions, and severity of nearshore problems; 2) priorities for nearshore features, shoreforms, developments, and restoration objectives; 3) thoughts about ecosystem servicesiii and trade-offs among them; and 4) visions of a future, restored Puget Sound nearshore and the role of science in attaining this vision. The study is framed by two hypotheses from the Advocacy Coalition Framework (ACF), which suggests that groups of policy advocates form around shared “policy core beliefs” which can transcend traditional categories of stakeholders.(PDF contains 3 pages)

Effects of Lorentz local field correction on propagation properties of few-cycle pulse in dense Λ-type atomic medium

By solving numerically the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, we investigate the effects of Lorentz local field correction (LFC) on the propagation properties of few-cycle laser pulse in a dense A-type three-level atomic medium. We find that: when the area of the input pulse is larger, split of pulse occurs and the number of the sub-pulses with LFC is larger than that without LFC; at the same distance, the time interval between the first sub-pulse and the second sub-pulse in the case without LFC is longer than that with LFC, the time of pulse appearing in the case without LFC is later than that in the case with LFC, and the two phenomena are more obvious with propagation distance increasing; time evolution rules of the populations of levels vertical bar 1 >, vertical bar 2 > and vertical bar 3 > in the two cases with and without LFC are much different. When the area of the input pulse is smaller, effects of LFC on time evolutions of the pulse and populations are remarkably smaller than those in the case of larger area pulse. (c) 2008 Elsevier B.V. All rights reserved.

Sound velocities and equation of state of iron-rich (Mg,Fe)O

Ultralow-velocity zones (ULVZs) are small structures at the base of the mantle characterized by sound velocities up to 30% lower than those of surrounding mantle. In this thesis, we propose that iron-rich (Mg,Fe)O plays a key role in the observed sound velocities, and argue that chemically distinct, iron-enriched structures are consistent with both the low sound velocities and the measured shapes of ULVZs.