Resolvent Modes Research Articles

Dynamic roughness perturbation of a turbulent boundary layer

AbstractThe zero-pressure-gradient turbulent boundary layer over a flat plate was perturbed by a temporally oscillating, spatial impulse of roughness, and the downstream response of the flow field was interrogated by hot-wire anemometry and particle-image velocimetry. The key features common to impulsively perturbed boundary layers, as identified in Jacobi & McKeon (J. Fluid Mech., 2011), were investigated, and the unique contributions of the dynamic perturbation were isolated by contrast with an appropriately matched static impulse of roughness. In addition, the dynamic perturbation was decomposed into separable large-scale and small-scale structural effects, which in turn were associated with the organized wave and roughness impulse aspects of the perturbation. A phase-locked velocity decomposition of the entire downstream flow field revealed strongly coherent modes of fluctuating velocity, with distinct mode shapes for the streamwise and wall-normal velocity components. Following the analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), the roughness perturbation was treated as a forcing of the Navier–Stokes equation and a linearized analysis employing a modified Orr–Sommerfeld operator was performed. The experimentally ascertained wavespeed of the input disturbance was used to solve for the most amplified singular mode of the Orr–Sommerfeld resolvent. These calculated modes were then compared with the streamwise and wall-normal velocity fluctuations. The discrepancies between the calculated Orr–Sommerfeld resolvent modes and those experimentally observed by phase-locked averaging of the velocity field were postulated to result from the violation of the parallel flow assumption of Orr–Sommerfeld analysis, as well as certain non-equilibrium effects of the roughness. Additionally, some difficulties previously observed using a quasi-laminar eigenmode analysis were also observed under the resolvent approach; however, the resolvent analysis was shown to provide reasonably accurate predictions of velocity fluctuations for the forced Orr–Sommerfeld problem over a portion of the boundary layer, with potential applications to designing efficient flow control strategies. The combined experimental and analytical effort provides a new opportunity to examine the non-equilibrium and forcing effects in a dynamically perturbed flow.

Signatures of Nonlinear Dynamics in an Idealized Atmospheric Model

Abstract Signatures of nonlinear dynamics are analyzed by studying the phase-space tendencies of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography. Nonlinear, stochastic, low-order prototypes of the full QG3 model are constructed in the phase space of this model’s empirical orthogonal functions using the empirical model reduction (EMR) approach. The phase-space tendencies of the EMR models closely match the full QG3 model’s tendencies. The component of these tendencies that is not linearly parameterizable is shown to be dominated by the interactions between “resolved” modes rather than by multiplicative “noise” associated with unresolved modes. The method of defining the leading resolved modes and the interactions between them plays a key role in understanding the nature of the QG3 model’s dynamics, whether linear or nonlinear, deterministic or stochastic.

Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry

This paper presents a significant advancement in the referencing technique applied to frequency comb spectrometry (cFTS) that we proposed and demonstrated recently. Based on intermediate laser oscillators, it becomes possible to access the full delay range set by the repetition rate of the frequency combs, overcoming the principal limitation observed in the method based on passive optical filters. With this new referencing technique, the maximum spectral resolution given by each comb tooth is achievable and continuous scanning will improve complex reflectometry measurements. We present a demonstration of such a high resolution cFTS system, providing a spectrometry measurement at 100 MHz of resolution (0.003 cm(-1)) with a spectral signal to noise ratio of 440 for a 2 seconds measurement time. The resulting spectrum is composed of 105 · 10(3) resolved spectral elements, each corresponding to a single pair of optical modes (one for each combs). To our knowledge, this represents the first cFTS measurement over the full spectral range of the sources in a single shot with resolved individual modes at full resolution.

Analytic continuation average spectrum method for transport in quantum liquids

Recently, we have applied the analytic continuation averaged spectrum method (ASM) to calculate collective density fluctuations in quantum liquid [27]. Unlike the maximum entropy (MaxEnt) method, the ASM approach is capable of revealing resolved modes in the dynamic structure factor in agreement with experiments. In this work we further develop the ASM to study single-particle dynamics in quantum liquids with dynamical susceptibilities that are characterized by a smooth spectrum. Surprisingly, we find that for the power spectrum of the velocity autocorrelation function there are pronounced differences in comparison with the MaxEnt approach, even for this simple case of smooth unimodal dynamic response. We show that for liquid para-hydrogen the ASM is closer to the centroid molecular dynamics (CMD) result while for normal liquid helium it agrees better with the quantum mode coupling theory (QMCT) and with the MaxEnt approach.

Analytic continuation average spectrum method for quantum liquids

We revisit the problem of determining the real-frequency density response in quantum fluids via analytical continuation of imaginary-time quantum Monte Carlo data. We demonstrate that the average spectrum method (ASM) is capable of revealing resolved modes in the dynamic structure factor of both ortho-deuterium and liquid para-hydrogen, in agreement with experiments and quantum mode-coupling theories, while the maximum entropy approach yields only a smooth unimodal spectrum. Outstanding issues are discussed. Our work provides the first application of the ASM method in realistic off-lattice systems.

Comparative test–retest reliability of metabolite values assessed with magnetic resonance spectroscopy of the brain. The LCModel versus the manufacturer software

Objective: Reproducibility is an essential strength of any diagnostic technique for cross-sectional and longitudinal works. To determine in vivo short-term comparatively, the test–retest reliability of magnetic resonance spectroscopy (MRS) of the brain was compared using the manufacturer's software package and the widely used linear combination of model (LCModel) technique.Methods: Single-voxel 1H-MRS was performed in a series of patients with different pathologies on a 1.5 T clinical scanner. Four areas of the brain were explored with the point resolved spectroscopy technique acquisition mode; the echo time was 35 milliseconds and the repetition time was 2000 milliseconds. We enrolled 15 patients for every area, and the intra-individual variations of metabolites were studied in two consecutive scans without removing the patient from the scanner. Curve fitting and analysis of metabolites were made with the software of GE and the LCModel. Spectra non-fulfilling the minimum criteria of quality in relation to linewidths and signal/noise ratio were rejected.Results: The intraclass correlation coefficients for the N-acetylaspartate/creatine (NAA/Cr) ratios were 0.93, 0.89, 0.9 and 0.8 for the posterior cingulate gyrus, occipital, prefrontal and temporal regions, respectively, with the GE software. For the LCModel, the coefficients were 0.9, 0.89, 0.87 and 0.84, respectively. For the absolute value of NAA, the GE software was also slightly more reproducible than LCModel. However, for the choline/Cr and myo-inositol/Cr ratios, the LCModel was more reliable than the GE software. The variability we have seen hovers around the percentages observed in previous reports (around 10% for the NAA/Cr ratios).Conclusion: We did not find that the LCModel software is superior to the software of the manufacturer. Reproducibility of metabolite values relies more on the observance of the quality parameters than on the software used.

Lateral and longitudinal mode pattern of broad ridge 405nm (Al, In)GaN laser diodes

The lateral mode profile of pulsed broad ridge 405nm (Al, In)GaN laser diodes grown on GaN and SiC substrates, respectively, is investigated by temporal and spectral resolved scanning near-field optical microscopy. During the first microsecond of the pulse, we observe changes both in the spatial mode profile and in the spectral regime caused by thermal and carrier induced modification of the waveguide refractive index, before stable filaments build up. In quasi-cw operation, a correlation between the lateral mode profile and the corresponding spatial resolved longitudinal mode pattern can be found. The results show that different filaments have different effective refractive indices and thus build up separate longitudinal mode combs.

Reduced Atmospheric Models Using Dynamically Motivated Basis Functions

Abstract Nonlinear deterministic reduced models of large-scale atmospheric dynamics are constructed. The dynamical framework is a quasigeostrophic three-level spectral model with realistic mean state and variability as well as Pacific–North America (PNA) and North Atlantic Oscillation (NAO) patterns. The study addresses the problem of finding appropriate basis functions for efficiently capturing the dynamics and a comparison between different choices of basis functions; it focuses on highly truncated models, keeping only 10–15 modes. The reduced model is obtained by a projection of the equations of motion onto a truncated basis spanned by empirically determined modes. The total energy metric is used in the projection; the nonlinear terms of the low-order model then conserve total energy. Apart from retuning the coefficient of horizontal diffusion, no empirical terms are fitted in the dynamical equations of the low-order model in order to properly preserve the physics of the system. Using the methodology of principal interaction patterns (PIPs), a basis is derived that carefully compromises minimizing tendency error with maximizing explained variance in the resolved modes. A new PIP algorithm is introduced that is more compact and robust than earlier PIP algorithms; a top-down approach is adopted, removing modes from the system one by one. The mean state and standard deviation of the streamfunction as well as transient momentum fluxes are well reproduced by a PIP model with only 10 modes. Probability density functions are accurately modeled and autocorrelation functions are captured fairly well using 15 modes. Reduced models based on PIPs are substantially superior to reduced models based on empirical orthogonal functions (EOFs). The leading PIPs have a higher projection onto the PNA and NAO teleconnection patterns than the corresponding EOFs. Both with EOFs and PIPs, the interactions between the resolved modes are predominantly linear and the improvement of PIP models on EOF models stems entirely from better modeling these linear interactions although the full nonlinear tendencies are optimized. There is considerable influence of smaller-scale modes on the large-scale modes due to nonlinear coupling that is not well captured by either EOFs or PIPs. This nonlinear backscattering possibly plays a role in generating the low-frequency variability of the model. The results call for a nonlinear and/or stochastic closure scheme in which PIPs may be suitable basis functions.

Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb

The control of the broadband frequency comb emitted from a mode-locked femtosecond laser has permitted a wide range of scientific and technological advances--ranging from the counting of optical cycles for next-generation atomic clocks to measurements of phase-sensitive high-field processes. A unique advantage of the stabilized frequency comb is that it provides, in a single laser beam, about a million optical modes with very narrow linewidths and absolute frequency positions known to better than one part in 10(15) (ref. 5). One important application of this vast array of highly coherent optical fields is precision spectroscopy, in which a large number of modes can be used to map internal atomic energy structure and dynamics. However, an efficient means of simultaneously identifying, addressing and measuring the amplitude or relative phase of individual modes has not existed. Here we use a high-resolution disperser to separate the individual modes of a stabilized frequency comb into a two-dimensional array in the image plane of the spectrometer. We illustrate the power of this technique for high-resolution spectral fingerprinting of molecular iodine vapour, acquiring in a few milliseconds absorption images covering over 6 THz of bandwidth with high frequency resolution. Our technique for direct and parallel accessing of stabilized frequency comb modes could find application in high-bandwidth spread-spectrum communications with increased security, high-resolution coherent quantum control, and arbitrary optical waveform synthesis with control at the optical radian level.

High-fidelity line-by-line optical waveform generation and complete characterization using FROG

A stable optical frequency comb with 20-GHz spacing is shaped by a compact integrated silica arrayed waveguide grating (AWG) pair to produce optical waveforms with unprecedented fidelity. Complete characterization of both the intensity and phase of the crafted optical fields is accomplished with cross-correlation frequency resolved optical gating (XFROG) which has been optimized for periodic waveforms with resolvable modes. A new method is proposed to quantify, in a single number, the quality of the match in both the amplitude and phase between the measured optical waveform and the target waveform.

AlN thin film as waveguide for shear acoustic waves

A set of shear acoustic waves in the 78–195MHz range composed of a surface skimming bulk wave and highly resolved shear acoustic plate modes has been simultaneously excited in a thin ST-cut quartz plate by means of transducers with a 1μm thick sputtered AlN thin film used as a waveguiding layer. The effect of coating the transducers face with AlN is shown to increase the propagation speed of the first 13 plate modes in the ST-cut quartz, but then to decreases the propagation speed of plate modes higher than the 14th.

Low-Order Stochastic Mode Reduction for a Prototype Atmospheric GCM

Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a three-layer quasigeostrophic model. This model climate has reasonable approximations of the North Atlantic Oscillation (NAO) and Pacific–North America (PNA) patterns. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition in the total energy metric. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with 10 or less resolved modes capture the statistics of the original model very well, including the variances and temporal correlations with high pattern correlations of the transient eddy fluxes. A budget analysis establishes that the low-order stochastic models are highly nonlinear with significant contributions from both additive and multiplicative noise. This is in contrast to previous stochastic modeling studies. These studies a priori assume a linear model with additive noise and regression fit the resolved modes. The multiplicative noise comes from the advection of the resolved modes by the unresolved modes. The most straightforward low-order stochastic climate models experience climate drift that stems from the bare truncation dynamics. Even though the geographic correlation of the transient eddy fluxes is high, they are underestimated by a factor of about 2 in the a priori procedure and thus cannot completely overcome the large climate drift in the bare truncation. Also, variants of the reduced stochastic modeling procedure that experience no climate drift with good predictions of both the variances and time correlations are discussed. These reduced models without climate drift are developed by slowing down the dynamics of the bare truncation compared with the interactions with the unresolved modes and yield a minimal two-parameter regression fitting strategy for the climate modes. This study points to the need for better optimal basis functions that optimally capture the essential slow dynamics of the system to obtain further improvements for the reduced stochastic modeling procedure.

Low-Order Stochastic Mode Reduction for a Realistic Barotropic Model Climate

Abstract This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a realistic barotropic model climate. This barotropic model climate has reasonable approximations of the Arctic Oscillation (AO) and Pacific/North America (PNA) teleconnections as its two leading principal patterns of low-frequency variability. The systematic strategy consists first of the identification of slowly evolving climate modes and faster evolving nonclimate modes by use of an empirical orthogonal function (EOF) decomposition. The low-order stochastic climate model predicts the evolution of these climate modes a priori without any regression fitting of the resolved modes. The systematic stochastic mode reduction strategy determines all correction terms and noises with minimal regression fitting of the variances and correlation times of the unresolved modes. These correction terms and noises account for the neglected interactions between the resolved climate modes and the unresolved nonclimate modes. Low-order stochastic models with only four resolved modes capture the statistics of the original barotropic model modes quite well. A budget analysis establishes that the low-order stochastic models are dominated by linear dynamics and additive noise. The linear correction terms and the additive noise stem from the linear coupling between resolved and unresolved modes, and not from nonlinear interactions between resolved and unresolved modes as assumed in previous studies.

Angle resolved ion scattering spectroscopy reveals the local topography around atoms in a liquid surface

Neutral impact collision ion scattering spectroscopy under normal incidence is known to yield the concentration depth profiles of all elements except hydrogen at the surface of liquids and other amorphous material. In the evaluation of the data one tactically has to assume that the top surface layer and the adjacent layers are laterally homogeneous. In the present paper we establish that the angular resolved mode of this spectroscopy is able to test with high accuracy whether the lateral homogeneity is valid and-if this is not the case-in which way the top layer is structured. In particular, it is possible to map out the local environment of selected atoms. We expect that this so far inaccessible information on the local topography at liquid surfaces will have an impact on the understanding of reactions at the gas/liquid interface.

Resolution of Sub-Rouse Modes of Polystyrene by Dissolution

The properties of the softening “glass to rubber” dispersion of two archetypal amorphous polymers, polystyrene and polyisobutylene, appear to differ greatly. Previously, these differences have been explained by the larger intermolecular coupling between the repeat units in executing the local segmental motions in polystyrene than polyisobutylene. Dissolution of polystyrene into a solvent with a lower glass temperature certainly diminishes the intermolecular coupling and could make the softening dispersion of the polystyrene solution resemble bulk polyisobutylene. Creep compliance measurements of solutions of polystyrene in tri-m-tolyl phosphate are used to show that this expectation is the case. At 17% polystyrene, the properties of the softening dispersion of the solution are nearly identical to that of bulk polyisobutylene, including the appearance of a resolved sub-Rouse mode.

Low frequency fluctuations and locked states in a multi-mode semiconductor laser with external cavity

The low frequency fluctuations (LFF) in a multi-mode semiconductor laser in an external cavity is investigated experimentally and theoretically. The results of the dynamical behaviors not only of the total intensity but also of a few frequency resolved dominant modes of the solitary laser are presented. We demonstrate experimentally and numerically that the so-called locked state (synchronous Sisyphus effect) we reported previously in which the dropout events occur with a high degree of periodicity persists even when the laser operates on a large number of solitary cavity modes. We show that slow energy transfer between solitary modes is a common effect when the laser undergoes LFFs or is in the locked state and that this effect is predicted by the multi-mode Lang–Kobayashi equations to be noise driven.

ANALYSIS AND PROCESSING OF RECEIVED SIGNALS IN BOREHOLES

This study is a part of a project to develop a borehole sonar for acoustic imaging of the geological structure of the rock formation near to a deviated or horizontal borehole performed while drilling. The purpose of the sonar is to provide a direct measure of the distance and the direction to bed boundaries parallel to the borehole. This paper gives a theoretical analysis of the effect of the borehole and the drillstring on the received response on sensors positioned on the drillstring and proposes a method for processing the received signal to enable the determination of the direction of an incoming plane wave and time of arrival. In the first part of this paper, the response at any position in a fluid filled borehole is determined for an incoming plane P-wave. It is shown that the response is quite complicated and consists of several vibrating modes with resonance structure. Secondly, the paper presents how the received signals can be decomposed and the individual modes can be resolved by utilizing the orthogonal properties of the mode functions. The individual mode functions are resolved by performing a spatial Fourier transform of the sensor signals. A requirement is that the sensors are uniformly distributed around the circumference of the drillstring and that the number of sensors is at least two times the number of significant modes. It is demonstrated that the spatial and temporal characteristics of the resolved modes can then be exploited to determine the time of arrival and the angle of direction of the incoming reflected waves.

The North Pacific Acoustic Laboratory (NPAL) experiment.

The North Pacific Acoustic Laboratory program augmented the existing ATOC acoustic network with a sparse, two-dimensional receiving array installed west of Sur Ridge, California, from July 1998 through June 1999, to receive transmissions from the 75-Hz ATOC source north of Kauai. The NPAL array consisted of four 20-element vertical arrays, each with a 700-m aperture, and one 40-element vertical array with a 1400-m aperture. The arrays were deployed transverse to the 3900-km acoustic path from the Kauai source and had a total horizontal aperture of 3600 m. Data collected with the billboard array and the U.S. Navy SOSUS receivers are being used (i) to study the temporal, vertical, and horizontal coherence of long-range, low-frequency resolved rays and modes, (ii) to study 3-D propagation effects, (iii) to examine directional ambient noise properties, and (iv) to improve basin-scale ocean nowcasts via assimilation of acoustic data and other data types into models. In addition to acoustic data, environmental data along the path from the Kauai source to the billboard array were acquired by two oceanographic sub-surface moorings and by two XBT/CTD/ADCP transects along the path. The experiment will be described and some preliminary results presented.

Surface and bulk spin-wave resonances in La0.7Mn1.3O3films

In this work, we present the measurements of exchange-dominatednonpropagating surface and bulk spin-wave modes in the La-deficientepitaxial La0.7Mn1.3O3 films prepared by dc-magnetronsputtering. The angular and temperature dependences of the modes observedare discussed. The main result obtained is the observation of the spin-waveresonance (SWR) consisting of a series (17) of well resolved standingspin-wave modes in the perpendicular external magnetic field geometry. Thesurface spin-wave modes have been observed in manganites for the firsttime. As the magnetization is rotated out of perpendicular to the filmsurface, a `critical angle', φcr, is fixed, at which thesurface and first spin-wave modes have been transformed into the uniformmode. It is shown that only the uniform mode exists in the region0<φ<φcr. The surface mode data are consistent with thesurface-inhomogeneity model in which the surface-anisotropy field acts onthe surface spin. Possible origins of the surface anisotropy are discussed.Based on the temperature and angular dependences of SWR spectra, the mainmicroscopic parameters (the spin-wave stiffness, exchange constant andg-factor value) are established.

The North Pacific Acoustic Laboratory (NPAL) Experiment

The North Pacific Acoustic Laboratory program augmented the existing ATOC acoustic network with a sparse, two-dimensional receiving array installed west of Sur Ridge, CA, close to an existing U.S. Navy SOSUS array, during July 1998 to receive transmissions from the 75-Hz ATOC source north of Kauai. The NPAL array consisted of four 20-element vertical arrays, each with a 700-m aperture, and one 40-element vertical array with a 1400-m aperture. The arrays were deployed transverse to the 3900-km path from the Kauai source and had a total horizontal aperture of 3600 m. Data collected with the two-dimensional array and the U.S. Navy SOSUS receivers will be used to (i) study the temporal, vertical, and horizontal coherence of long-range, low-frequency resolved rays and modes, (ii) study 3D propagation effects, (iii) examine directional ambient noise properties, and (iv) to improve basin-scale ocean nowcasts via assimilation of acoustic data and other data types into models. Environmental data along the path from the Kauai source to the two-dimensional array were acquired by two oceanographic subsurface moorings and by two XBT/CTD/ADCP transects along the path, one at the beginning and one at the end of the experiment. We describe the experiment and offer some preliminary data.