Stability of systems containing a heat source : the Rayleigh criterion
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Chu, Boa-Teh↗
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Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi
Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.
Lobo, Matthew↗
Production of monodisperse sprays.
Monodisperse sprays production technique using Rayleigh criterion for breakup of capillary jets by mechanically vibrating uniform size capillary needles arranged in parallel
VIBRATION EFFECT↗
Study report on laser storage and retrieval of image data
The theoretical foundation is presented for a system of real-time nonphotographic and nonmagnetic digital laser storage and retrieval of image data. The system utilizes diffraction-limited laser focusing upon thin metal films, melting elementary holes in the metal films in laser focus. The metal films are encapsulated in rotating flexible mylar discs which act as the permanent storage carries. Equal sized holes encompass two dimensional digital ensembles of information bits which are time-sequentially (bit by bit) stored and retrieved. The bits possess the smallest possible size, defined by the Rayleigh criterion of coherent physical optics. Space and time invariant reflective read-out of laser discs with a small laser, provides access to the stored digital information. By eliminating photographic and magnetic data processing, which characterize the previous state of the art, photographic grain, diffusion, and gamma-distortion do not exist. Similarly, magnetic domain structures, magnetic gaps, and magnetic read-out are absent with a digital laser disc system.
Becker, C. H.↗
A general method to determine the stability of compressible flows
Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.
Guenther, R. A.↗
Diversity imaging techniques in lidar
Diversity imaging techniques have been successfully employed in conventional microwave range-Doppler imaging radars to obtain high resolution images of both natural and man-made targets. These techniques allow microwave radars to achieve image resolution which would otherwise require excessively large antennas. Recent advances in coherent laser radar techniques and signal processing have led to the development of range-Doppler imaging laser radars. While much of the theory and signal processing techniques used in microwave radars can be brought to bear on laser radars, the significant difference in wavelength results in issues peculiar to laser radar systems. Both the fundamental concepts and specific applications of diversity imaging techniques applied to laser radar imaging systems will be discussed. Angle, frequency, and bistatic angle degrees of freedom can be employed in a coherent laser radar imaging system to achieve image resolution which exceeds the traditional Rayleigh criterion associated with the receive aperture. In diversity imaging, angle and frequency degrees of freedom can be used to synthesize an effective aperture providing range and Doppler target information. The ability to vary the bistatic angle provides an additional means of synthesizing an effective aperture. Both simulated and experimentally obtained laser radar images of spinning and/or tumbling objects utilizing both angular and frequency diversity will be presented. In coherent laser radar systems, image quality can be dominated by laser speckle effects. In particular, the signal-to-noise ratio (SNR) of a coherent laser radar image is at most unity in the presence of fully developed speckle. Diversity techniques can be utilized to improve the image SNR; simple incoherent averaging of images utilizing temporal and polarization degrees of freedom can significantly improve image SNR. Both the SNR and image resolution (as defined by the synthetic aperture) contribute to image quality. The relationship between the available degrees of freedom and image quality are discussed.
Schultz, K. I.↗
Shear coaxial injector instability mechanisms
There is no definitive knowledge of which of several concurrent processes ultimately results in unstable combustion within liquid rocket chambers employing shear coaxial injectors. Possible explanations are a detrimental change in the atomization characteristics due to a decrease in the gas-to-liquid velocity ratio, a change in the gas side injector pressure drop allowing acoustic coupling to the propellant feed system or the disappearance of a stabilizing recirculation region at the base of the LOX post. The aim of this research effort is to investigate these proposed mechanisms under conditions comparable to actual engine operation. Spray characterization was accomplished with flash photography and planar laser imaging to examine the overall spray morphology and liquid jet breakup processes and with a PDPA to quantify the spatial distribution of droplet size and mean axial velocity. A simplified stability model based on the Rayleigh criterion was constructed for the flow dynamics occurring within the chamber and injector to evaluate the potential coupling between the chamber and injector acoustic modes and was supported by high frequency measurements of chamber and injector pressure oscillations. To examine recirculation within the LOX post recess, velocity measurements were performed in the recess region by means of LDV. Present experiments were performed under noncombusting conditions using LOX/GH2 stimulants at pressures up to 4 MPa.
Puissant, C.↗
Numerical aperture limits on efficient ball lens coupling of laser diodes to single-mode fibers with defocus to balance spherical aberration
The potential capabilities and limitations of single ball lenses for coupling laser diode radiation to single-mode optical fibers have been analyzed; parameters important to optical communications were specifically considered. These parameters included coupling efficiency, effective numerical apertures, lens radius, lens refractive index, wavelength, magnification in imaging the laser diode on the fiber, and defocus to counterbalance spherical aberration of the lens. Limiting numerical apertures in object and image space were determined under the constraint that the lens perform to the Rayleigh criterion of 0.25-wavelength (Strehl ratio = 0.80). The spherical aberration-defocus balance to provide an optical path difference of 0.25 wavelength units was shown to define a constant coupling efficiency (i.e., 0.56). The relative numerical aperture capabilities of the ball lens were determined for a set of wavelengths and associated fiber-core diameters of particular interest for single-mode fiber-optic communication. The results support general continuing efforts in the optical fiber communications industry to improve coupling links within such systems with emphasis on manufacturing simplicity, system packaging flexibility, relaxation of assembly alignment tolerances, cost reduction of opto-electronic components and long term reliability and stability.
Wilson, R. Gale↗
On the Origin of the Saturnian Satellite System: Did Iapetus Form In-Situ?
Current models of planet and satellite formation are marred by our lack of understanding regarding the turbulent state of accretion disks. According to the Rayleigh criterion, Keplerian disks are hydrodynamically stable. Indeed, it has been argued that a carefully designed Taylor Couette experiment shows stability in the case of positive radial gradients in specific angular momentum even for high Reynolds numbers [1], in agreement with numerical simulations which consistently show turbulence decay [2]. Other possible sources of turbulence may fail due to low ionization, may decay as the optical depth decreases due to dust coagulation, may involve unrealistic boundary conditions, or result in limited transport. The difficulty stems not only from the degree of turbulence, but also from the kind of turbulence, and whether it may be characterized by an alpha parameter.
Mosqueira, I.↗
Two-photon interferometry for high-resolution imaging
We discuss advantages of using non-classical states of light for two aspects of optical imaging: creating of miniature images on photosensitive substrates, which constitutes the foundation for optical lithography, and conversely, imaging of micro objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately a half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and multi-photon sensitive material or detector, this limit can be surpassed. In the present work, we give a rigorous quantum mechanical treatment of this problem, address some particularly widespread misconceptions and discuss the requirements arising on the way of turning the research on quantum imaging into a practical technology.
quantum technology↗
Convective instabilities in SN 1987A
Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.
Benz, Willy↗
Control of Combustion-Instabilities Through Various Passive Devices
It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.
Frendi, Kader↗
Stability of fluid flow in a cylindrical annulus
Helical flow in an annulus between two coaxial cylinders is investigated with regard to its stability against the formation of helical vortices of the type known as Taylor's annular vortices. Assuming the annulus to be small and the velocities to vary linearly with radius, it is shown that the problem can be reduced to the classical case of flow between two rotating cylinders. An appropriate stability criterion for helical flows is derived from Rayleigh's stability criterion applicable to such flows.
Ludwieg, H.↗
A relationship between potential vorticity and zonal wind on Jupiter
We present evidence from analysis of Voyager data and numerical experiments that in Jupiter's troposphere at midlatitudes the potential vorticity is given simply by the reciprocal of the streamfunction. This relationship agrees with the results of a vortex-tube stretching analysis of the Voyager wind-field data of the Great Red Spot and White Oval BC, whereas other published models do not. The derivative of streamfunction with respect to potential vorticity is negative definite, and in the quasigeostrophic limit the relationship is neutrally stable with respect to Arnold's second stability theorem. Numerical experiments indicate that the relationship is also neutrally stable in the primitive shallow-water system. This resolves a long-standing question as to how Jupiter's cloud-top winds are able to violate the Rayleigh-Kuo stability criterion, and constrains the two-layer model to a single free parameter.
Dowling, Timothy E.↗
Thermal buckling of symmetrically laminated composite plates
This paper discusses an investigation into the thermal buckling of symmetrically laminated composite plates. In this study thermal buckling is investigated for laminates under two different simple support conditions, fixed and sliding. These laminates are subjected to the conditions of a uniform temperature change, and a temperature change varying linearly along the length of the plate. The effects of the principal material axes not being aligned with the edges of the plate are also investigated. The buckling response is studied using variational methods, specifically the Trefftz criterion. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response and the buckling response.
Meyers, C. A.↗
Electrohydrodynamic Rayleigh-Taylor bulk instability
Stability criterion for initially static, stratified fluid subject to electrical stress
Melcher, J. R.↗
A generalized effective potential for differentially rotating plasmas
Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi and Pharr [Astrophys. J. 936, 145 (2022)]), confined either between two Alfvénic resonances or an Alfvénic resonance and a boundary.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Two-dimensional modelling of compressive failure in delaminated laminates
An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites. The delaminated region is elliptic in shape, separating a thick isotropic plate from a thin orthotropic layer whose material axes coincide with the ellipse axes. The growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem. Post-buckling solution for the elliptic section is obtained using the Rayleigh-Ritz method while an energy balance criterion based on a self-similar disbond growth governs the fracture. The parameters controlling the growth or arrest of the delamination damage are identified as the fracture energy, disbond depth and elastic properties of the materials from both sides of the delaminating interface. By varying the degree of material anisotropy relative to the loading axis a range in growth behavior was found including stable or unstable crack growth parallel to or normal to the loading axis.
Chai, H.↗