Mathematical Aspects of Hydrodynamics

The workshop dealt with the partial differential equations that describe fluid motion and related topics. These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation, inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction

Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer

It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However, there are very few mathematical results on the compressible fluid despite the extensive studies when the fluid is governed by the incompressible Navier-Stokes equations. This paper aims to introduce a new approach to study the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime where a subtle quasi-compressible and Stokes iteration is developed. As a byproduct, we show the spectral instability of subsonic boundary layer.Comment: 35pages. All comments are welcom

Aeronautical Engineering: A continuing bibliography with indexes (supplement 205)

This bibliography lists 517 reports, articles and other documents introduced into the NASA scientific and technical information system in September 1986

Bibliography of Lewis Research Center technical publications announced in 1988

This bibliography contains abstracts of the technical reports that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1988. Subject, author, and corporate source indexes are also included. All the publications were announced in the 1988 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Multi-modal MHD oscillations in the solar corona, and their use in coronal seismology

The solar atmosphere is a dynamic, inhomogeneous environment which acts as a natural plasma laboratory for a keen community of observers and researchers at the forefront of modern physics. Colossal plasma non-uniformities on the Sun are seen to host a wide variety of magnetoacoustic oscillatory motions, which may be used as probes into the local plasma conditions using the theory of long wavelength, large scale magnetohydrodynamics (MHD): this process is known as coronal seismology. The focus of this thesis is to contribute to the detailed observation of these waves and their use in coronal seismology, particularly the usefulness of observing multiple harmonics and understanding of dispersion. Fast kink-mode oscillations of coronal loops, observed as rapidly decaying transverse displacements, are a well-understood wave mode used for seismology. The simultaneous detection of multiple harmonics can provide more information, allowing one to match the observed dispersion with that predicted by theory. Extreme ultraviolet observations of a coronal loop hosting a standing kink oscillation are analysed using image processing and time series techniques. The presence of two simultaneous harmonics is revealed, a fundamental mode at a period of ∼ 8 minutes and its third harmonic at ∼ 2.6 minutes. The ratio of periods P1/3P3 was found to be ∼ 0.87, whose departure from unity indicates a non-uniform distribution of kink speed through the loop. For all locations, the ratio of damping time to period for the two harmonics were found to agree within error, validating the widely assumed 1d resonant absorption theory used to explain a kink oscillation’s rapid damping. This is the first time a measurement of the signal quality for a higher harmonic of a kink oscillation has been reported with spatially resolved data. One exciting development in coronal seismology is the recent detection of decay-less oscillations, which are a different regime of fast-kink oscillations omnipresent in coronal loops. The first detection of a coronal loop exhibiting multi-modal decay-less oscillations is presented, in which both the loop’s fundamental mode (P1 = 10.3 +1.5 −1.7 minutes) and its second harmonic (P2 = 7.4 +1.1 −1.3 minutes) are detected. To make this detection possible, the observational data was passed through a novel motion magnification algorithm to accentuate transverse oscillations. An illustration of seismology using the ratio P1/2P2 ∼ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations, and adds credence to their interpretation as standing kink mode oscillations. There is a myriad of MHD oscillation modes, and whilst fast-kink modes are observed as transverse displacements of the plasma non-uniformity, slow modes may be observed as intensity enhancements. Analysis of such propagating slow modes observed in a fan of coronal loops above a sunspot is performed. The instantaneous velocities and periods of these intensity enhancements are measured and compared in different temperature passbands and azimuthal angles. The waves seen in the 171˚A channel (∼ 0.6 MK) appeared slower than when observed co-spatially in the 193˚A (∼ 1.58 MK). This contradicts the expectation that the phase speed is approximately the local sound speed, which varies as the square root of the temperature. This discrepancy is resolved by attributing the difference in apparent velocity to different inclination angles, which are estimated to be 9° ± 3° from the vertical for the waves seen in 193 A, and 19° ± 4° when seen in 171 A. This provides some evidence supporting the theory that coronal loops are formed of several distinct, unresolved strands of different temperature. From the theoretical point of view, the dispersion relation governing slow MHD modes in the presence of a wave-induced misbalance between the plasma heating and cooling mechanisms is developed. The thin flux tube approximation is used to account for finite-β effects, and thermal conduction is also included. The dispersion relation in the limits of weak non-adiabaticity and strong non-adiabaticity with finite-β is identified. It is found that the characteristic timescales of this imbalance (e.g. damping time) may be expressed in terms of the partial derivatives of the combined heating/cooling function with respect to constant gas pressure and constant magnetic pressure. Moreover, these characteristic timescales for the thermal misbalance coincide with typical MHD wave periods for a large range of densities and temperatures typical of the corona. Thus in the general case the dispersion on slow waves by the wave-induced thermal misbalance should not be neglected, and its inclusion may resolve some contradictions that have arisen when attributing the rapid damping of slow modes to thermal conduction or compressive viscosity alone. Instability criteria for the slow mode and entropy (thermal) mode are expressed in terms of a parameterisation of the unknown coronal heating function, under this thin flux tube approximation. Finally, noting that observations of slow modes in the corona do not show over-stability, and that the thermal mode does not appear to be unstable in general (with the exception of coronal rain), a new way of constraining the coronal heating function is presented

Aeronautical Engineering - A special bibliography with indexes /supplement 1/

Annotated reference bibliography on aeronautical engineering document