Theoretical models and numerical studies of waves in a three-fluid medium
Mathematical models of wave propagation in three-fluid plasma and numerical solutions to dispersion and propagation properties
Murphree, D. L.↗
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Application of wave mechanics theory to fluid dynamics problems: Fundamentals
The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.
Krzywoblocki, M. Z. V.↗
Transverse low frequency wave in a two fluid solar wind
Investigation is made of the properties of low frequency transverse waves in a two-fluid solar wind having a radial magnetic field and radial streaming velocity. In order to examine what effects this streaming medium has on the waves, linearly polarized waves are decomposed into left and right circularly polarized waves. Computation is made of analytic expressions valid to first order for the radial amplitude and phase dependence of these constituent waves. It is shown that after travelling a given distance r, these waves have different amplitudes and phases. The former result causes their superposition to become elliptical rather than linear. The latter causes the axis of the ellipse of polarization to rotate through a well-defined angle. Analytic expressions are obtained for the eccentricity of the ellipse and for the angle of rotation. In analogy with regular Faraday rotation, in which the plane of polarization of a linear polarized wave rotates, the effect is denoted as generalized Faraday rotation.
Solodyna, G. V.↗
Alfven waves in a thermally stratified fluid
The properties of Alfven waves propagating along a uniform horizontal field in a highly conducting incompressible medium in the presence of strong convective instability are examined in the Boussinesq approximation. In particular, it is sought to determine whether there are exact solutions to the dynamical equations in the presence of convective forces. It is shown that a class of exact solutions of arbitrary amplitude, but of limited form, which may be of some physical interest, does exist. For large amplitudes, any mixtures of polarization states are shown to cause scattering into new modes.
Parker, E. N.↗
A theoretical study of aerodynamic noise generation
Study focuses on physical mechanism of waves in fluid such as air. Strong interaction between energy of wave and fluid particle motion causes energy of wave to be dissipated. Dissipation depends not only on momentum, time-rate, and force, but also upon nature and magnitude of entropic-flow effects.
Peter, A. C.↗
A study of longitudinal oscillations of propellant tanks and wave propagations in feed lines. Part 1 - Propagating pressure waves in a fluid-filled cylindrical shell
Theory and equations for propagating pressure waves in liquid filled cylindrical shells
Kanno, J. S.↗
Nonlinear harmonics coupled by parallel wave propagations in a time-dependent plasma flow
In a time-dependent flow, nonlinear harmonics can be excited by coupling between linear waves and flow-induced harmonic waves. Examining the dispersion relations and selection rules for the coupling, we investigate nonlinearly coupled harmonics for waves propagating along the magnetic field line in a magnetized plasma, as well as waves in an unmagnetized plasma. The coupled harmonics in a plasma flow are described by analytic dispersion relations and selection rules. This nonlinear coupling is corroborated by the particle-in-cell simulation. Here, the coupled-harmonics model describes a mechanism for the excitation of nonlinear harmonics from linear waves in a time-dependent flow. The spectral analysis of the dispersion relation provides a useful way to evaluate the spatiotemporal behavior of a plasma flow.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Finite Element Simulation of the Acoustic Pressure Inside a Beverage Container for Non-Thermal, Ultrasound-based Pasteurization
The purpose of this effort is to investigate whether large acoustic pressure waves can be transmitted inside beverage containers to enable pasteurization. Acoustic waves are known to induce large nonlinear compressive forces and shock waves in fluids, suggesting that compression waves may be capable of damaging bacteria inside beverage containers without appreciably increasingly the temperature or altering the freshness and flavor of the beverage contents. Although a combined process such as thermosonication (e.g., sonication with heating) is likely more efficient, it is instructive to compute the acoustic pressure field distribution inside the beverage container. The COMSOL simulations used two and three-dimensional models of beverage containers placed in a water bath to compute the acoustic pressure field. A limitation of these COMSOL models is that they cannot determine the bacterial lysis efficiency, rather the models provide an indirect metric of bacterial lysis based on the magnitude of the pressure field and its distribution.
42 ENGINEERING↗
Traveling and standing waves in binary-fluid convection in finite geometries
The effect of finite geometry on the competition between traveling waves and standing waves in systems with a Hopf bifurcation to a state with spatial structure is considered in the linear and weakly nonlinear regimes. The spatial structure observed by Kolodner et al. (1986) in binary-fluid convection is explained in terms of the reflection of the linear traveling waves. The reflection coefficient is calculated, and is found to go to zero as the frequency of the waves becomes small. The pattern expected in a saturated nonlinear state is discussed.
Cross, M. C.↗
Internal solitary waves in a linearly stratified fluid
The mode shapes for internal solitary waves propagating in a linearly stratified fluid of finite depth are determined in the limit of weak stratification. The solutions obtained for both a fixed upper boundary and a free surface are compared with known results for exponential stratification. The profound changes which occur depending on whether the upper surface is fixed or free are derived from the strong influence of the free surface when the stratification is weak. Evidence is presented supporting the conjecture that the free surface can no longer effect qualitative differences in the modal structure when the fluid is heavily stratified.
Weidman, P. D.↗
Application of wave mechanics theory to fluid dynamics problems: Boundary layer on a circular cylinder including turbulence
The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.
Krzywoblocki, M. Z. V.↗
The generation and propagation of internal gravity waves in a rotating fluid
The present investigation is concerned with an extension of a study conducted bu Maxworthy (1979) on internal wave generation by barotropic tidal flow over bottom topography. A short series of experiments was carried out during a limited time period on a large (14-m diameter) rotating table. It was attempted to obtain, in particular, information regarding the plan form of the waves, the exact character of the flow over the obstacle, and the evolution of the waves. The main basin was a dammed section of a long free surface water tunnel. The obstacle was towed back and forth by a wire harness connected to an electronically controlled hydraulic piston, the stroke and period of which could be independently varied. Attention is given to the evolution of the wave crests, the formation of solitary wave groups the evolution of the three-dimensional wave field wave shapes, the wave amplitudes, and particle motion.
Maxworthy, T.↗
Nearly incompressible fluids. II - Magnetohydrodynamics, turbulence, and waves
The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). Based on a singular expansion technique, modified systems of fluid equations are obtained for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions. NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. It is shown that three distinct NI descriptions exist corresponding to each of the three possible plasma beta regimes. The detailed theory of weakly compressible corrections to the various incompressible MHD descriptions is presented, and the implications for the solar wind are discussed.
Zank, G. P.↗
Nonlinear dynamics of small-scale Alfvén waves
Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k ⊥ d i ≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k ⊥ d i ~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k ⊥ ρ s , k ⊥ d e , or k ∥ d i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d i . We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Surface waves in an incompressible fluid - Resonant instability due to velocity shear
The effects of velocity shear on the resonance absorption of incompressible MHD surface waves are studied. It is found that there are generally values of the velocity shear for which the surface wave decay rate becomes zero. In some cases, the resonance absorption goes to zero even for very small velocity shears. It is also found that the resonance absorption can be strongly enhanced at other values of the velocity shear, so the presence of flows may be generally important for determining the effects of resonance absorption, such as might occur in the interaction of p-modes with sunspots. Resonances leading to instability of the global surface mode can exist, and instability can occur for velocity shears significantly below the Kelvin-Helmholtz threshold. These instabilities may play a role in the development or turbulence in regions of strong velocity shear in the solar wind or the earth's magnetosphere.
Hollweg, Joseph V.↗
Gravity jitter response slosh wave excitation on the fluid in a rotating dewar
The present study investigates the dynamical behavior of fluids, in particular, the effect of surface tension on partially filled fluids in a rotating dewar in a microgravity environment. It is shown that there is a group of wave trains, both in longitudinal and transverse modes, with various frequencies and wavelengths of slosh waves generated by the restoring field force field of gravity jitters and centrifugal forces. The longest wave periods of slosh waves, either the longitudinal or transverse modes, are found to be responsible for the production of wave modes with the highest ratio of maximum wave amplitude to wavelength. The lower frequency slosh waves are the wave modes with higher wave energy than that of the higher frequency slosh waves.
Hung, R. J.↗
Circularly polarized inertial wave vectors in rotating fluids
The Navier-Stokes equations for a rotating fluid are harmonically analyzed for planar motion in an infinite half-space. All solutions are shown to be a sum of two inertial wave vectors, one circularly polarized to the left (CPL) and the other circularly polarized to the right (CPR). These basic solutions are therefore presented in the same nomenclature and form as that found useful by experimentalists in analyzing flow data (called 'rotary spectra'). The CPL wave acts counter to the Coriolis force and consequently has a slower phase speed and larger damping than the CPR wave. At resonance (forcing frequency = Coriolis frequency) the CPR wave has an infinite phase speed and no damping and is the important component leading to the singular nature of the solutions for certain boundary conditions. All possible resonant singularities are explicitly shown. The unsteady development of these unbounded (limited space structure), cyclic (no time origin or structure) flows is presented to show that with time structure the resonant singularities evolve in a self-similar manner.
Cogley, A. C.↗