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Results for “fluid wave harmonics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

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↗
NASA NTRS1976

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.↗
NASA NTRS1987

Particle and fluid simulations of resistive current-driven electrostatic ion cyclotron waves

The results from 1-D numerical simulations of electrostatic ion cyclotron waves (EIC) are presented for a model in which the electrons are a resistive (collisional) fluid. Simulations of both the kinetic and fluid descriptions are performed and compared in order to assess the fundamental limitations of fluid theory for EIC waves. The effect of ion-neutral collisions is also included using a simple Monte Carlo technique. It is found that a small ion-neutral collision frequency destroys the frequency harmonic coupling of kinetic EIC waves and tends to validate the fluid description. The saturation amplitude of the current-driven EIC instability is in agreement with recent laboratory experiments. The coherent nature (extremely narrow spectral width) and phase velocity agree with ground based (coherent backscatter radars) and in situ observations of current-driven EIC waves in the high latitude ionosphere.

Seyler, Charles E.↗
DOE OSTI2023

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↗
NASA NTRS1989

Reciprocal relations for transmission coefficients - Theory and application

The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.

Qu, Jianmin↗
NASA NTRS2001

Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog

The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic field. For the large length scales of the Sun, the flow cycle period tends to be very long. The period, however, can be made to be 22 years, provided the buoyancy frequency (stability) is sufficiently small, thus placing the proposed flow near the base of the convection zone where a dynamo is now believed to operate.

Mayr, Hans G.↗
NASA NTRS1993

A Cascade Model of Wave Turbulence with Applications to Surface Gravity and Capillary Waves

A heuristic approach to the derivation of power spectra of wave motion is described and applied to capillary waves. The case of gravity waves studied earlier is briefly reviewed. In contract to the previous studies, the nonlinearity of the wave motion is not required to be small, and the mean number of resonantly interacting wave harmonics is not limited to a smallest possible number (which is 4 for gravity waves on a deep fluid and 3 for capillary waves). The main external parameter of the problem is the input flux Q of the wave energy related to the mean wind velocity. Depending on its value, wave spectra take various forms---from that corresponding to the weak-turbulence limit to that corresponding to the saturated (Phillips') wave spectra...

Glazman, Roman E.↗
DOE OSTI2023

Electromagnetic Waves in Cold Plasmas

A collisionless fluid model of a plasma is presented and solved to first order in the cold, high frequency limit. From this model, a homogeneous system of linear equations is obtained for a harmonic electric field perturbation from which the Appleton-Hartree equation is derived. Moreover, the polarization states of electromagnetic waves in cold, collisionless plasmas are examined. Complete sets of equations governing the reflection and transmission of electromagnetic waves in both non magnetized and magnetized plasmas are obtained. In solving the boundary problem, the Booker quartic is derived and the nature of its roots discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

On acoustic radiation from a vibrating panel

An experimental and numerical study of the response and radiation from an acoustically loaded aircraft panel is presented. In the experiment, the panel is excited by a normally incident, harmonic wave. Measurements of the panel response and the resulting transmitted pressure are made in both the near- and acoustic far-fields. The numerical computations model the experiment and in particular account for the full coupling between the panel and the surrounding three dimensional acoustic fluid. The results demonstrate that for a sufficiently high excitation level, the panel response becomes nonlinear. The nonlinearity is characterized by the appearance of harmonics and subharmonics in the power spectral densities of the panel motion and consequently in the resulting acoustic radiation. The primary characteristic of the far-field acoustic radiation is the increase in harmonic content relative to the fundamental and subharmonics with increasing distance from the panel. This is shown to be a result of linear and weakly nonlinear wave propagation effects. The numerical results show that the radiated far-field pressure is strongly dependent on the position of the measurement point with respect to the panel center. The experimental and numerical results are in good qualitative agreement.

Frendi, Abdelkader↗
DOE OSTI2023

Excitation of toroidally localized harmonics of global Alfvén eigenmodes

Abstract The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvénic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvénic waves, from the lower frequency (≈30 kHz–≈200 kHz) toroidal Alfvén eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz–3 MHz) global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2 nd harmonic GAE through the intrinsic non-linearity of Global Alfvén modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvénic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2 nd harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength ( n ≈ 20) 2 nd harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1983

Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements

Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.

Kalinowski, A. J.↗
NASA NTRS1983

Propagating plane harmonic waves through finite length plates of variable thickness using finite element techniques

An analysis is given using finite element techniques which addresses the propagaton of a uniform incident pressure wave through a finite diameter axisymmetric tapered plate immersed in a fluid. The approach utilized in developing a finite element solution to this problem is based upon a technique for axisymmetric fluid structure interaction problems. The problem addressed is that of a 10 inch diameter axisymmetric fixed plate totally immersed in a fluid. The plate increases in thickness from approximately 0.01 inches thick at the center to 0.421 inches thick at a radius of 5 inches. Against each face of the tapered plate a cylindrical fluid volume was represented extending five wavelengths off the plate in the axial direction. The outer boundary of the fluid and plate regions were represented as a rigid encasement cylinder as was nearly the case in the physical problem. The primary objective of the analysis is to determine the form of the transmitted pressure distribution on the downstream side of the plate.

Clark, J. H.↗
NASA NTRS1992

Acoustic intensity calculations for axisymmetrically modeled fluid regions

An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones.

Hambric, Stephen A.↗
NASA NTRS1993

Stability of oscillatory two phase Couette flow

We investigate the stability of two phase Couette flow of different liquids bounded between plane parallel plates. One of the plates has a time dependent velocity in its own plane, which is composed of a constant steady part and a time harmonic component. In the absence of time harmonic modulations, the flow can be unstable to an interfacial instability if the viscosities are different and the more viscous fluid occupies the thinner of the two layers. Using Floquet theory, we show analytically in the limit of long waves, that time periodic modulations in the basic flow can have a significant influence on flow stability. In particular, flows which are otherwise unstable for extensive ranges of viscosity ratios, can be stabilized completely by the inclusion of background modulations, a finding that can have useful consequences in many practical applications.

Coward, Adrian V.↗
NASA NTRS2004

Overcoming Geometry-Induced Stiffness with IMplicit-Explicit (IMEX) Runge-Kutta Algorithms on Unstructured Grids with Applications to CEM, CFD, and CAA

My goal is to develop and implement efficient, accurate, and robust Implicit-Explicit Runge-Kutta (IMEX RK) methods [9] for overcoming geometry-induced stiffness with applications to computational electromagnetics (CEM), computational fluid dynamics (CFD) and computational aeroacoustics (CAA). IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using implicit methods. Current algorithms in CEM can only simulate purely harmonic (up to lOGHz plane wave) EM scattering by fighter aircraft, which are assumed to be pure metallic shells, and cannot handle the inclusion of coatings, penetration into and radiation out of the aircraft. Efficient MEX RK methods could potentially increase current CEM capabilities by 1-2 orders of magnitude, allowing scientists and engineers to attack more challenging and realistic problems.

Kanevsky, Alex↗
DOE OSTI2022

Evidence of Nonlinear Seismic Effects in the Earth from Downhole Distributed Acoustic Sensors

Seismic velocities and elastic moduli of rocks are known to vary significantly with applied stress, which indicates that these materials exhibit nonlinear elasticity. Monochromatic waves in nonlinear elastic media are known to generate higher harmonics and combinational frequencies. Such effects have the potential to be used for broadening the frequency band of seismic sources, characterization of the subsurface, and safety monitoring of civil engineering infrastructure. However, knowledge on nonlinear seismic effects is still scarce, which impedes the development of their practical applications. To explore the potential of nonlinear seismology, we performed three experiments: two in the field and one in the laboratory. The first field experiment used two vibroseis sources generating signals with two different monochromatic frequencies. The second field experiment used a surface orbital vibrator with two eccentric motors working at different frequencies. In both experiments, the generated wavefield was recorded in a borehole using a fiber-optic distributed acoustic sensing cable. Both experiments showed combinational frequencies, harmonics, and other intermodulation products of the fundamental frequencies both on the surface and at depth. Laboratory experiments replicated the setup of the field test with vibroseis sources and showed similar nonlinear combinations of fundamental frequencies. Amplitudes of the nonlinear signals observed in the laboratory showed variation with the saturating fluid. These results confirm that nonlinear components of the wavefield propagate as body waves, are likely to generate within rock formations, and can be potentially used for reservoir fluid characterization.

58 GEOSCIENCES↗
NASA NTRS1995

Simulation study of the role of ion kinetics in low-frequency wave train evolution

The evolution of uniform, parallel propagating, low-frequency (less than or approx. ion cyclotron) wave trains is followed with a one-dimensional hybrid numerical code with fluid electrons and particle ions. We show that moderate amplitude (delta B/B less than 1/2) wave trains give instabilities and saturated states which differ completely from pure fluid evolution. This is most clearly seen when beta greater than 1 and instability exists for wavenumbers both below and above the wavenumber of an inital, left-handed wave train or pump wave. For corresponding parameters a fluid theory gives only a narrow range of instability above the pump wavenumber where decay and beat instabilities can occur. in simulations wave energy inverse cascades to smaller wavenumbers and into a greater number of forward than backward going waves. In fluids energy by decay goes mostly to backward ones of smaller wavenumber, and energy by beat goes mostly to forward ones of larger wavenumber. Neither fluid instability explains simulation results. The instability is saturated by thermalizing ions and sometimes exciting small wavenumber electrostatic or acoustic modes. In contrast, saturation in fluids first occurs by generating the harmonics of the growing linear modes. Harmonic generation is mostly absent in simulations. Simulations are carried out to long times and mostly reach a limit beyond which no further significant evolution can occur. Application to Alfvenic fluctuations in the solar wind is discussed.

Vasquez, Bernard J.↗
NASA NTRS1986

A finite element surface impedance representation for steady-state problems

A procedure for determining the scattered pressure field resulting from a monochromatic harmonic wave that is incident upon a layer energy absorbing structure is treated. The situation where the structure is modeled with finite elements and the surrounding acoustic medium (water or air) is represented with either acoustic finite elements, or some type of boundary integral formulation, is considered. Finite element modeling problems arise when the construction of the structure, at the fluid structure interface, are nonhomogeneous and in particular, when the inhomogeneities are small relative to the acoustic wave length. An approximate procedure is presented for replacing the detailed microscopic representation of the layered surface configuration with an equivalent simple surface impedance finite element, which is especially designed to work only at limited frequencies. An example problem is presented using NASTRAN. However, the procedure is general enough to adapt to practically any finite element code having a steady state option.

Kalinowski, A. J.↗