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NASA NTRS1985

The penetration of mountain waves into the middle atmosphere

A linear nonhydrostatic model of gravity waves forced by a bell-shaped ridge is used to investigate the penetration of mountain waves into the stratosphere and mesosphere during winter and fall. Gravity waves with horizontal scales less than 30 km are found to be trapped near the tropopause and the stratopause in regions of strong winds. The effect of trapping these modes produces a disturbance whose structure broadens with height. In the mesosphere the disturbance appears 20-40 km downstream from the forcing depending on the strength of the intervening winds. Wavebreaking associated with the mountain wave is predicted in the lower stratosphere as a result of wave superposition; no individual harmonic reaches breaking amplitude. In the mesosphere, wave breakdown is more prevalent, and the disturbance spectrum is relatively more monochromatic as a result of the filtering of the shorter scale modes by the lower atmosphere.

Schoeberl, M. R.↗

NASA NTRS2012

Explaining Polarization Reversals in STEREO Wave Data

Recently Breneman et al. reported observations of large amplitude lightning and transmitter whistler mode waves from two STEREO passes through the inner radiation belt (L<2). Hodograms of the electric field in the plane transverse to the magnetic field showed that the transmitter waves underwent periodic polarization reversals. Specifically, their polarization would cycle through a pattern of right-hand to linear to left-hand polarization at a rate of roughly 200 Hz. The lightning whistlers were observed to be left-hand polarized at frequencies greater than the lower hybrid frequency and less than the transmitter frequency (21.4 kHz) and right-hand polarized otherwise. Only righthand polarized waves in the inner radiation belt should exist in the frequency range of the whistler mode and these reversals were not explained in the previous paper. We show, with a combination of observations and simulated wave superposition, that these polarization reversals are due to the beating of an incident electromagnetic whistler mode wave at 21.4 kHz and linearly polarized, symmetric lower hybrid sidebands Doppler-shifted from the incident wave by +/-200 Hz. The existence of the lower hybrid waves is consistent with the parametric decay mechanism of Lee and Kuo whereby an incident whistler mode wave decays into symmetric, short wavelength lower hybrid waves and a purely growing (zero-frequency) mode. Like the lower hybrid waves, the purely growing mode is Doppler-shifted by 200 Hz as observed on STEREO. This decay mechanism in the upper ionosphere has been previously reported at equatorial latitudes and is thought to have a direct connection with explosive spread F enhancements. As such it may represent another dissipation mechanism of VLF wave energy in the ionosphere and may help to explain a deficit of observed lightning and transmitter energy in the inner radiation belts as reported by Starks et al.

Breneman, A.↗

NASA NTRS1985

Local effects of gravity wave propagation and saturation

In recent years, gravity waves were recognized to play a major role in the dynamics of the middle atmosphere. Perhaps the major effect of such motions are the reversal of the vertical shear of the mean zonal wind and the occurrence of a large turbulent diffusivity in the mesosphere due to gravity wave saturation. Yet, despite the importance of these gravity wave effects, the processes and the consequences of gravity wave propagation and saturation are only beginning to be understood in detail. The linear saturation theory predicts drag and turbulent diffusion due to saturating wave motion. This theory, however, fails to address a number of issues that are certain to be important for gravity wave propagation and saturation in the middle atmosphere. These issues, including wave transience, wave superposition, local convective adjustment, and nonlinearity, are discussed.

Fritts, D. C.↗

NASA NTRS1987

Evidence for a saturated spectrum of atmospheric gravity waves

The slope and power spectral density of atmospheric velocity fluctuations versus vertical wavenumber at large wavenumbers are observed to be nearly independent of altitude. It is suggested that such a universality is due to saturation of short vertical-scale fluctuations. A brief review of linear gravity wave saturation theory indicates a physical basis for such spectra. It is demonstrated that observed saturation spectra are not solely due to individually saturated waves but most likely result from amplitude limiting instabilities arising from wave superposition. It is also shown that, while the spectrum is saturated at large wavenumbers, the total kinetic energy per unit mass and the characteristic vertical wavelength increase with altitude. Both of these predictions are consistent with observations.

Smith, Steven A.↗

NASA NTRS1990

Transition delay and relaminarization of turbulent flow

Several techniques used for delaying transition both in air and water are overviewed, among them uniform surface heating, localized surface heating, and the application of broad-band disturbance-wave cancellation using the wave superposition principle. It is pointed out that localized heating, in air, can effectively delay transition along a flat plate and reduce viscous drag. Attention is focused on an experiment where the feasibility of relaminarizing turbulent flow over a flat plate with an upstream concave-convex curvature, in air, has been demonstrated using localized heating on the concave part of the curved surface. The flow over the curved surface investigated by thermal mapping using an infrared technique is also covered.

Maestrello, Lucio↗

NASA NTRS2002

Solar Supergranulation Revealed as a Superposition of Traveling Waves

40 years ago two new solar phenomena were described: supergranulation and the five-minute solar oscillations. While the oscillations have since been explained and exploited to determine the properties of the solar interior, the supergranulation has remained unexplained. The supergranules, appearing as convective-like cellular patterns of horizontal outward flow with a characteristic diameter of 30 Mm and an apparent lifetime of 1 day, have puzzling properties, including their apparent superrotation and the minute temperature variations over the cells. Using a 60-day sequence of data from the MDI (Michelson-Doppler Imager) instrument onboard the SOHO (Solar and Heliospheric Observatory) spacecraft, we show that the supergranulation pattern is formed by a superposition of traveling waves with periods of 5-10 days. The wave power is anisotropic with excess power in the direction of rotation and toward the equator, leading to spurious rotation rates and north-south flows as derived from correlation analyses. These newly discovered waves could play an important role in maintaining differential rotation in the upper convection zone by transporting angular momentum towards the equator.

Gizon, L.↗

NASA NTRS2017

Transverse eV Ion Heating by Random Electric Field Fluctuations in the Plasmasphere

Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2-3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07-0.2 eV/h for protons and 0.007-0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti approx. 0.3 eV could potentially explain the observations.

Artemyev, A. V.↗

NASA NTRS1993

Superposition of nonlinear plasma waves

We report results showing that spatially periodic Bernstein-Greene-Kruskal (BGK) waves, which are exact nonlinear traveling wave solutions of the Vlasov-Maxwell equations for collisionless plasmas, satisfy a nonlinear principle of superposition in the small amplitude limit. The analysis explicates the notion of superimposed BGK waves which, as recent numerical calculations suggest, is crucial in the proper description of the time-asymptotic state of a plasma when a large amplitude electrostatic wave undergoes nonlinear Landau damping.

Buchanan, Mark↗

NASA NTRS1992

ULF wave electric fields at synchronous orbit during substorms

Characteristics of the wave electric fields in the frequency range 3 to 22 mHz in the equatorial plane (on GEOS 2) during four substorms were investigated. During intervals of about ten min duration after the substorm onset, large electric fields appear at synchronous orbit. In particular, 3 to 4 spectral peaks in the wave electric field data can be discerned. The dominant models occur at approximately 6 and approximately 10 mHz. Additional peaks exist around 15 and 20 mHz. Although the sense of polarization of these modes varies, these modes tend to have right handed polarization with a typical ellipticity of 0.2. The major axis usually points to the east, lying at an angle of 0 to 50 deg with the azimuthal direction. Mapped into the ionosphere, this corresponds to a north-west orientation. New wave activity appears some 30 to 40 min after the onset lasting about 10 min. The wave properties of these events are relatively close to those events occurring near the substorm onset, except for the orientation angle of the major axis which is now 140 to 180 deg. Because the magnetometer data is not available, the generation mechanism of the waves studied is hard to identify. There is some evidence that these waves are a superposition of compressional waves, produced by the collapse of the magnetotail, and the field line resonances, triggered by these compressional waves.

Laakso, Harri↗

NASA NTRS1986

The relation of gravity waves and turbulence in the mesosphere

Since researchers couldn't prove that the mesospheric turbulence layers are generated by the simultaneously existing short-period gravity waves, they invoked other generation mechanisms than wave breaking. Possible mechanisms like lateral convection (Rottger 1980a), quasi-geostrophic flows at mesoscales (Lilly, 1983) or vortical modes of motion as seen in the ocean (Muller and Pujalet, 1984) could be candidates. Researchers are inclined to see a connection of these layers or laminae with very-long-period internal waves because of the periodicity in their vertical structure and their long mean persistency. Rottger (1980b) had proposed that such structures are due the modulation of the me an temperature and wind profiles by internal waves. The superposition of random or short-term wave-induced wind and temperature fluctuations with the background profile, modulated by very-long-period waves (quasi-inertia waves) then would yield the observed effects, and could explain the vertical periodicity, the long-term mean persistency as well as some short-term variability of their intensity.

Rottger, J.↗

NASA NTRS1988

Evidence of gravity wave saturation and local turbulence production in the summer mesosphere and lower thermosphere during the STATE experiment

This study utilizes the unique data set obtained during the Structure and Atmospheric Turbulence Environment (STATE) experiment, conducted during June 1983 at Poker Flat, Alaska, to examine the structure and characteristics of the wave field near the summer mesopause. It is shown that the rocket and radar data together permit a much more detailed specification of wave parameters than would be possible using either data set alone. The results of this analysis suggest that the wave field near the summer mesopause is composed, in general, of a superposition of wave motions which act collectively to produce regions in which the wave field is convectively or dynamically unstable. These regions are found to correlate well with zones of enhanced turbulence and small-scale wave activity, suggesting the processes and effects of wave field saturation.

Fritts, David C.↗

NASA NTRS1976

On the causes of spectral enhancements in solar wind power spectra

Enhancements in power spectra of the solar-wind ion flux in the frequency neighborhood of 0.5 Hz had been noted by Unti et al. (1973). It was speculated that these were due to convected small-scale density irregularities. In this paper, 54 flux spectra calculated from OGO 5 data are examined. It is seen that the few prominent spectral peaks which occur were not generated by density irregularities, but were due to several different causes, including convected discontinuities and propagating transverse waves. A superposition of many spectra, however, reveals a moderate enhancement at a frequency corresponding to convected features with a correlation length of a proton gyroradius, consistent with the results of Neugebauer (1975).

Unti, T.↗

NASA NTRS1989

Higher order dispersion in the propagation of a gravity wave packet

To the first order of approximation, the complex amplitude of a wave packet in an anisotropic and dispersive medium is convected with the group of velocity. However, a gravity wave is a vector wave. Its wave packet must be formed by superposition of various wave numbers with corresponding frequencies, as is the case for scalar waves, and additionally by superposing many eigenmodes which also depend on the wave number. To represent the vector wave packet self-consistently, it is found that a gradient term must be included in the expansion. For a Guassian wave packet, this gradient term is shown to have important implications on the velocity vector as represented by its hodograph. Numerical results show that the hodograph is influenced by the location of the relative position of interest from the center of a Gaussian pulse. Higher order expansion shows that an initial Gaussian wave packet will retain its Gaussian shape as it propagates, but the pulse will spread in all directions with its major axis undergoing a rotation. Numerical results indicate that these higher order dispersive effects may be marginally observable in the atmosphere.

Yeh, K. C.↗

NASA NTRS1991

A planar oblique wave model for the Euler equations

A numerical method in which any transition between neighboring states in a multidimensional flowfield is reconstructed by a pattern of oblique waves. The wave pattern is obtained from a superposition of model waves which arise in a local linearization based on Rankine-Hugoniot averaging. The strengths and orientations of these waves are derived from a minimum path length rule applied in state space. Two test cases with comparisons to other methods in planar flow problems are presented to demonstrate the strengths of the method, and to point out its weaknesses.

Parpia, Ijaz H.↗

NASA NTRS1988

On the receptivity of free shear layers to two-dimensional external excitation

In this paper, the receptivity of a typical free shear layer to pulse-type and periodic excitation is studied. This is done by solving the initial-value problem completely and studing its long-time behavior. This leads to a wave packet for the pulse. By the superposition of many wave packets, a spatial instability mode when the flow is convectively unstable is generated. This establishes a general and simple relationship between the receptivities for pulse-type and sinusoidal excitations. It is found that a shear layer is very receptive to high-frequency disturbances that are generated near the centerline of the layer.

Balsa, Thomas F.↗

NASA NTRS2012

Wavespace-Based Coherent Deconvolution

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Bahr, Christopher J.↗

NASA NTRS1979

Turboprop interior noise studies

The modal theory of acoustoelasticity is applied to the determination of the sound levels caused by a prescribed external sound excitation which is transmitted through a cylindrical shell. A circumferential traveling pressure wave excitation is studied as representative of a propeller sound field. It is shown how other excitations such as point mechanical loading, plane wave and reverberation random may be synthesized by superposition of circumferential waves. Representative numerical results illustrate the importance of structural and acoustic frequency matching in the determination of interior sound levels and clarify the role of the cylindrical shell ring frequency. An exploratory study of a double wall geometry is conducted.

Dowell, E. H.↗

NASA NTRS2019

Co- and Counter-Propagating Wave Effects in an Absorbing Medium

In this semi-tutorial paper, we revisit the interference phenomena caused by pairs of copropagating or counter-propagating transverse electromagnetic waves by letting the host medium be absorbing. We first consider plane waves in an unbounded medium, summarize the standingwave solution of the Maxwell equations, and discuss specific effects caused by nonvanishing absorption. We then consider the superposition of plane and spherical waves in the context of fartfield electromagnetic scattering by a particle. To this end we modify the classical Jones lemma by allowing nonzero absorption in the host medium and consider its most obvious consequences such as forward- and backscattering interference. The physical similarity of the two scenarios (superpositions of plane waves and superpositions of plane and spherical waves) is discussed.

Interference↗