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At least 1,225 records · Page 68

Modulational stability of periodic solutions of the Kuramoto-Sivaskinsky equation

We study the long-wave, modulational, stability of steady periodic solutions of the Kuramoto-Sivashinsky equation. The analysis is fully nonlinear at first, and can in principle be carried out to all orders in the small parameter, which is the ratio of the spatial period to a characteristic length of the envelope perturbations. In the linearized regime, we recover a high-order version of the results of Frisch, She, and Thual, which shows that the periodic waves are much more stable than previously expected.

Papageorgiou, Demetrios T.↗

Millimeter-wave Sensor Image Enhancement

Images of an airborne scanning radiometer operating at a frequency of 98 GHz were analyzed. The mm wave images were obtained using the JPL mm wave imaging sensor. The goal was to enhance the information content of these images and make their interpretation easier for human analysis. A visual interpretative approach was used for information extraction from the images. This included application of nonlinear transform techniques for noise reduction and for color, contrast, and edge enhancement. Results of the techniques on selected mm wave images are shown.

Wilson, William J.↗

Soliton Properties of Coupled g-Mode Oscillations

Several features typical of solitons are also exhibited by stellar g-modes when coupled into "sets" that have unique rotation rates relative to the star. Enhanced nuclear burning due to weakly nonlinear amplitudes in a small portion of the stellar core holds each set together against dispersion. As the nonlinear regions of each set rotate past each other they have a complex interaction (shown in a video), yet emerge from this with their original wave forms. Other similarities with solitons we mentioned, including the physical origin of a phase shift. in longitude due to the interaction. These similarities suggest that a fully nonlinear derivation of g-mode sets may be able to show that their large amplitude regions approach true solitons.

Wolff, Charles L.↗

Equilibrium wave spectrum and sea state bias in satellite altimetry

For a well-developed sea at equilibrium with a constant wind, the energy-containing range of the wavenumber spectrum for wind-generated gravity waves is approximated by a generalized power law involving the angular spread function and mu, interpreted as a fractal codimension of a small surface patch. Dependence of mu on the wave age is estimated, and the 'Phillips constant', beta, along with the low-wavenumber boundary, k0, of the inertial subrange are analyzed on the basis of the wave action and energy conservation principles. The resulting expressions are employed to evaluate various non-Gaussian statistics of a weakly nonlinear sea surface, which determine the sea state bias in satellite altimetry. The locally accelerated decay of the spectral density function in a high-wavenumber dissipation subrange is pointed out as an important factor of wave dynamics and the geometrical optics treatment of the sea state bias. The analysis is carried out in the approximation of a unidirectional wave field and confined to the case of a well-developed sea.

Glazman, Roman E.↗

Nonlinear analysis of a family of LC tuned inverters

Four widely used self-oscillating dc-to-square-wave parallel inverters which employ an inductor-capacitor tuned network to determine the oscillation frequency are reduced to a common equivalent RLC network, The techniques of singular-point analysis and state-plane interpretations are employed to describe the steady-state and transient behavior of these circuits and to elucidate the three possible modes of operation: quasi-harmonic, relaxation, and discontinuous. Design guidelines are provided through a study of the influence of circuit parameter variations on the characteristics of oscillation and on frequency stability. Several examples are provided to illustrate the usefulness of this analysis when studying such problems as transistor emitter-to-base junction breakdown during oscillations and the design of starting circuits to insure self-excited oscillations in these inverters.

Lee, F. C. Y.↗

Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system

It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.

Whelan, D. A.↗

Structure and evolution of small-amplitude intermediate shock waves

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier-Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine-Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.

Kennel, C. F.↗

Acoustic nonlinearity in dispersive solids

An investigation to consider the effects of dispersion on the generation of the static acoustic wave component is presented. It is considered that an acoustic toneburst may be modeled as a modulated continuous waveform and that the generated initial static displacement pulse may be viewed as a modulation-confined disturbance. A theoretical model for the generation of the acoustic modulation solitons evolved is developed and experimental evidence in samples of vitreous silica demonstrating the essential validity of the model is provided.

Cantrell, John H.↗

On nonlinear cascades of enstrophy over the tropics at 200 mb during two Northern Hemisphere summers

Diagnostic computations of nonlinear cascades of enstrophy have been performed in the wavenumber domain for two northern summers. Attention is focused on the interactions among the waves, the interaction between the zonal flow and a given wave and the exchanges due to the beta effect. It is found that two wave ranges (low and intermediate wavenumbers) cascade enstrophy to two ranges of wavenumbers. Calculations are also performed to evaluate the contribution from the standing (92-day mean) and transient modes to the nonlinear enstrophy cascade.

Chen, T.-C.↗

Nonlinear feedbacks between stratocumulus and synoptic-scale systems

The research progress for FY-91 is presented. Wintertime and springtime stratocumulus observations for a number of 5-day periods were collected. Close correlations between the mean 850 and 500 mb trough positions and cloud cover over marine areas were found. A linear study of the radiatively-driven interaction between stratocumulus and synoptic-scale waves was completed. Shallow surface-bound traveling waves are created that are strongly dependent on the phase relation between cloud and low-level flow. A nonlinear model is now under development that will permit a more detailed investigation of these interactions. Finally, a nonlinear study of the modifications of the background flow by boundary layer roll vortices was revised for submission for publication. The research plans for FY-92 are included.

Clark, John H. E.↗

Nonlinear evolution of protostellar disks and light modulations in young stellar objects

An evolutionary model of dynamical processes in protostellar disks is described and illustrated with graphs of typical results. The effective transport mechanisms are discussed, including thermal convection, nonaxisymmetric gravitational instabilities in the outer regions of disks, and wave propagation. Consideration is then given to the stages of dynamical evolution, FU Ori outburst phenomena, unsteady accretion-disk flows, and nonlinear feedback as a mechanism to modulate mass transfer. The simulations show that mass redistribution is determined by angular-momentum transfer, which in turn is regulated by the effective viscosity generated by convectively driven turbulence. Significant mass transfer occurs as a result of mixing of infalling material with disk gas and is affected by the tidal torque associated with the growth of nonaxisymmetric disturbances in the outer disk. The time scale for disk evolution is found to be about 1 Myr.

Lin, D. N. C.↗

Correspondence between discrete and continuous models of excitable media: trigger waves

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Non-NASA Center↗

An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks

The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.

HECC↗

Solitonlike solutions in loop current eddies

The application of the nonlinear quasi-geostrophic equations to an isolated eddy in the western continental slope region in the Gulf of Mexico is examined for a two-layer ocean model with bottom topography. In the linear limit, solutions are topographic nondispersive waves. Form-preserving solutions, or solitons, have been found. The solution is shown to be a limiting form for a nonlinear dispersive system propagating northward along the topographic waveguide in the western continental slope region in the Gulf of Mexico. Using satellite-tracked drifter data, a linear relationship is found between the amplitude of the deduced stream function of the eddy and its observed translational velocity over the continental slope, which supports the hypothesis that some mesoscale eddies interacting with the continental slope behave as solitons.

Nakamoto, Shoichiro↗

Modeling the Dynamics of the Middle Atmosphere and Lower Thermosphere Under the Influence of Gravity Waves

Our Numerical Spectral Model (NSM), which extends from the ground up into the thermosphere, is non-linear, time-dependent and has been employed for 2D and 3D applications. The standard version of the NSM incorporates Hines' Doppler Spread Parameterization for small scale gravity waves (GW), but planetary waves generated in the troposphere have also been incorporated. The NSM has been applied to describe: (1) the anomalous seasonal variations of the zonal circulation and temperature in the upper mesosphere, (2) the equatorial oscillations (quasi-biennial and semi-annual oscillations (QBO and SAO)) extending from the stratosphere into the upper mesosphere, (3) the diurnal and semi-diurnal tides, and (4) the planetary waves that are excited in the mesosphere. With the emphasis to provide understanding, we present here results from numerical experiments with the NSM that shed light on the GW processes that are of central importance in the mesosphere and lower thermosphere. These are our conclusions: (1) The large semiannual variations in the diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength, but variations in eddy viscosity associated with GW interactions are also important. (2) The semidiurnal tide (SDT) and its phase in particular, is strongly influenced by the mean zonal circulation. The SDT, individually, is also amplified by GW. But the DT filters out GW such that the GW interaction effectively reduces the amplitude of the SDT, producing a strong nonlinear interaction between the DT and SDT. (3) Without external time dependent energy or momentum sources, planetary waves (PW) are generated in the model for zonal wavenumbers 1 to 4, which have amplitudes in the mesosphere above 50 km as large as 40 m/s and periods between 50 and 2 days. The waves are generated primarily during solstice conditions, which indicates that the baroclinic instability (associated with the GW induced reversal in the latitudinal temperature gradient) is playing an important role. Numerical experiment show that GW, directly, also greatly amplify the PW. A common feature of the PW generated in summer and winter is that their vertical wavelengths throughout the mesosphere are large, which indicates that the waves are not propagating freely but are generated throughout the region. Another common feature is that the PW propagate preferentially westward in summer and eastward in winter, being launched from the westward and eastward zonal winds that prevail respectively in summer and winter at altitudes below 80 km. (4) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT. In summary we conclude that GW play major roles in generating and amplifying the dynamical components in the MLT region and, acting principally through wave filtering, produce important non-linear interactions between the components.

Mayr, H. G.↗

Ultrasonic nondestructive materials characterization

A brief review of ultrasonic wave propagation in solid materials is presented with consideration of the altered behavior in anisotropic and nonlinear elastic materials in comparison with isotropic and linear elastic materials. Some experimental results are described in which ultrasonic velocity and attenuation measurements give insight into materials microstructure and associated mechanical properties. Recent developments with laser beam non-contact generation and detection of ultrasound are presented. The results of several years of experimental measurements using high-power ultrasound are discussed, which provide substantial evidence of the inability of presently accepted theories to fully explain the interaction of ultrasound with solid materials. Finally, a special synchrotron X-ray topographic system is described which affords the possibility of observing direct interaction of ultrasonic waves with the microstructural features of real crystalline solid materials for the first time.

Green, R. E., Jr.↗

Determination of the effects of nozzle nonlinearities upon nonlinear stability of liquid propellant rocket motors

The research is reported concerning the development of a three-dimensional nonlinear nozzle admittance relation to be used as a boundary condition in the nonlinear combustion instability theories for liquid propellant rocket engines. The derivation of the nozzle wave equation and the application of the Galerkin method are discussed along with the nozzle response.

Zinn, B. T.↗