scholarly journals Localization of high-frequency waves propagating in a locally periodic medium

2010 ◽  
Vol 140 (5) ◽  
pp. 897-926 ◽  
Author(s):  
G. Allaire ◽  
L. Friz
Keyword(s):  
High Frequency ◽  
Bloch Wave ◽  
Positive Definite ◽  
Length Scale ◽  
Periodic Media ◽  
Finite Multiplicity ◽  
Quadratic Potential ◽  
Countable Sequence ◽  
High Frequency Waves ◽  
Envelope Functions

AbstractWe study the homogenization and localization of high-frequency waves in a locally periodic media with period ε. We consider initial data that are localized Bloch-wave packets, i.e. that are the product of a fast oscillating Bloch wave at a given frequency ξ and of a smooth envelope function whose support is concentrated at a point x with length scale $\sqrt\varepsilon$. We assume that (ξ, x) is a stationary point in the phase space of the Hamiltonian λ(ξ, x), i.e. of the corresponding Bloch eigenvalue. Upon rescaling at size $\sqrt\varepsilon$ we prove that the solution of the wave equation is approximately the sum of two terms with opposite phases which are the product of the oscillating Bloch wave and of two limit envelope functions which are the solution of two Schrödinger type equations with quadratic potential. Furthermore, if the full Hessian of the Hamiltonian λ(ξ, x) is positive definite, then localization takes place in the sense that the spectrum of each homogenized Schrödinger equation is made of a countable sequence of finite multiplicity eigenvalues with exponentially decaying eigenfunctions.

Short and Long Length-Scale Disturbances Leading to Rotating Stall in an Axial Compressor Stage With Different Stator/Rotor Gaps

2002 ◽  
Vol 124 (3) ◽  
pp. 376-384 ◽  
Author(s):  
M. Inoue ◽  
M. Kuroumaru ◽  
S. Yoshida ◽  
M. Furukawa
Keyword(s):  
High Frequency ◽  
Wavelet Transforms ◽  
Axial Compressor ◽  
Leading Edge ◽  
Rotating Stall ◽  
Short Length ◽  
Length Scale ◽  
Compressor Stage ◽  
Stall Inception ◽  
High Frequency Waves

The transient processes of rotating stall evolution have been investigated experimentally in a low-speed axial compressor stage with three stator-rotor gaps. The pressure traces at eight circumferential locations on the casing wall near the rotor leading edge have been analyzed by the wavelet transforms. With the appropriate mother wavelets, the evolution of short and long length-scale disturbances leading to the stall can be captured clearly. Behavior of these disturbances is different depending on the stator-rotor gap. For the large and middle gap, the stall inception is detected by a spiky short length-scale disturbance, and the number of spiky waves increases to generate the high frequency waves. They become the short length-scale part-span stall cells at the mild stall for the large gap, while they turn into a big stall cell with growth of a long length-scale disturbance for the middle gap. In the latter case, therefore, the stalling process was identified with “high-frequency stall inception.” For the small stator-rotor gap, the stalling process is identified with “long wavelength stall inception” and supported the recent computational model for the short wavelength stall inception by showing that closing the rotor-stator gaps suppressed the growth of short length-scale disturbances. From the measurement of the pressure field traces on the casing wall, a hypothesis has been developed that the short length-scale disturbance should result from a separation vortex from a blade surface to reduce circulation. The processes of the stall evolution are discussed on this hypothesis.

First VIKING results: high frequency waves

1988 ◽  
Vol 37 (3) ◽  
pp. 469-474 ◽  
Author(s):  
A Bahnsen ◽  
M Jespersen ◽  
E Ungstrup ◽  
R Pottelette ◽  
M Malingre ◽  
...  
Keyword(s):  
High Frequency ◽  
High Frequency Waves

Preferential acceleration of heavy ions from thermal velocities

1968 ◽  
Vol 46 (10) ◽  
pp. S638-S641 ◽  
Author(s):  
D. B. Melrose
Keyword(s):  
Frequency Spectrum ◽  
High Frequency ◽  
Heavy Ions ◽  
Crab Nebula ◽  
Low Frequency ◽  
High Frequency Waves ◽  
Hydromagnetic Waves ◽  
The Crab Nebula ◽  
Low Frequency Waves

The acceleration of ions from thermal velocities is analyzed to determine conditions under which heavy ions can be preferentially accelerated. Two accelerating mechanisms involving high-and low-frequency hydromagnetic waves respectively are considered. Preferential acceleration of heavy ions occurs for high-frequency waves if the frequency spectrum falls off faster than (frequency)−1. For the low-frequency waves heavy ions are less effectively accelerated than lighter ions. However, very heavy ions can be preferentially accelerated, the abundances of the very heavy ions being enhanced by a factor Ai over the thermal abundances. Acceleration of ions in the envelope of the Crab nebula is considered as an example.

Implementation of the Ffowcs Williams-Hawkings Equation: Predicting the Far Field Noise From Airfoils While Using Boundary Layer Tripping Mechanisms

2018 ◽  
Author(s):  
Andrew L. Bodling ◽  
Anupam Sharma
Keyword(s):  
Boundary Layer ◽  
High Frequency ◽  
Permeable Surface ◽  
Far Field ◽  
Trailing Edge ◽  
Extraneous Noise ◽  
Field Noise ◽  
High Frequency Waves

A study was done to investigate how boundary layer tripping mechanisms can affect the ability of a permeable surface FW-H solver to predict the far field noise emanating from an airfoil trailing edge. The far field noise in a baseline airfoil as well as the baseline airfoil fitted with fin let fences was analyzed. Two numerical boundary layer tripping mechanisms were implemented. The results illustrated the importance of choosing a permeable integration surface that is outside any high frequency waves emanating from the trip region. The results also illustrated the importance of choosing a boundary layer tripping mechanism that minimizes any extraneous noise so that an integration surface can be taken close to the airfoil.

scholarly journals A new asymptotic method for the modeling of near-field accelerograms

1984 ◽  
Vol 74 (2) ◽  
pp. 539-557
Author(s):  
P. Bernard ◽  
R. Madariaga
Keyword(s):  
High Frequency ◽  
Near Field ◽  
Dislocation Model ◽  
Rupture Propagation ◽  
Time Step ◽  
Change Of Variables ◽  
High Frequency Waves ◽  
Stopping Phases ◽  
Simple Integration ◽  
Frequency Radiation

Abstract We study high-frequency radiation from a dislocation model of rupture propagation at the earthquake source. We demonstrate that in this case all the radiation emanates from the rupture front and, by a change of variables, that at any instant of time the high-frequency waves reaching an observer come from a line on the fault plane that we call isochrone. An asymptotic approximation to near-source velocity and acceleration is obtained that involves a simple integration along the isochrones for every time step. It is shown that wave front discontinuities (critical or stopping phases) are radiated every time an isochrone becomes tangent to a barrier. This leads to what we call the critical ray approximation which is given in a closed form. The previous results are compared with discrete wavenumber synthetics obtained by Bouchon (1982) for the Gilroy 6 recording of the Coyote Lake earthquake of 1980. The fit between the asymptotic and full numerical method is extremely good. The critical ray approximation permits the identification of different phases in Bouchon's synthetics and the prediction of the behavior of the signal in the vicinity of their arrival time.

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