Nonlinear Interaction of High-Intensity Disturbances into the Supersonic Boundary Layer

2012 ◽  
Vol 7 (1) ◽  
pp. 38-52
Author(s):  
Natalya Terekhova
Keyword(s):  
Boundary Layer ◽  
Nonlinear Model ◽  
Nonlinear Interaction ◽  
High Intensity ◽  
Plane Waves ◽  
Nonlinear Process ◽  
Supersonic Boundary Layer ◽  
Two Dimensional ◽  
Longitudinal Dynamics ◽  
Second Order Nonlinearity

A nonlinear model of interaction of disturbances in the regime of coupled combinatorial relations is used to explain the dynamics of unstable waves. The model includes effects of self-action and combinatorial interaction of unstable waves. Considered effects in the boundary layer with M = 2 controlled disturbance large enough intensity. In the second case when M = 5,35 examines the interrelationship of two-dimensional perturbations of various nature – vortex and acoustic. Shows the direction of impact of the different components of the nonlinear process. Found that this model of the second order nonlinearity can accurately describe the features of longitudinal dynamics of plane waves

The production of subharmonic waves in the nonlinear evolution of wavepackets in boundary layers

1999 ◽  
Vol 399 ◽  
pp. 301-318 ◽  
Author(s):  
MARCELLO A. F. MEDEIROS ◽  
MICHAEL GASTER
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Interaction ◽  
Strong Influence ◽  
Nonlinear Evolution ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Tollmien Schlichting ◽  
Acoustic Excitations ◽  
Dimensional Wave

The nonlinear evolution of wavepackets in a laminar boundary layer has been studied experimentally. The packets were generated by acoustic excitations injected into the boundary layer through a small hole in the plate. Various packets with different phases relative to the envelope were studied. It was found that for all the packets the nonlinearity involved the appearance of oblique modes of frequency close to the subharmonic of the dominant two-dimensional wave. Moreover, the results confirmed that the phase had a strong influence on the strength of the nonlinear interaction. The experimental observations also indicated that although a subharmonic resonance appeared to be present in the process, it alone could not explain the nonlinear behaviour. The experiment demonstrated that the process must also involve a mechanism that generates oblique waves of frequency lower than the Tollmien–Schlichting band.

scholarly journals Current drive by high intensity, pulsed, electron cyclotron wave packets

2019 ◽  
Vol 203 ◽  
pp. 01009
Author(s):  
Abhay K. Ram ◽  
Kyriakos Hizanidis ◽  
Richard J. Temkin
Keyword(s):  
Wave Packet ◽  
Nonlinear Interaction ◽  
High Intensity ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Electron Cyclotron ◽  
Current Drive ◽  
Particle Interactions ◽  
Wave Particle Interactions ◽  
Energy And Momentum

The nonlinear interaction of electrons with a high intensity, spatially localized, Gaussian, electro-magnetic wave packet, or beam, in the electron cyclotron range of frequencies is described by the relativistic Lorentz equation. There are two distinct sets of electrons that result from wave-particle interactions. One set of electrons is reflected by the ponderomotive force due to the spatial variation of the wave packet. The second set of electrons are energetic enough to traverse across the wave packet. Both sets of electrons can exchange energy and momentum with the wave packet. The trapping of electrons in plane waves, which are constituents of the Gaussian beam, leads to dynamics that is distinctly different from quasilinear modeling of wave-particle interactions. This paper illustrates the changes that occur in the electron motion as a result of the nonlinear interaction. The dynamical differences between electrons interacting with a wave packet composed of ordinary electromagnetic waves and electrons interacting with a wave packet composed of extraordinary waves are exemplified.

Nonlinear instability of a supersonic boundary layer with two-dimensional roughness

2014 ◽  
Vol 752 ◽  
pp. 497-520 ◽  
Author(s):  
Olaf Marxen ◽  
Gianluca Iaccarino ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Boundary Layer ◽  
Large Amplitude ◽  
Supersonic Boundary Layer ◽  
Secondary Instability ◽  
Secondary Wave ◽  
Nonlinear Instability ◽  
Transient Growth ◽  
Primary Wave ◽  
Two Dimensional ◽  
Lower Amplitude

AbstractNonlinear instability in a supersonic boundary layer at Mach 4.8 with two-dimensional roughness is investigated by means of spatial direct numerical simulations (DNS). It was previously found that an important effect of a two-dimensional roughness is to increase significantly the amplitude of two-dimensional waves downstream of the roughness in a certain frequency band through enhanced instability and transient growth, while waves outside this band are damped. Here, we investigate the nonlinear secondary instability induced by a large-amplitude two-dimensional wave, which has received a significant boost in amplitude from this additional roughness-induced amplification. Both subharmonic and fundamental secondary excitation of the oblique secondary waves are considered. We found that even though the growth rate of the secondary perturbations increases compared to their linear amplification, only in some of the cases was a fully resonant state attained by the streamwise end of the domain. A parametric investigation of the amplitude of the primary wave, the phase difference between the primary and the secondary waves, and the spanwise wavenumber has also been performed. The transient growth experienced by the primary wave was found to not influence the secondary instability for most parameter combinations. For unfavourable phase relations between the primary and the secondary waves, the phase speed of the secondary wave decreases significantly, and this hampers its growth. Finally, we also investigated the strongly nonlinear stage, for which both the primary and the subharmonic secondary waves had a comparable, finite amplitude. In this case, the growth of the primary waves was found to vanish downstream of the transient growth region, resulting in a lower amplitude than in the absence of the large-amplitude secondary wave. This feedback also decreases the amplification rate of the secondary wave.

Characteristics of Weakly Nonlinear Interaction of the Instability Waves in a Supersonic Boundary Layer

2008 ◽  
Vol 3 (3) ◽  
pp. 3-13
Author(s):  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov
Keyword(s):  
Boundary Layer ◽  
Nonlinear Interaction ◽  
Stationary Wave ◽  
Supersonic Boundary Layer ◽  
Weakly Nonlinear ◽  
Instability Waves ◽  
Wave Characteristics ◽  
Initial Stage ◽  
Hydrodynamical Stability

The results of an experimental study of weakly nonlinear interaction mechanisms of the instability waves in a supersonic boundary layer on flat plate at Mach number М = 2 are presented in the paper. The downstream evolution of artificial disturbances of small amplitude was studied experimentally. The wave characteristics of traveling disturbances were determined. Obtained, that disturbances evolution at basic frequency was happen in according to the linear theory of hydrodynamical stability. Confirmed, that subharmonical resonance on asymmetrical wave triplet was the reason of amplification of the high inclined subharmonic pulsations. The role of high-frequency disturbances was not significant in the region of weakly nonlinear interactions. The initial stage of a parametrical resonance was characterized by appearance of a stationary wave, jumps of a phase on 180° on frequency of a subharmonic in a cross-section direction, and also not symmetry in amplitude β-spectra.

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