Wave Interaction Theory and LFC

1992 ◽  
pp. 223-232
Author(s):  
Philip Hall
Keyword(s):  
Wave Interaction ◽  
Interaction Theory

Spectral Evolution of a Blocking Episode and Comparison with Wave Interaction Theory

1981 ◽  
Vol 38 (10) ◽  
pp. 2092-2111 ◽  
Author(s):  
Stephen J. Colucci ◽  
Arthur Z. Loesch ◽  
Lance F. Bosart
Keyword(s):  
Wave Interaction ◽  
Interaction Theory ◽  
Spectral Evolution

Tilted Beam-Surface Wave Interaction (Theory of the Clinotron)

2009 ◽  
Vol 68 (3) ◽  
pp. 185-216
Author(s):  
V. Ya. Maleyev ◽  
V. M. Kontorovich
Keyword(s):  
Surface Wave ◽  
Wave Interaction ◽  
Interaction Theory ◽  
Beam Surface

Generalized theory of the stabifity of shock waves in magnetogasdynamics

1971 ◽  
Vol 6 (3) ◽  
pp. 615-627 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Shock Waves ◽  
Electric Field ◽  
Boundary Conditions ◽  
Wave Interaction ◽  
Shock Structure ◽  
Interaction Theory ◽  
Single Treatment ◽  
Special Cases ◽  
The Stability ◽  
Incident Waves

Stability of MGD shock waves can be investigated either by disturbing the shock discontinuity by incident waves and then considering whether the response of the shock is unique and determinate or not, or by studying the behaviour of the dissipative shock structure with variations in the magnitudes of the dissipations. Both approaches yield the same results, which appears at first sight to be a coincidence. In this paper we show, from a single treatment that includes each as special cases, why the two methods yield the same conclusions.Also, by including the Hall term on Ohm's law, we are able to resolve the uncertainty about the stability of switch-on and switch-off shocks that occurs in the usual MHD treatment of the problem. Finally, it is shown that the Hall term also introduces the possibility of electric field layers in the unsteady shock and thereby reduces the number of shock boundary conditions. This throws some doubt on the value of the wave-interaction theory for shocks in real plasmas.

scholarly journals Exact coherent structures in stably stratified plane Couette flow

2017 ◽  
Vol 826 ◽  
pp. 583-614 ◽  
Author(s):  
D. Olvera ◽  
R. R. Kerswell
Keyword(s):  
Couette Flow ◽  
Coherent Structures ◽  
Wave Interaction ◽  
Stable Stratification ◽  
Boundary Region ◽  
Interaction Theory ◽  
Plane Couette Flow ◽  
Edge Tracking ◽  
Kolmogorov Scale ◽  
Rayleigh Benard

The existence of exact coherent structures in stably stratified plane Couette flow (gravity perpendicular to the plates) is investigated over Reynolds–Richardson number ($Re$–$Ri_{b}$) space for a fluid of unit Prandtl number $(Pr=1)$ using a combination of numerical and asymptotic techniques. Two states are repeatedly discovered using edge tracking – EQ7 and EQ7-1 in the nomenclature of Gibson & Brand (J. Fluid Mech., vol. 745, 2014, pp. 25–61) – and found to connect with two-dimensional convective roll solutions when tracked to negative $Ri_{b}$ (the Rayleigh–Bénard problem with shear). Both these states and Nagata’s (J. Fluid Mech., vol. 217, 1990, pp. 519–527) original exact solution feel the presence of stable stratification when $Ri_{b}=O(Re^{-2})$ or equivalently when the Rayleigh number $Ra:=-Ri_{b}Re^{2}Pr=O(1)$. This is confirmed via a stratified extension of the vortex wave interaction theory of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). If the stratification is increased further, EQ7 is found to progressively spanwise and cross-stream localise until a second regime is entered at $Ri_{b}=O(Re^{-2/3})$. This corresponds to a stratified version of the boundary region equations regime of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58–85). Increasing the stratification further appears to lead to a third, ultimate regime where $Ri_{b}=O(1)$ in which the flow fully localises in all three directions at the minimal Kolmogorov scale which then corresponds to the Osmidov scale. Implications for the laminar–turbulent boundary in the ($Re$–$Ri_{b}$) plane are briefly discussed.

scholarly journals Route to thermalization in the α-Fermi–Pasta–Ulam system

2015 ◽  
Vol 112 (14) ◽  
pp. 4208-4213 ◽  
Author(s):  
Miguel Onorato ◽  
Lara Vozella ◽  
Davide Proment ◽  
Yuri V. Lvov
Keyword(s):  
Wave Interaction ◽  
Discrete Systems ◽  
Interaction Theory ◽  
Random Waves ◽  
Wave Interactions ◽  
Weakly Nonlinear ◽  
Time Dynamics ◽  
Resonant Wave ◽  
Resonant Interactions ◽  
The One

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed.

scholarly journals DIGITIZED NONLINEAR BEAM AND WAVE INTERACTION THEORY OF TRAVELING WAVE TUBE AMPLIFIERS

2013 ◽  
Vol 28 ◽  
pp. 73-88 ◽  
Author(s):  
Weifeng Peng ◽  
Yu Lu Hu ◽  
Zan Cao ◽  
Zhong-Hai Yang
Keyword(s):  
Traveling Wave ◽  
Wave Interaction ◽  
Interaction Theory ◽  
Traveling Wave Tube ◽  
Wave Tube ◽  
Nonlinear Beam

Nonlinear exact coherent structures in pipe flow and their instabilities

2019 ◽  
Vol 868 ◽  
pp. 341-368 ◽  
Author(s):  
Ozge Ozcakir ◽  
Philip Hall ◽  
Saleh Tanveer
Keyword(s):  
Unstable Mode ◽  
Travelling Waves ◽  
Wave Interaction ◽  
Reynolds Numbers ◽  
Large Reynolds Number ◽  
Interaction Theory ◽  
Asymptotic Results ◽  
Instability Modes ◽  
Viscous Core ◽  
The Waves

In this paper, we present computational results of some two-fold azimuthally symmetric travelling waves and their stability. Calculations over a range of Reynolds numbers ($Re$) reveal connections between a class of solutions computed by Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) (henceforth called the WK solution) and the $Re\rightarrow \infty$ vortex–wave interaction theory of Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). In particular, the continuation of the WK solutions to larger values of $Re$ shows that the WK solution bifurcates from a shift-and-rotate symmetric solution, which we call the WK2 state. The WK2 solution computed for $Re\leqslant 1.19\times 10^{6}$ shows excellent agreement with the theoretical $Re^{-5/6}$, $Re^{-1}$ and $O(1)$ scalings of the waves, rolls and streaks respectively. Furthermore, these states are found to have only two unstable modes in the large $Re$ regime, with growth rates estimated to be $O(Re^{-0.42})$ and $O(Re^{-0.92})$, close to the theoretical $O(Re^{-1/2})$ and $O(Re^{-1})$ asymptotic results for edge and sinuous instability modes of vortex–wave interaction states (Deguchi & Hall, J. Fluid Mech., vol. 802, 2016, pp. 634–666) in plane Couette flow. For the nonlinear viscous core states (Ozcakir et al., J. Fluid Mech., vol. 791, 2016, pp. 284–328), characterized by spatial a shrinking of the wave and roll structure towards the pipe centre with increasing $Re$, we continued the solution to $Re\leqslant 8\times 10^{6}$ and we find only one unstable mode in the large Reynolds number regime, with growth rate scaling as $Re^{-0.46}$ within the class of symmetry-preserving disturbances.

Analytic Exploration of the Accuracy of Pierce’s Three-Wave Beam-Wave Interaction Theory of Traveling-Wave Tubes

2018 ◽  
Vol 46 (7) ◽  
pp. 2505-2511 ◽  
Author(s):  
Hai-Jian Qiu ◽  
Yu-Lu Hu ◽  
Quan Hu ◽  
Xiao-Fang Zhu ◽  
Bin Li
Keyword(s):  
Traveling Wave ◽  
Wave Beam ◽  
Wave Interaction ◽  
Interaction Theory ◽  
Beam Wave ◽  
Traveling Wave Tubes ◽  
Beam Wave Interaction
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