Continuous spectrum analysis of roughness-induced transient growth

2009 ◽  
Vol 21 (11) ◽  
pp. 114105 ◽  
Author(s):  
N. A. Denissen ◽  
E. B. White
Keyword(s):  
Continuous Spectrum ◽  
Spectrum Analysis ◽  
Transient Growth

scholarly journals The Bakerian Lecture— On radiant matter spectroscopy. A new method of spectrum analysis

1883 ◽  
Vol 35 (224-226) ◽  
pp. 262-271 ◽  
Keyword(s):  
Continuous Spectrum ◽  
Spectrum Analysis ◽  
New Method ◽  
Great Intensity ◽  
Negative Pole

For several years I have been examining the phenomena presented by various substances when struck by the molecular discharge from the negative pole in a highly exhausted tube. I have ventured to call this discharge “ radiant matter,” and under its influence a large number of substances emit phosphorescent light, some faintly and others with great intensity. On examining the emitted light in the spectroscope most bodies give a faint continuous spectrum, with a more or less decided concentration in one part of the spectrum, the superficial colour of the phosphorescing substance being governed by this preponderating emission in -one or other part of the spectrum. Sometimes, but more rarely, the spectrum of the phosphorescent light is discontinuous, and it is to bodies manifesting this phenomenon that my attention has been specially directed.

Transient growth associated with continuous spectra of the Batchelor vortex

2012 ◽  
Vol 697 ◽  
pp. 35-59 ◽  
Author(s):  
X. Mao ◽  
S. J. Sherwin
Keyword(s):  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Vortex Core ◽  
Azimuthal Angle ◽  
Original Position ◽  
Local Analysis ◽  
Transient Growth ◽  
Transient Effects ◽  
Potential Region ◽  
Optimal Perturbation

AbstractThe spectrum of the Batchelor vortex can be broadly split into a discrete spectrum, a potential spectrum and a free-stream spectrum where, since the last two spectra are both continuous, they can also be considered as one continuous spectrum. The discrete spectrum has been extensively studied but the continuous spectrum has received limited attention in the context of vortex flow. A local transient growth study is conducted and the contribution of the discrete spectrum and the continuous spectrum to the transient growth is separated by constructing optimal perturbations on the discrete or continuous sub-eigenspaces separately. It is found that the significant transient growth is mainly due to the non-normality of the continuous eigenmodes/spectrum whilst the discrete eigenmodes/spectrum have little contribution to the transient energy growth. A matrix-free method, which reduces to the local analysis when appropriate periodic boundary conditions are imposed, is also applied to investigate the transient growth in both a plane of constant azimuthal angle and a plane constant axial location. Previously studies by other authors have demonstrated that at zero azimuthal wavenumber the transient growth reaches infinitely large values over infinite time intervals while the optimal perturbations are located far from the vortex core. Therefore we limited our scope to small values of the time horizon so as to obtain reasonably strong transient effects stemming from physically relevant optimal perturbations. Two mechanisms of transient growth are observed: namely a redistribution of the azimuthal velocity to the azimuthal vorticity and interaction between out-of-vortex-core structures with those within the vortex core. A direct numerical simulation (DNS) of the vortex perturbed by optimal perturbations is conducted to investigate the nonlinear development of the optimal perturbations. In the azimuthally constant decomposed case, it is found that the optimal perturbation induces a string of bubble structures to be generated as a consequence of the non-orthogonality of continuous eigenmodes and the breakdown bubble is induced by viscous diffusion, while in the axially constant decomposition transient growth analysis, it is observed that the optimal perturbations associated with the continuous eigenmodes drive the vortex to vibrate around the initial vortex centre before eventually returning to its original position at larger times. This transient effect provides a mechanism for the ‘vortex meandering’ observed in previous experimental and numerical studies. These optimal perturbations associated with the continuous spectrum with out-of-vortex-core structures are observed to be activated by anisotropic inflow perturbations in the potential region.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

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