Proper Orthogonal Decomposition of Solar Photospheric Motions

Vecchio, A.; Carbone, V.; Lepreti, F.; Primavera, Leonardo; Sorriso‐Valvo, L.; Veltri, P.; Alfonsi, Giancarlo; Straus, T.

doi:10.1103/physrevlett.95.061102

Cited by 29 publications

(29 citation statements)

References 24 publications

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“…Other kinds of masks derived from the properties of the observations themselves have been used by Vecchio et al (2005). These masks are based upon a Proper Orthogonal Decomposition (POD) of the velocity field, which is nothing less than the computation of eigenvalues and eigenvectors of that vector field.…”

Section: Spatial Filters: Spatially Resolved Solar Imagesmentioning

confidence: 99%

The quest for the solar g modes

Appourchaux

Belkacem

Broomhall

et al. 2010

Astron Astrophys Rev

125

127

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A ce compte, toutes les sciences ne seraient que des applications inconscientes du calcul des probabilités ; condamner ce calcul, ce serait condamner la science tout entière." "From this point of view all the sciences would only be unconscious applications of the calculus of probabilities. And if this calculus be condemned, then the whole of the sciences must also be condemned."Henri Poincaré, 1914, La Science et l'hypothèseAbstract Solar gravity modes (or g modes) -oscillations of the solar interior for which buoyancy acts as the restoring force -have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core.Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -from both data and data-analysis perspectives -to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.

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Section: Spatial Filters: Spatially Resolved Solar Imagesmentioning

confidence: 99%

The quest for the solar g modes

Appourchaux

Belkacem

Broomhall

et al. 2010

Astron Astrophys Rev

125

127

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“…This approach makes use of the proper orthogonal decomposition (POD) technique, initially developed to study coherent structures in channel flow turbulence and recently applied to various astrophysical problems (Rees et al 2000;Carbone et al 2002;Lawrence et al 2004;Vecchio et al 2005;Vecchio 2006). As the POD technique is not yet widely known, we describe it in some detail in the following.…”

Section: A2 the Proper Orthogonal Decomposition Approachmentioning

confidence: 99%

The solar chromosphere at high resolution with IBIS

Vecchio

Cauzzi

Reardon

2008

A&A

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Context. The exact nature of the quiet solar chromosphere and especially its temporal variation, are still subjects of intense debate. One of the contentious issues is the possible role of the magnetic field in structuring the quieter solar regions. Aims. We characterize the dynamics of the quiet inter-network chromosphere by studying the occurrence of acoustic shocks and their relation with the concomitant photospheric structure and dynamics, including small scale magnetic structures.Methods. We analyze a comprehensive data set that includes high-resolution chromospheric (Ca ii 854.2 nm) and photospheric (Fe i 709.0 nm) spectra obtained with the IBIS imaging spectrometer in two quiet-Sun regions. This is complemented by highresolution sequences of MDI magnetograms of the same targets. From the chromospheric spectra we identify the spatio-temporal occurrence of the acoustic shocks. We compare it with the photospheric dynamics by means of both Fourier and wavelet analysis and study the influence of magnetic structures on the phenomenon. Results. Mid-chromospheric shocks occur within the general chromospheric dynamics pattern of acoustic waves propagating from the photosphere. In particular, they appear as a response to underlying powerful photospheric motions at periodicities nearing the acoustic cut-off, consistent with 1-D hydrodynamical modeling. However, their spatial distribution within the supergranular cells is highly dependent on the local magnetic topology, both at the network and internetwork scale. We find that large portions of the internetwork regions undergo very few shocks, since they are "shadowed" by the horizontal component of the magnetic field. The latter is betrayed by the presence of chromospheric fibrils, observed in the core of the Ca ii line as slanted structures with distinct dynamical properties. The shadow mechanism also appears to operate on the very small scales of inter-network magnetic elements, and provides for a very pervasive influence of the magnetic field even in the quietest region analyzed. Conclusions. The magnetic field might play a larger role in structuring the quiet solar chromosphere than normally assumed. The presence of fibrils highlights a clear disconnection between the photospheric dynamics and the response of the geometrically overlaying chromosphere. As these results hold for a mid-chromospheric indicator such as the Ca ii 854.2 line, it is expected that diagnostics formed in higher layers, such as UV lines and continua, will be affected to a greater extent by the presence of magnetic fields, even in quiet regions. This is relevant for the chromospheric models that make use of such diagnostics.

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“…The KL technique is optimal for modeling or reconstructing a signal in the sense that, for a given number of modes, the projection into the subspace used for modeling contains the most kinetic energy possible on average, or, equivalently, the decay of the tail of the empirical eigenspectrum is always faster (or at most as fast) than the tail of the spectrum based on any other possible basis, Fourier spectrum included. This technique has proven to give rather satisfactory results in several different cases (Alfonsi and Primavera [74][75][76][77], Alfonsi et al [78][79][80], Carbone et al [81], Vecchio et al [82], and Zhang et al [83]). …”

Section: Overview Of Karhunen-loève Decomposition Techniquementioning

confidence: 99%

Numerical Simulations of Wave-Induced Flow Fields around Large-Diameter Surface-Piercing Vertical Circular Cylinder

Alfonsi

2015

Computation

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A computational analysis is performed on the diffraction of water waves induced by large-diameter, surface-piercing, vertical circular cylinder. With reference to linear-wave cases, the phenomenon is preliminarly considered in terms of velocity potential, a simplified theoretical framework in which both hypotheses of inviscid fluid and irrotational flow are incorporated. Then, and as a first-approximation analysis, the Euler equations in primitive variables are considered (a framework in which the fluid is still handled as inviscid, but the field can be rotational). Finally, the real-fluid behavior is analyzed, by numerically integrating the full Navier-Stokes equations (viscous fluid and rotational field) in their velocity-pressure formulation, by following the approach of the Direct Numerical Simulation (DNS, no models are used for the fluctuating portion of the velocity field). For further investigation of the flow fields, the swirling-strength criterion for flow-structure extraction, and the Karhunen-Loève (KL) decomposition technique for the extraction of the most energetic flow modes respectively, are applied to the computed fields. It is found that remarkable differences exist between the wave-induced fields, as derived within the different computing frameworks tested.

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Proper Orthogonal Decomposition of Solar Photospheric Motions

Cited by 29 publications

References 24 publications

The quest for the solar g modes

The quest for the solar g modes

The solar chromosphere at high resolution with IBIS

Numerical Simulations of Wave-Induced Flow Fields around Large-Diameter Surface-Piercing Vertical Circular Cylinder

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