An analytical model for Rayleigh–Brillouin scattering spectra in gases

Ma, Yong; Fan, Fan; Liang, Kun; Li, Hao; Yu, Yin; Zhang, Bo

doi:10.1088/2040-8978/14/9/095703

Cited by 25 publications

(30 citation statements)

References 20 publications

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“…in gases with pressures larger than 5 bar, liquids or solid states). However, as discussed in [21], the temperature derived from a simulated reference RB spectrum at a pressure of 1000 hPa and temperature of 292 K has an offset of 8.4% with respect to the reference value. Thus, also this V3 analytical model needs further improvement before it can be used for temperature retrievals from RB spectra at atmospheric conditions.…”

Section: Resultsmentioning

confidence: 95%

“…As an alternative, an analytical RB line shape model, recently developed by Ma et al [21,22] and based on the superposition of three Voigt-functions, was shown to deliver improved performance in temperature retrieval over the three-Gaussian model, especially at pressure values larger than 1000 hPa [21]. The temperature in this V3-model are directly derived from the Brillouin shift as it is usually done with RB spectra measured in the hydrodynamic regime (e.g.…”

Section: Resultsmentioning

confidence: 99%

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Temperature retrieval from Rayleigh-Brillouin scattering profiles measured in air

Witschas¹,

Gu²,

Ubachs³

2014

Opt. Express

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In order to investigate the performance of two different algorithms for retrieving temperature from Rayleigh-Brillouin (RB) line shapes, RB scattering measurements have been performed in air at a wavelength of 403 nm, for a temperature range from 257 K to 330 K, and atmospherically relevant pressures from 871 hPa to 1013 hPa. One algorithm, based on the Tenti S6 line shape model, shows very good accordance with the reference temperature. In particular, the absolute difference is always less than 2 K. A linear correlation yields a slope of 1.01 ± 0.02 and thus clearly demonstrates the reliability of the retrieval procedure. The second algorithm, based on an analytical line shape model, shows larger discrepancies of up to 9.9 K and is thus not useful at its present stage. The possible reasons for these discrepancies and improvements of the analytical model are discussed. The obtained outcomes are additionally verified with previously performed RB measurements in air, at 366 nm, temperatures from 255 K to 338 K and pressures from 643 hPa to 826 hPa [Appl. Opt. 52, 4640 (2013)]. The presented results are of relevance for future lidar studies that might utilize RB scattering for retrieving atmospheric temperature profiles with high accuracy.

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Section: Resultsmentioning

confidence: 95%

Section: Resultsmentioning

confidence: 99%

Temperature retrieval from Rayleigh-Brillouin scattering profiles measured in air

Witschas¹,

Gu²,

Ubachs³

2014

Opt. Express

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“…For the physical process and the experimental set-up of spontaneous RBS and coherent RBS, readers are referred to references [64,65]. The one-dimensional, linearized nature and lack of boundary conditions make the hydrodynamic equations simple and allow for analytical solutions for the Rayleigh-Brillouin scattering problem [24,25,28]. The spectrum of the scattered light is characterized by the Knudsen number (Kn), which is here the ratio of the mean free path of gas molecules to the characteristic length scale (L) of the system, identified as the scattering wave length k 2p .…”

Section: Formulationmentioning

confidence: 99%

“…Leaving aside non-linear configurations, conventional Navier-Stokes equations also fail to describe some of the linear flow problems accurately. For example, it is unsuccessful in describing the actual spectrum shapes in the Rayleigh-Brillouin scattering problem [23][24][25][26][27][28].…”

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confidence: 99%

Recasting Navier–Stokes equations

et al. 2019

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Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermomechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes equations fail.Öttinger [11] also proposed earlier a substitute for the classical Navier-Stokes in his phenomenological GENERIC formalism. In the GENERIC formulation, Öttinger [11] demonstrated that by assuming the row and the column, which are associated with the mass density in the friction matrix to be identically zero, leads to the conventional Navier-Stokes equations. A more general form of friction matrix that includes the basic fact that particles operate diffusive motions, leads to a revised set of transport equations that contain two velocities, which are very similar in nature to the volume and mass velocities. Durst et al [12] based their arguments on that the absence of mass diffusion terms in the continuity equation contradicts constitutive relations for momentum and heat diffusion: when the fluid properties changes spatially in the presence of momentum and heat diffusions, there should also be present the mass diffusion. They later derived the Extended Navier-Stokes equations [12,13,17] based on the mass-diffusion controlled formalism. A late suggestion to substitute the Navier-Stokes is given by Svärd [18].Generally, there are a number of experimental data that standard Navier-Stokes fail to predict. Shock wave structure predictions are a ubiquitous example of Navier-Stokes failure [4,6,19,20]. Experimental data of water flows in carbon nanotubes or confined pores is another research topic showing large deviations from the classical Hagen-Poiseuille equation [21,22]. A convincing theoretical interpretation of this data is still lacking. Leaving aside non-linear configurations, conventional Navier-Stokes equations also fail to describe some of the linear flow problems accurately. For example, it is unsuccessful in describing the actual spectrum shapes in the Rayleigh-Brillouin scattering problem [23][24][25][26][27][28].In the current work, we provide new insights into the ...

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“…Currently, the Tenti S6 model is a well-recognized RBS model for lidar application [14] , which was recently validated in air in labo-ratory conditions. [15] For this consideration, parameterization of the Tenti S6 model based on a linear combination of three Gaussian lines [16] or three Voigt-functions [17] are performed by different research groups.…”

Section: Introductionmentioning

confidence: 99%