Structure of turbulence in stratified media

Bolgiano, R.

doi:10.1029/jz067i008p03015

Cited by 80 publications

(51 citation statements)

References 5 publications

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“…As argued by Rincon (2007), a good starting point is the Bolgiano-Obukhov (BO59, see Oboukhov 1959;Bolgiano 1962) phenomenology, which is based on the following assumptions: (i) a constant spectral flux of buoyancy fluctuations follows from the temperature/energy equation, (ii) a balance between the inertial and buoyancy terms in the momentum equation, and (iii) isotropy of motions. BO59…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Supergranulation and multiscale flows in the solar photosphere

Rincon

Roudier

Schekochihin

et al. 2017

A&A

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The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future highresolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.

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Section: Theoretical Considerationsmentioning

confidence: 99%

Supergranulation and multiscale flows in the solar photosphere

Rincon

Roudier

Schekochihin

et al. 2017

A&A

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“…It is indeed well established that a variety of characteristic power law regimes can be derived for all kinds of turbulent complex flows depending on the detailed physical processes at work in the flow (e.g. shear turbulence (Lumley 1967;Lohse & Müller-Groeling 1996), stably and unstably stratified turbulence (Obukhov 1959;Bolgiano 1959Bolgiano , 1962L'vov 1991), MHD turbulence (Schekochihin et al 2008, and references therein)) and on the relevant range of scales (e.g. injection, inertial or dissipation range) for each physical field in the problem.…”

Section: Sub-granulation Scales: An Injection-diffusive Range ?mentioning

confidence: 99%

On the power spectrum of solar surface flows

Rieutord

Roudier

Rincon

et al. 2010

A&A

113

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Context. The surface of the Sun provides us with a unique and very detailed view of turbulent stellar convection. Studying its dynamics can therefore help us make significant progress in stellar convection modelling. Many features of solar surface turbulence like the supergranulation are still poorly understood. Aims. The aim of this work is to give new observational constraints on these flows by determining the horizontal scale dependence of the velocity and intensity fields, as represented by their power spectra, and to offer some theoretical guidelines to interpret these spectra. Methods. We use long time-series of images taken by the Solar Optical Telescope (SOT) on board the Hinode satellite; we reconstruct both horizontal (by granule tracking) and vertical (by Doppler effect) velocity fields in a field-of-view of ∼ 75×75 Mm 2 . The dynamics in the subgranulation range can be investigated with unprecedented precision thanks to the absence of seeing effects and the use of the modulation transfer function of SOT for correcting the spectra. Results. At small subgranulation scales down to 0.4 Mm the spectral density of kinetic energy associated with vertical motions exhibits a k −10/3 -like power law, while the intensity fluctuation spectrum follows either a k −17/3 or a k −3 -like power law at the two continuum levels investigated (525 and 450 nm respectively). We discuss the possible physical origin of these scalings and interpret the combined presence of k −17/3 and k −10/3 power laws for the intensity and vertical velocity as a signature of buoyancy-driven turbulent dynamics in a strongly thermally diffusive regime. In the mesogranulation range and up to a scale of 25 Mm, we find that the amplitude of the vertical velocity field decreases like λ −3/2 with the horizontal scale λ. This behaviour corresponds to a k 2 spectral power law. Still in the 2.5-10 Mm mesoscale range, we find that intensity fluctuations in the blue continuum also follow a k 2 power law. In passing we show that granule tracking cannot sample scales below 2.5 Mm. We finally further confirm the presence of a significant supergranulation energy peak at 30 Mm in the horizontal velocity power spectrum and show that the emergence of a pore erases this spectral peak. We tentatively estimate the scale height of the vertical velocity field in the supergranulation range and find 1 Mm; this value suggests that supergranulation flows are shallow.

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“…Physically, f β (k) accounts for stirring of a mode k by all other modes; it is solenoidal, zero-mean, white noise in time, isotropic and homogeneous in time and space. Its correlation function is thus given by 18) where the forcing amplitude D is proportional to the energy dissipation rate . As elaborated in Sukoriansky et al [6], the proportionality factor is not adjustable; it is calculated from the energy balance considerations.…”

Section: Langevin Equation With the Renormalized Temperature Green Fumentioning

confidence: 99%

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

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Structure of turbulence in stratified media

Cited by 80 publications

References 5 publications

Supergranulation and multiscale flows in the solar photosphere

Supergranulation and multiscale flows in the solar photosphere

On the power spectrum of solar surface flows

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

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