scholarly journals Analytic derivation of the inertial range of compressible turbulence

2021 ◽  
Vol 33 (7) ◽  
pp. 071706
Author(s):  
I. Goldman
Keyword(s):  
Inertial Range ◽  
Compressible Turbulence ◽  
Analytic Derivation

Cascades of temperature and entropy fluctuations in compressible turbulence

2019 ◽  
Vol 867 ◽  
pp. 195-215 ◽  
Author(s):  
Jianchun Wang ◽  
Minping Wan ◽  
Song Chen ◽  
Chenyue Xie ◽  
Lian-Ping Wang ◽  
...  
Keyword(s):  
Velocity Field ◽  
Velocity Component ◽  
Three Dimensional ◽  
Passive Scalar ◽  
Inertial Range ◽  
Compressible Turbulence ◽  
Equilibrium Relation ◽  
Geometrical Properties ◽  
Conditional Averaging ◽  
Incompressible Turbulence

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

scholarly journals A Kolmogorov-like exact relation for compressible polytropic turbulence

2014 ◽  
Vol 742 ◽  
pp. 230-242 ◽  
Author(s):  
Supratik Banerjee ◽  
Sébastien Galtier
Keyword(s):  
Sound Speed ◽  
Transfer Rate ◽  
Inertial Range ◽  
Compressible Turbulence ◽  
Polytropic Index ◽  
Energy Transfer Rate ◽  
Exact Relation ◽  
Point Correlation ◽  
The Mean ◽  
High Reynolds

AbstractCompressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term $\mathcal{S}$ which may act as a source or a sink for the mean energy transfer rate. At subsonic scales, we predict dimensionally that the isotropic $k^{-5/3}$ energy spectrum for the density-weighted velocity field ($\rho ^{1/3} \boldsymbol {v}$), previously obtained for isothermal turbulence, is modified by a polytropic contribution, whereas at supersonic scales $\mathcal{S}$ may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.

scholarly journals Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
Benjamin D. G. Chandran ◽  
Jean C. Perez
Keyword(s):  
Solar Wind ◽  
Heating Rate ◽  
Three Dimensional ◽  
Power Spectra ◽  
Inertial Range ◽  
Magnetic Flux Tube ◽  
Analytic Model ◽  
Mhd Turbulence ◽  
Background Magnetic Field ◽  
Turbulent Heating

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona and out to a heliocentric distance  $r$ of 21 solar radii  $(R_{\odot })$ . We launch outward-propagating ‘ $\boldsymbol{z}^{+}$ fluctuations’ into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating ‘ $\boldsymbol{z}^{-}$ fluctuations’. Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions and divides the $\boldsymbol{z}^{+}$ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of $\boldsymbol{z}^{+}$ and $\boldsymbol{z}^{-}$ fluctuations in our simulations evolve toward a $k_{\bot }^{-3/2}$ scaling at $r>10R_{\odot }$ , where $k_{\bot }$ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the $\boldsymbol{z}^{+}$ power spectra are much flatter between the coronal base and $r\simeq 4R_{\odot }$ . We argue that these spectral scalings are caused by: (i) high-pass filtering in the upper chromosphere; (ii) the anomalous coherence of inertial-range $\boldsymbol{z}^{-}$ fluctuations in a reference frame propagating outwards with the $\boldsymbol{z}^{+}$ fluctuations; and (iii) the change in the sign of the radial derivative of the Alfvén speed at $r=r_{\text{m}}\simeq 1.7R_{\odot }$ , which disrupts this anomalous coherence between $r=r_{\text{m}}$ and $r\simeq 2r_{\text{m}}$ . At $r>1.3R_{\odot }$ , the turbulent heating rate in our simulations is comparable to the turbulent heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind.

Compressible turbulence in one dimension

1998 ◽  
Vol 249 (1-2) ◽  
pp. 83-86 ◽  
Author(s):  
J. Fleischer ◽  
P. Diamond
Keyword(s):  
Compressible Turbulence ◽  
One Dimension

Large-Eddy Simulation of Combustion Oscillation in Premixed Combustor

1999 ◽  
Author(s):  
Tomoya Murota ◽  
Masaya Ohtsuka
Keyword(s):  
Large Eddy Simulation ◽  
Present Method ◽  
Premixed Combustion ◽  
Compressible Turbulence ◽  
Flamelet Model ◽  
Turbulent Premixed Flame ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Combustion Oscillation ◽  
Combustion Flow

To analyze combustion oscillation in the premixed combustor, a large-eddy simulation program for premixed combustion flow was developed. The subgrid scale (SGS) model of eddy viscosity type for compressible turbulence (Speziale et al., 1988) was adopted to treat the SGS fluxes. The fractal flamelet model, which utilizes the fractal properties of the turbulent premixed flame to obtain the reaction rate, was developed. Premixed combustion without oscillation was analyzed to verify the present method. The computational results showed good accordance with experimental data (Rydén et al., 1993). The combustion oscillation of an “established buzz” type in the premixed combustor (Langhorne, 1988) was also analyzed. The present method succeeded in capturing the oscillation accurately. The detailed mechanism was investigated. The appearance of the non-heat release region, which is generated because the supply of the unburnt gas into the combustion zone stagnates, and its disappearance play an important role.

A prioriassessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

2013 ◽  
Vol 14 (9) ◽  
pp. 43-61 ◽  
Author(s):  
N.S. Vaghefi ◽  
M.B. Nik ◽  
P.H. Pisciuneri ◽  
C.K. Madnia
Keyword(s):  
Compressible Turbulence ◽  
Scalar Dissipation ◽  
Subgrid Scale
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