Stochastic turbulence for Burgers equation driven by cylindrical Lévy process

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [Formula: see text] tends towards zero. The inviscid limit describes the strong stochastic turbulence.

The interstellar medium in young supernova remnants: key to the production of cosmic X-rays and $\gamma $-rays

We review recent progress in elucidating the relationship between high-energy radiation and the interstellar medium (ISM) in young supernova remnants (SNRs) with ages of ∼2000 yr, focusing in particular on RX J1713.7−3946 and RCW 86. Both SNRs emit strong nonthermal X-rays and TeV $\gamma $ γ -rays, and they contain clumpy distributions of interstellar gas that includes both atomic and molecular hydrogen. We find that shock–cloud interactions provide a viable explanation for the spatial correlation between the X-rays and ISM. In these interactions, the supernova shocks hit the typically pc-scale dense cores, generating a highly turbulent velocity field that amplifies the magnetic field up to 0.1–1 mG. This amplification leads to enhanced nonthermal synchrotron emission around the clumps, whereas the cosmic-ray electrons do not penetrate the clumps. Accordingly, the nonthermal X-rays exhibit a spatial distribution similar to that of the ISM on the pc scale, while they are anticorrelated at sub-pc scales. These results predict that hadronic $\gamma $ γ -rays can be emitted from the dense cores, resulting in a spatial correspondence between the $\gamma $ γ -rays and the ISM. The current pc-scale resolution of $\gamma $ γ -ray observations is too low to resolve this correspondence. Future $\gamma $ γ -ray observations with the Cherenkov Telescope Array will be able to resolve the sub-pc-scale $\gamma $ γ -ray distribution and provide clues to the origin of these cosmic $\gamma $ γ -rays.

Magnetic fields from multiplicative chaos

ABSTRACT An analytical model for fully developed three-dimensional incompressible turbulence was recently proposed in the hydrodynamics community, based on the concept of multiplicative chaos. It consists of a random field represented by means of a stochastic integral, which, with only a few parameters, shares many properties with experimental and numerical turbulence, including in particular energy transfer through scales (the cascade) and intermittency (non-Gaussianity) that is most conveniently controlled with a single parameter. Here, we propose three models extending this approach to magnetohydrodynamic turbulence. Our formulae provide physically motivated 3D models of a turbulent velocity field and magnetic field coupled together. Besides its theoretical value, this work is meant to provide a tool for observers: a dozen of physically meaningful free parameters enter the description, which is useful to characterize astrophysical data.

Effect of wall heating on street canyon ventilation

<p>Understanding the dynamics of mass and heat exchange between a street canyon and the overlying atmosphere is crucial to predict air quality and microclimatic conditions within dense urban areas. Previous studies have demonstrated that the bulk transfer between the street and the overlying flow is entirely governed by the intensity of turbulent fluctuations within the street. The aim of this experimental study is to evaluate how the geometry of the street canyon and the solar radiation on building façades influence the turbulent velocity field within a two-dimensional street canyon and thus the global street canyon ventilation. The study was carried in a wind tunnel. The boundary conditions inside the canyon were modified by heating its windward and leeward walls and by changing the cavity aspect-ratio. The flow field in a cross-section of the street canyon was measured with particle image velocimetry. Temperatures were measured by means of thermocouples. The velocity and vorticity fields are analysed and discussed.</p>