اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe distribution of shock waves in driven supersonic turbulence
55
0
0.0
(
0
)
تأليف
Michael D. Smith
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Supersonic turbulence generates distributions of shock waves. Here, we analyse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and self-gravity. We can identify the nature of the turbulence by measuring the distribution of the shock strengths. We find that uniformly driven turbulence possesses a power law distribution of fast shocks with the number of shocks inversely proportional to the square root of the shock jump speed. A tail of high speed shocks steeper than Gaussian results from the random superposition of driving waves which decay rapidly. The energy is dissipated by a small range of fast shocks. These results contrast with the exponential distribution and slow shock dissipation associated with decaying turbulence. A strong magnetic field enhances the shock number transverse to the field direction at the expense of parallel shocks. A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion shocks. Finally, we examine the dynamics to demonstrate how the power-law behaviour arises.
قيم البحث
اقرأ أيضاً
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to t
he conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $mathcal{M}$, up to $mathcal{M}sim30$. The PDF width, $sigma_{s}$, follows the relation $sigma_{s}^2 = ln (1+b^2 {mathcal M}^2)$, with $bapprox0.38$. However, the PDF exhibits a negative skewness that increases with increasing $mathcal{M}$, so much of the growth of $sigma_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $mathcal{M}$, which may have a significant impact on theoretical models of star formation.
In this paper we analyze crowd turbulence from both classical and quantum perspective. We analyze various crowd waves and collisions using crowd macroscopic wave function. In particular, we will show that nonlinear Schr{o}dinger (NLS) equation is fun
damental for quantum turbulence, while its closed-form solutions include shock-waves, solitons and rogue waves, as well as planar de Broglies waves. We start by modeling various crowd flows using classical fluid dynamics, based on Navier-Stokes equations. Then, we model turbulent crowd flows using quantum turbulence in Bose-Einstein condensation, based on modified NLS equation. Keywords: Crowd behavior dynamics, classical and quantum turbulence, shock waves, solitons and rogue waves
Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $sigma^2_{rho/rho_0}$, is of particular in
terest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $sigma^2_{rho/rho_0}$ all share a common feature -- the variance is assumed to be isotropic. This assumption does not hold when a trans/sub-Alfvenic mean magnetic field, $vec{B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $sigma_{rho/rho_0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $sigma_{rho/rho_0}^2$ in the high Mach number $(mathcal{M})$ limit as small-scale density fluctuations become suppressed by the strong $vec{B}_0$. The model reduces to the isotropic $sigma_{rho/rho_0}^2-mathcal{M}$ relation in the hydrodynamical limit. To validate our model, we calculate $sigma_{rho/rho_0}^2$ from 12~high-resolution, three-dimensional, supersonic, sub-Alfvenic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented over-densities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvenic $vec{B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.
We have obtained a contiguous set of long-slit spectra of a shock wave in the Cygnus Loop to investigate its structure, which is far from the morphology predicted by 1D models. Proper motions from Hubble Space Telescope images combined with the known
distance to the Cygnus Loop provide an accurate shock speed. Earlier analyses of shock spectra estimated the shock speed, postshock density, temperature, and elemental abundances. In this paper we determine several more shock parameters: a more accurate shock speed, ram pressure, density, compression ratio, dust destruction efficiency, magnetic field strength, and vorticity in the cooling region. From the derived shock properties we estimate the emissivities of synchrotron emission in the radio and pion decay emission in the gamma rays. Both are consistent with the observations if we assume simple adiabatic compression of ambient cosmic rays as in the van der Laan mechanism. We also find that, although the morphology is far from that predicted by 1D models and the line ratios vary dramatically from point to point, the average spectrum is matched reasonably well by 1D shock models with the shock speed derived from the measured proper motion. A subsequent paper will analyze the development of turbulence in the cooling zone behind the shock.
Radiative shock waves in the Cygnus Loop and other supernova remnants show different morphologies in [O III] and H{alpha} emission. We use HST spectra and narrowband images to study the development of turbulence in the cooling region behind a shock o
n the west limb of the Cygnus Loop. We refine our earlier estimates of shock parameters that were based upon ground-based spectra, including ram pressure, vorticity and magnetic field strength. We apply several techniques, including Fourier power spectra and the Rolling Hough Transform, to quantify the shape of the rippled shock front as viewed in different emission lines. We assess the relative importance of thermal instabilities, the thin shell instability, upstream density variations, and upstream magnetic field variations in producing the observed structure.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
