论文标题
分层气氛中的湍流：对群内培养基的影响
Turbulence in stratified atmospheres: implications for the intracluster medium
论文作者
论文摘要
簇内培养基（ICM）中的气体运动受分层湍流的控制。分层的湍流与Kolmogorov（各向同性，均质）湍流根本不同。动能不仅从大尺度到小鳞片，而且还将其转化为浮力势能。为了了解ICM中的密度和速度波动，我们进行了高分辨率（$ 1024^2 \ times 1536 $网格点）中性湍流的流体动力学模拟（带有RMS MACH数量$ \ MATHCAL {M MATHCAL {M} \ BOUTS 0.25 $）和分层的不同级别，由The Crichardson $ $ \ \ Mathm Quali niress $ \ \ \ \ \ \ \ Mathm { $ \ mathrm {ri} = 0 $（无分层）到$ \ mathrm {ri} = 13 $（强分层）。我们量化了不同分层的密度，压力和速度场，因为观察性研究经常使用表面亮度波动来推断ICM的湍流气体速度。我们发现对数密度波动的标准偏差（$σ_s$），其中$ s = \ ln（ρ/\ left <ρ（z）\ right>）$，随着$ \ mathrm {ri} $的增加而增加。对于弱分层的亚音湍流（$ \ mathrm {ri} \ lyseSim10 $，$ \ mathcal {m} <1 $），我们得出了一个新的$σ_s$ - $ \ $ \ MATHCAL {M} $ - $σ_s^2=\ln(1+b^2\mathcal{M}^4+0.09\mathcal{M}^2\mathrm{Ri}H_P/H_S)$, where $b=1/3$--$1$ is the turbulence driving parameter, and $H_P$ and $H_S$ are the pressure and entropy scale heights respectively.我们进一步发现，密度波动的功率谱，$ p（ρ_k/\ left <ρ\ right>）$，随着$ \ mathrm {ri} $的增加而增加，而速度功率谱是不变的。因此，密度和速度功率光谱之间的比率很大程度上取决于$ \ mathrm {ri} $。另一方面，压力波动独立于分层，仅取决于$ \ natercal {m} $。
The gas motions in the intracluster medium (ICM) are governed by stratified turbulence. Stratified turbulence is fundamentally different from Kolmogorov (isotropic, homogeneous) turbulence; kinetic energy not only cascades from large to small scales, but it is also converted into buoyancy potential energy. To understand the density and velocity fluctuations in the ICM, we conduct high-resolution ($1024^2\times 1536$ grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number $\mathcal{M}\approx 0.25$) and different levels of stratification, quantified by the Richardson number $\mathrm{Ri}$, from $\mathrm{Ri}=0$ (no stratification) to $\mathrm{Ri}=13$ (strong stratification). We quantify the density, pressure and velocity fields for varying stratification because observational studies often use surface brightness fluctuations to infer the turbulent gas velocities of the ICM. We find that the standard deviation of the logarithmic density fluctuations ($σ_s$), where $s=\ln(ρ/\left<ρ(z)\right>)$, increases with $\mathrm{Ri}$. For weakly stratified subsonic turbulence ($\mathrm{Ri}\lesssim10$, $\mathcal{M}<1$), we derive a new $σ_s$--$\mathcal{M}$--$\mathrm{Ri}$ relation, $σ_s^2=\ln(1+b^2\mathcal{M}^4+0.09\mathcal{M}^2\mathrm{Ri}H_P/H_S)$, where $b=1/3$--$1$ is the turbulence driving parameter, and $H_P$ and $H_S$ are the pressure and entropy scale heights respectively. We further find that the power spectrum of density fluctuations, $P(ρ_k/\left<ρ\right>)$, increases in magnitude with increasing $\mathrm{Ri}$, whereas the velocity power spectrum is invariant. Thus, the ratio between density and velocity power spectra strongly depends on $\mathrm{Ri}$. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal{M}$.
