Turbulence in stratified atmospheres: implications for the intracluster medium. (arXiv:2001.06494v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Mohapatra_R/0/1/0/all/0/1">Rajsekhar Mohapatra</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Federrath_C/0/1/0/all/0/1">Christoph Federrath</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sharma_P/0/1/0/all/0/1">Prateek Sharma</a>
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 ($1024^2times 1536$ 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
($sigma_s$), where $s=ln(rho/left
$mathrm{Ri}$. For weakly stratified subsonic turbulence
($mathrm{Ri}lesssim10$, $mathcal{M}<1$), we derive a new
$sigma_s$--$mathcal{M}$--$mathrm{Ri}$ relation,
$sigma_s^2=ln(1+b^2mathcal{M}^4+0.09mathcal{M}^2mathrm{Ri}H_P/H_S)$, 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(rho_k/left
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 $mathcal{M}$.
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 ($1024^2times 1536$ 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
($sigma_s$), where $s=ln(rho/left<rho(z)right>)$, increases with
$mathrm{Ri}$. For weakly stratified subsonic turbulence
($mathrm{Ri}lesssim10$, $mathcal{M}<1$), we derive a new
$sigma_s$–$mathcal{M}$–$mathrm{Ri}$ relation,
$sigma_s^2=ln(1+b^2mathcal{M}^4+0.09mathcal{M}^2mathrm{Ri}H_P/H_S)$, 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, $P(rho_k/left<rhoright>)$, 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 $mathcal{M}$.
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