Decay of Turbulence in Fluids with Polytropic Equations of State. (arXiv:2001.05156v1 [astro-ph.GA])

<a href="http://arxiv.org/find/astro-ph/1/au:+Lim_J/0/1/0/all/0/1">Jeonghoon Lim</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Cho_J/0/1/0/all/0/1">Jungyeon Cho</a>

We present numerical simulations of decaying hydrodynamic turbulence

initially driven by solenoidal (divergence-free) and compressive (curl-free)

driving. Most previous numerical studies for decaying turbulence assume an

isothermal equation of state (EOS). Here we use a polytropic EOS, $P$ $propto$

$rho^{gamma}$, with polytropic $gamma$ ranging from 0.7 to 5/3. We mainly

aim at determining the effects of polytropic $gamma$ and driving schemes on

the decay law of turbulence energy, E $propto$ $t^{-alpha}$. We additionally

study probability density function (PDF) of gas density and skewness of the

distribution in polytropic turbulence driven by compressive driving. Our

findings are as follows. First of all, we find that even if polytropic $gamma$

does not strongly change scaling relation of the decay law, the driving schemes

weakly change the relation; in our all simulations, turbulence decays with

$alpha$ $approx$ 1, but compressive driving yields smaller $alpha$ than

solenoidal driving at the same sonic Mach number. Second, we calculate

compressive and solenoidal velocity components separately and compare their

decay rates in turbulence initially driven by compressive driving. We find that

the former decays much faster so that it ends up having a smaller fraction than

the latter. Third, the density PDF of compressively driven turbulence with

polytropic $gamma$ $>$ 1 deviates from log-normal distribution: it has a

power-law tail at low density as in the case of solenoidally driven turbulence.

However, as it decays, the density PDF becomes approximately log-normal. We

discuss why decay rates of compressive and solenoidal velocity components are

different in compressively driven turbulence and astrophysical implication of

our findings.

We present numerical simulations of decaying hydrodynamic turbulence

initially driven by solenoidal (divergence-free) and compressive (curl-free)

driving. Most previous numerical studies for decaying turbulence assume an

isothermal equation of state (EOS). Here we use a polytropic EOS, $P$ $propto$

$rho^{gamma}$, with polytropic $gamma$ ranging from 0.7 to 5/3. We mainly

aim at determining the effects of polytropic $gamma$ and driving schemes on

the decay law of turbulence energy, E $propto$ $t^{-alpha}$. We additionally

study probability density function (PDF) of gas density and skewness of the

distribution in polytropic turbulence driven by compressive driving. Our

findings are as follows. First of all, we find that even if polytropic $gamma$

does not strongly change scaling relation of the decay law, the driving schemes

weakly change the relation; in our all simulations, turbulence decays with

$alpha$ $approx$ 1, but compressive driving yields smaller $alpha$ than

solenoidal driving at the same sonic Mach number. Second, we calculate

compressive and solenoidal velocity components separately and compare their

decay rates in turbulence initially driven by compressive driving. We find that

the former decays much faster so that it ends up having a smaller fraction than

the latter. Third, the density PDF of compressively driven turbulence with

polytropic $gamma$ $>$ 1 deviates from log-normal distribution: it has a

power-law tail at low density as in the case of solenoidally driven turbulence.

However, as it decays, the density PDF becomes approximately log-normal. We

discuss why decay rates of compressive and solenoidal velocity components are

different in compressively driven turbulence and astrophysical implication of

our findings.

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