[논문]DECAY OF TURBULENCE IN FLUIDS WITH POLYTROPIC EQUATIONS OF STATE

Lim, Jeonghoon; Cho, Jungyeon

doi:10.5303/jkas.2020.53.2.49

[국내논문] DECAY OF TURBULENCE IN FLUIDS WITH POLYTROPIC EQUATIONS OF STATE 원문보기

Journal of the Korean astronomical society = 천문학회지, v.53 no.2, 2020년, pp.49 - 57

Lim, Jeonghoon (Department of Astronomy and Space Science, Chungnam National University) , Cho, Jungyeon (Department of Astronomy and Space Science, Chungnam National University)

Abstract ▼ AI-Helper

We present numerical simulations of decaying hydrodynamic turbulence initially driven by solenoidal (divergence-free) and compressive (curl-free) drivings. Most previous numerical studies for decaying turbulence assume an isothermal equation of state (EOS). Here we use a polytropic EOS, P ∝ ργ, with polytropic exponent γ ranging from 0.7 to 5/3. We mainly aim at determining the effects of γ and driving schemes on the decay law of turbulence energy, E ∝ t-α. 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 γ does not strongly change the decay law, the driving schemes weakly change the relation; in our all simulations, turbulence decays with α ≈ 1, but compressive driving yields smaller α 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 γ > 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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표/그림 (12)

표 Table 1 Simulation runs and parameter values
그림 Figure 1. Time evolution of 〈v²〉 in decaying turbulence initially driven by solenoidal driving with γ = 0.7 (blue), 1.0 (red), 1.5(cyan), or 5/3 (green), where 〈· · ·〉 indicates spatial averaging.
그림 Figure 2. Same as Figure 1, but for the decay of the standard deviation of the density fluctuation σ_ρ/ρ₀ .
그림 Figure 3. Same as Figure 1, but for compressively driven turbulence.
그림 Figure 4. Same as Figure 2, but for compressively driven turbulence.
그림 Figure 5. Decay of the ratio of compressive (upper panels) and solenoidal (bottom panels) velocity components in compressivelydriven turbulence.
그림 Figure 6. Decay of solenoidal and compressive velocity components in compressively driven turbulence.
그림 Figure 7. Same as Figure 5 but for solenoidally driven turbulence and showing the compressive ratio only.
그림 Figure 8. PDF of the logarithmic density s = ln(ρ/ρ₀) of decaying polytropic turbulence initially driven by compressive driving with M_s ∼ 1.
그림 Figure 9. Same as Figure 8, but for M_s ∼ 3.
표 Table 2 Skewness of the PDFs presented in Figures 8 and 9
그림 Figure 10. Time evolution of the skewness of the density PDFs shown in Figure 8 (top panel) and Figure 9 (bottom panel).

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