An official website of the United States government
We present a technique to measure the time-resolved velocity and ion sound speed in magnetized, supersonic high-energy-density plasmas. We place an inductive (“b-dot”) probe in a supersonic pulsed-power-driven plasma flow and measure the magnetic field advected by the plasma. As the magnetic Reynolds number is large (RM > 10), the plasma flow advects a magnetic field proportional to the current at the load. This enables us to estimate the flow velocity as a function of time from the delay between the current at the load and the signal at the probe. The supersonic flow also generates a hydrodynamic bow shock around the probe, the structure of which depends on the upstream sonic Mach number. By imaging the shock around the probe with a Mach–Zehnder interferometer, we determine the upstream Mach number from the shock Mach angle, which we then use to determine the ion sound speed from the known upstream velocity. We use the sound speed to infer the value of Z̄Te, where Z̄ is the average ionization and Te is the electron temperature. We use this diagnostic to measure the time-resolved velocity and sound speed of a supersonic (MS ∼ 8), super-Alfvénic (MA ∼ 2) aluminum plasma generated during the ablation stage of an exploding wire array on the Magpie generator (1.4 MA, 250 ns). The velocity and Z̄Te measurements agree well with the optical Thompson scattering measurements reported in the literature and with 3D resistive magnetohydrodynamic simulations in GORGON.
more »
« less
Density and velocity correlations in isothermal supersonic turbulence
ABSTRACT In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work, we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution function (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed, and compressive) and 4 rms Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.
more »
« less
- Award ID(s):
- 2009870
- PAR ID:
- 10440601
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 525
- Issue:
- 1
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 297-310
- Size(s):
- p. 297-310
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Supersonic isothermal turbulence is a common process in astrophysical systems. In this work, we explore the energy in such systems. We show that the conserved energy is the sum of the kinetic energy (K) and Helmholtz free energy (F). We develop analytic predictions for the probability distributions,P(F) andP(K), as well as their nontrivial joint distribution,P(F,K). We verify these predictions with a suite of driven turbulence simulations, finding excellent agreement. The turbulence simulations were performed at Mach numbers ranging from 1 to 8, and three modes of driving: purely solenoidal, purely compressive, and mixed. We find thatP(F) is discontinuous atF= 0, with the discontinuity increasing with Mach number and compressive driving.P(K) resembles a lognormal with a negative skew. The joint distribution,P(F,K), shows a bimodal distribution, with gas either existing at highFand highKor at lowFand lowK.more » « less
-
ABSTRACT Simulations of isolated giant molecular clouds (GMCs) are an important tool for studying the dynamics of star formation, but their turbulent initial conditions (ICs) are uncertain. Most simulations have either initialized a velocity field with a prescribed power spectrum on a smooth density field (failing to model the full structure of turbulence) or ‘stirred’ turbulence with periodic boundary conditions (which may not model real GMC boundary conditions). We develop and test a new GMC simulation setup (called turbsphere) that combines advantages of both approaches: we continuously stir an isolated cloud to model the energy cascade from larger scales, and use a static potential to confine the gas. The resulting cloud and surrounding envelope achieve a quasi-equilibrium state with the desired hallmarks of supersonic ISM turbulence (e.g. density PDF and a ∼k−2 velocity power spectrum), whose bulk properties can be tuned as desired. We use the final stirred state as initial conditions for star formation simulations with self-gravity, both with and without continued driving and protostellar jet feedback, respectively. We then disentangle the respective effects of the turbulent cascade, simulation geometry, external driving, and gravity/MHD boundary conditions on the resulting star formation. Without external driving, the new setup obtains results similar to previous simple spherical cloud setups, but external driving can suppress star formation considerably in the new setup. Periodic box simulations with the same dimensions and turbulence parameters form stars significantly slower, highlighting the importance of boundary conditions and the presence or absence of a global collapse mode in the results of star formation calculations.more » « less
-
Abstract We use in situ measurements from the first 19 encounters of Parker Solar Probe and the most recent five encounters of Solar Orbiter to study the evolution of the turbulent sonic Mach numberMt(the ratio of the amplitude of velocity fluctuations to the sound speed) with radial distance and its relationship to density fluctuations. We focus on the near-Sun region with radial distances ranging from about 11 to 80R⊙. Our results show that (1) the turbulent sonic Mach numberMtgradually moves toward larger values as it approaches the Sun, until at least 11R⊙, whereMtis much larger than the previously observed value of 0.1 at and above 0.3 au; (2) transonic turbulence withMt ∼ 1 is observed in situ for the first time and is found mostly near the Alfvén critical surface; (3) Alfvén Mach number of the bulk flowMAshows a strong correlation with the plasma beta, indicating that most of the observed sub-Alfvénic intervals correspond to a low-beta plasma; (4) the scaling relation between density fluctuations andMtgradually changes from a linear scaling at larger radial distances to a quadratic scaling at smaller radial distances; and (5) transonic turbulence is more compressible than subsonic turbulence, with enhanced density fluctuations and slightly flatter spectra than subsonic turbulence. A systematic understanding of compressible turbulence near the Sun is necessary for future solar wind modeling efforts.more » « less
-
We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy (u′ vs. t′) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., Cf and UVD+). iLES significantly overpredicts the peak values of u′, and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers.more » « less
