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Title: Viscous dissipation in two-dimensional compression of turbulence

Abstract

Nonradial hydrodynamic flow can be generated or amplified during plasma compression by various mechanisms, including the compression itself. In certain circumstances, the plasma may reach a viscous state; for example, in compression experiments seeking fusion, the fuel plasma may reach a viscous state late in the compression due in part to the rising fuel temperature. Here, we consider viscous dissipation of nonradial flow in the case of initially isotropic, three-dimensional (3D), turbulent flow fields compressed at constant velocity in two dimensions. Prior work in the case of 3D compressions has shown the possibility of effective viscous dissipation of nonradial flow under compression. We show that, theoretically, complete viscous dissipation of the nonradial flow should still occur in the 2D case when the plasma heating is adiabatic and the viscosity has the (strong) Braginskii temperature dependence (μ~T5/2). Futhermore, in the general case, the amount of compression required is very large even for modest initial Reynolds numbers, with the compression reaching an intermediate state dominated by variations only in the noncompressed direction. We show that both the nonlinearity and boundary conditions can play important roles in setting the characteristics and ease of the viscous dissipation.

Authors:
 [1]; ORCiD logo [1]
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  1. Princeton Univ., Princeton, NJ (United States). Dept. of Astrophysical Sciences
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1574890
Alternate Identifier(s):
OSTI ID: 1547667
Grant/Contract Number:  
NA0003764; NA0001836; SC0014664
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 26; Journal Issue: 8; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Davidovits, Seth, and Fisch, Nathaniel J. Viscous dissipation in two-dimensional compression of turbulence. United States: N. p., 2019. Web. doi:10.1063/1.5111961.
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Davidovits, Seth, & Fisch, Nathaniel J. Viscous dissipation in two-dimensional compression of turbulence. United States. https://doi.org/10.1063/1.5111961
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Davidovits, Seth, and Fisch, Nathaniel J. Wed . "Viscous dissipation in two-dimensional compression of turbulence". United States. https://doi.org/10.1063/1.5111961. https://www.osti.gov/servlets/purl/1574890.
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@article{osti_1574890,
title = {Viscous dissipation in two-dimensional compression of turbulence},
author = {Davidovits, Seth and Fisch, Nathaniel J.},
abstractNote = {Nonradial hydrodynamic flow can be generated or amplified during plasma compression by various mechanisms, including the compression itself. In certain circumstances, the plasma may reach a viscous state; for example, in compression experiments seeking fusion, the fuel plasma may reach a viscous state late in the compression due in part to the rising fuel temperature. Here, we consider viscous dissipation of nonradial flow in the case of initially isotropic, three-dimensional (3D), turbulent flow fields compressed at constant velocity in two dimensions. Prior work in the case of 3D compressions has shown the possibility of effective viscous dissipation of nonradial flow under compression. We show that, theoretically, complete viscous dissipation of the nonradial flow should still occur in the 2D case when the plasma heating is adiabatic and the viscosity has the (strong) Braginskii temperature dependence (μ~T5/2). Futhermore, in the general case, the amount of compression required is very large even for modest initial Reynolds numbers, with the compression reaching an intermediate state dominated by variations only in the noncompressed direction. We show that both the nonlinearity and boundary conditions can play important roles in setting the characteristics and ease of the viscous dissipation.},
doi = {10.1063/1.5111961},
journal = {Physics of Plasmas},
number = 8,
volume = 26,
place = {United States},
year = {Wed Aug 07 00:00:00 EDT 2019},
month = {Wed Aug 07 00:00:00 EDT 2019}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1063/1.5111961
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Cited by: 2 works
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Figures / Tables:

FIG. 1 FIG. 1: The evolution of the turbulent kinetic energy (TKE) as a function of (linear) compression ratio for two different initial conditions for a two-dimensional, constant velocity compression of an initially isotropic turbulent flowfield. The TKE evolves according to the linear viscous rapid distortion theory (RDT) solution, Eq. (23), withmore » Eqs. (21), (22), and (25). The red solid line shows two growth phases (increasing TKE with decreasing $\bar{L}$), each followed by a dissipation phase, corresponding to a different class of Fourier mode being dissipated. First modes with variation in the compression plane dissipate (kx|y ≠ 0), and then, after much more compression, modes with variation only in the noncompressed direction dissipate (kx = ky = 0). This point is emphasized by the dashed blue line, which uses the same initial condition, but with kx = ky = 0 modes removed. In addition to emphasizing the difference in mode behavior, this could also correspond to the linear behavior in a situation where such modes (kx = ky = 0) are disallowed, for example, by hard-wall boundary conditions. In both cases, the initial energy is normalized to 1, β = 5/2, and ReU = 375, see Sec. IV for more discussion.« less
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