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A. Lees and H. Aluie

Baropycnal Work: A Mechanism for Energy Transfer Across Scales.

Fluids, 4(2), 92 (2019). [Invited paper] ▾ Digest ▾

The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of "baropycnal work," which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1,024^3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.

X. Bian and H. Aluie

Decoupled cascades of kinetic and magnetic energy in magnetohydrodynamic turbulence.

Physical Review Letters, 122(13), 135101 (2019). ▾ Digest ▾

Flows which are coupled to magnetic fields (magnetohydrodynamic or MHD flows) are central to our understanding of a wide variety of systems ranging from the cosmological to the terrestrial. These include galaxies and clusters of galaxies, gas nebulae and the interstellar medium, star formation and evolution, solar wind and space weather, nuclear fusion, and metallurgy. In MHD flows, it is only total energy that is conserved and not magnetic and kinetic energy separately. As a manifestation of order emerging out of chaos (or permanence out of turbulence), we find that they are in fact conserved separately over a range of scales in turbulent flows. This essentially gives us two dynamical invariants (kinetic energy and magnetic energy) instead of just one (total energy). Invariants are highly prized quantities from which the governing laws of motion/evolution are derived. Our results have implications on the energetics and dissipation of these flows, the reconnection of magnetic field lines such as in solar flares, the amplification of magnetic field strength by dynamo action, and also on modeling efforts.

M. Sadek and H. Aluie

Extracting the Spectrum of a Flow by Spatial Filtering.

Physical Review Fluids, 3(12), 124610 (2018). ▾ Digest ▾

Can you gain “insight” by relinquishing some of your sight? Indeed, we show here how it is possible to quantify the energy content of various structures in a flow (i.e. measuring the spectrum) by observing the flow through “eyeglasses” of varying strength. In this paper, we show that the spectrum can be extracted within a local region by a straightforward filtering (averaging) in physical space which is equivalent to putting on weak eyeglasses. Our method guarantees energy conservation and can extract spectra of non-quadratic quantities self-consistently, such as kinetic energy in variable density flows, which the wavelet spectrum cannot. The method can be useful within coherent flow structures covering irregular regions, in multiphase flows, or in geophysical flows on Earth's curved surface.

H. Zhang et al.

Self-similar multimode bubble-front evolution of the ablative Rayleigh-Taylor instability in two and three dimensions.

Physical Review Letters, 121(18), 185002 (2018). ▾ Digest ▾

This paper completes the theoretical investigation of the ablative Rayleigh-Taylor Instability (aRTI) done in preceding works. Ablation (or mass evaporation) arises, for example, from radiative sources such in laser-driven plasmas or from UV stellar light in cold gaseous hydrogen clouds such as in the Eagle Nebula. Small-scale perturbations in the aRTI are often neglected because they are linearly stabilized by ablation. Here, we study the nonlinear evolution of these modes in the presence of an entire continuum of excitations, which we show lead to a self-similar growth of the instability. We find that while ablation reduces the growth of RTI if the initial perturbation is small, it enhances the growth if the perturbation is larger than a certain threshold. This is traced to enhanced vorticity generation due to ablation. Our work implies that the common practice of neglecting short wavelength modes in ICF and astrophysical modeling should be revisited.

J. Xin et al.

Two mode coupling of the ablative Rayleigh Taylor instability.

Physics of Plasmas, 26, 032703 (2019) ▾ Digest ▾

The paper explores the two mode coupling in ablative Rayleigh Taylor instability (RTI). These include coupling between short-short wavelengths and long-short wavelengths. We find that the presence of the short-wavelength mode in the long-short cases enhances the total ARTI bubble velocity. We also find that coupling of two short-wavelength modes forms a long-wavelength component which grows faster than each individual short-wavelength mode.

H. Aluie

Convolutions On The Sphere: Commutation With Differential Operators.

GEM: International Journal on Geomathematics, Springer, 10(9), 1-31 (2019) ▾ Digest ▾

This paper generalizes the definition of convolutions on spherical surfaces and proves that the new definition commutes with differential operators on the sphere. The motivation is to analyze (via coarse-graining) the multi-scale physics of flows in spherical geometries, such as atmospheric and oceanic flows, and in ICF. The paper provides the mathematical foundation for analyzing energy scale-transfer in the N. Atlantic Ocean. I had an unfortunate experience with the editorial process at another journal, Nonlinearity, the full account of which is here. I hope no one else has to go through such a nightmare scenario.

K. M. Woo et al.

Impact of Three Dimensional Hot Spot Flow Asymmetry on Ion Temperature Measurements in Inertial Confinement Fusion Experiments.

Physics of Plasmas, 25, 102710 (2018) ▾ Digest ▾

Deviations in inertial confinement fusion (ICF) implosions from 3D spherical symmetry lead to significant variations in inferred ion-temperature measurements in experiments. This work provides a consistent explanation for the 3D flow effects on inferred ion-temperature variations. It is shown that the effect of hot-spot flow asymmetry on variations in ion-temperature measurements is determined by six hot-spot flow parameters. Low wavenumber mode l=2 is shown to exhibit the largest total velocity variance and leads to inferred ion temperature well above the thermal ion temperature. The paper also provides a formula which allows for improving the predictions of thermal ion temperatures.

K. M. Woo et al.

Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions.

Physics of Plasmas, 25(5), 054603 (2018) ▾ Digest ▾

This paper studies the Rayleigh–Taylor instability in inertial confinement fusion implosions. It is shown that larger hot-spot volumes observed in low modes and the consequential pressure degradation can be explained in terms of increasing the residual kinetic energy. The low mode asymmetries are shown to cause the largest ion temperature variations in the mode spectrum.

D. Zhao, H. Aluie

The Inviscid Criterion for Decomposing Scales.

Physical Review Fluids, 3, 054603 (2018) ▾ Digest ▾

This paper pertains to the fundamental notion of "length-scale" and how to disentangle scale interactions in flows with significant density variations, such as high-speed, reactive, or multi-phase flows. A “length scale” in a fluid flow does not exist as an independent entity but is associated with the specific flow variable being analyzed. While this might seem obvious, we often discuss the “inertial range” or the “viscous range” of length scales in turbulence as if they exist independently of a flow variable, which in incompressible turbulence is the velocity field. How should we analyze “length-scales” in flows with significant density variations?

M. Buzzicotti, H. Aluie, L. Biferale, M. Linkmann

Energy transfer in turbulence under rotation.

Physical Review Fluids, 3, 034802 (2018) ▾ Digest ▾

Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C)/slow manifold. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk to the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism.

H. Zhang, R. Betti, V. Gopalaswamy, R. Yan, H. Aluie

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers.

Physical Review E, 97, 011203(R) (2018) ▾ Digest ▾

Ablation (or mass evaporation) arises, for example, from radiative sources such as lasers in laser-driven plasmas or from UV stellar light in cold gaseous hydrogen clouds such as in the Eagle Nebula. Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stabilized by ablation. Here, we show that modes of any wavelength can be destabilized if they are nonlinear (large amplitude perturbation). We find that for conditions found in laser fusion targets, the often neglected short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target.

M. Buzzicotti, M. Linkmann, H. Aluie, L. Biferale, J. Brasseur, C. Meneveau

Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence.

Journal of Turbulence, 19(2), 167-197 (2018) ▾ Digest ▾

Energy scale-transfer sensitivity to filtering kernel, including a novel class of Galerkin projectors.

H. Aluie, M. Hecht, G. Vallis

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach.

Journal of Physical Oceanography, 48 (2), 225-244 (2018) ▾ Digest ▾

This paper is a culmination of interdisciplinary work spanning applied mathematics, physical oceanography, and turbulence. What started off as a seemingly straightforward application of methods from turbulence to oceanic data turned out to require new theoretical developments in applied mathematics, considerable effort in numerical implementation, and a few years to finish. I believe this was a worthy investment to provide tools that will hopefully prove valuable in atmospheric and oceanic dynamics, in climate science, and also in general flows with spherical geometry such as imploding targets in inertial confinement fusion power. The mathematical developments underpinning this analysis are published here.

H. Aluie

Coarse-Grained Incompressible Magnetohydrodynamics: analyzing the turbulent cascades. (Invited paper)

New Journal of Physics, 19, 025008 (2017) ▾ Digest ▾

This work, which was mostly done in collaboration with G. Eyink, formulates the coarse-graining (or filtering) approach in MHD flows from a first-principles physics stand-point. The approach is a powerful framework to study the multi-scale physics of flows, including MHD turbulence. A key result is the proof that magnetic helicity, unlike energy, cannot undergo a cascade to arbitrarily small scales. Magnetic helicity is an important topological quantity in MHD flows that quantifies the degree of knottedness of magnetic field lines. The paper also reviews the concept of a cascade, but within the coarse-graining framework, and attempts to explain intuitively how “rough” flows can dissipate energy without the aid of viscous (or microphysical) processes.

R. Yan, R. Betti, J. Sanz, H. Aluie, B. Liu, A. Frank

Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability.

Physics of Plasmas, 23 (2), 022701 (2016) ▾ Digest ▾

This paper studies the single mode Rayleigh-Taylor instability (RTI) in the presence of ablation (or mass evaporation). Ablation arises, for example, from radiative sources such as lasers in laser-driven plasmas or from UV stellar light in cold gaseous hydrogen clouds such as in the Eagle Nebula. While ablation has been known to slow down and even suppress the RTI in the linear (small amplitude) regime, here we show that ablation can exacerbate the instability in the nonlinear regime due to vorticity generation.

M. K. Rivera, H. Aluie, R. E. Ecke

The direct enstrophy cascade of two-dimensional soap film flows.

Phys. Fluids, 26, 055105 (2014) ▾ Digest ▾

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G. L. Eyink, E. T. Vishniac, C. Lalescu, H. Aluie, K. Kanov, K. Burger, R. Burns, C. Meneveau, A. Szalay

Flux-freezing breakdown observed in high-conductivity magnetohydrodynamic turbulence.

Nature, 497, 466-469 (2013) ▾ Digest ▾

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H. Aluie

The range of scale coupling and the cascade in the presence of shocks.

arXiv:1101.0150 (submitted) ▾ Digest ▾

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H. Aluie

Scale decomposition in compressible turbulence.

Physica D: Nonlinear Phenomena, (in press) ▾ Digest ▾

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H. Aluie, S. Li, H. Li

Conservative cascade of kinetic energy in compressible turbulence.

Astrophysical Journal Letters, 751, L29 (2012) ▾ Digest ▾

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H. Aluie, S. Kurien

Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows.

Europhysics Letters, 96, 44006 (2011) ▾ Digest ▾

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H. Aluie

Compressible turbulence: The cascade and its locality.

Physical Review Letters, 106, 174502 (2011) ▾ Digest ▾

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H. Aluie, G. L. Eyink

Scale locality of magnetohydrodynamic turbulence.

Physical Review Letters, 104, 081101 (2010) ▾ Digest ▾

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G. L. Eyink, H. Aluie

Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining.

Physics of Fluids, 21, 115107 (2009) ▾ Digest ▾

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H. Aluie, G. L. Eyink

Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter.

Physics of Fluids, 21, 115108 (2009) ▾ Digest ▾

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G. L. Eyink, H. Aluie

The breakdown of Alfven's theorem in ideal plasma flows: Necessary conditions and physical conjectures.

Physica D: Nonlinear Phenomena, 223, 82 (2006) ▾ Digest ▾

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