arXiv subjects

Hussein Aluie

Publications and source records attributed to Hussein Aluie.

At least 19 recordsLinked to original sources

arXiv2025

Effects of External Magnetic Fields on the Multi-mode Rayleigh-Taylor Instability

The magneto-Rayleigh-Taylor instability (mRTI) is a key process in inertial confinement fusion and is thought to be widespread in the interstellar medium, where it can concentrate plasma into discrete structures. We present resistive MHD simulations of the nonlinear evolution of multi-mode mRTI in both two and three dimensions, examining the effects of uniform external magnetic fields oriented either parallel or perpendicular to the initial interface. In both 2-D and 3-D, weak parallel fields enhance mixing-zone growth, whereas stronger fields suppress it. For perpendicular fields, growth is initially inhibited but becomes enhanced at later times. These behaviors arise from magnetic tension, which modifies flow anisotropy, buoyancy, drag, and vortex dynamics. The interplay of these mechanisms governs the distinct ways in which magnetic fields influence mRTI evolution.

physics.flu-dyn↗

arXiv2025

Harmonic Extension for Multiscale Analysis and Modeling Near Boundaries, with an Ocean Application

Treatment of fields near domain boundaries is a long-standing problem in signal processing that has come into renewed focus following recent efforts in convolution-based multiscale coarse-graining and in machine-learned parameterizations due to ocean boundary artifacts. Here, we propose a general method for extending fields beyond the domain boundaries by solving a Laplace boundary-value problem. Construction of the harmonic extension is well-posed, including uniqueness, and is consistent with the boundary conditions by design. The formulation applies to irregular boundaries such as discretized coastlines. The harmonic extension is physically desirable since it has minimum spatial variability among all admissible extensions satisfying the boundary conditions. The method is simple to implement using well-established numerical approaches, and is broadly applicable to extending oceanic variables over land boundaries. Other applications include machine learning parametrization and subgrid modeling of wall-bounded flows and multiphase flows. We demonstrate the method by extending sea-surface temperature (SST) over land using fixed temperature (Dirichlet) and no-flux (Neumann) boundary conditions: the land-filled solution is smooth with SST values between the coastal minimum and maximum.

physics.ao-ph↗

arXiv2024

A Theory for Wind Work on Oceanic Mesoscales and Submesoscales

Previous studies focused primarily on wind stress being proportional to wind velocity relative to the ocean velocity, which induces a curl in wind stress with polarity opposite to the ocean mesoscale vorticity, resulting in net negative wind work. However, there remains a fundamental gap in understanding how wind work on the ocean is related to the ocean's vortical and straining motions. While it is possible to derive budgets for ocean vorticity and strain, these do not provide the energy channeled into vortical and straining motions by wind stress. An occasional misconception is that a Helmholtz decomposition can separate vorticity from strain, with the latter mistakenly regarded as being solely due to the potential flow accounting for divergent motions. In fact, strain is also an essential constituent of divergence-free (or solenoidal) flows, including the oceanic mesoscales in geostrophic balance where strain-dominated regions account for approximately half the KE. There is no existing fluid dynamics framework that relates the injection of kinetic energy by a force to how this energy is deposited into vortical and straining motions. Here, we show that winds, on average, are just as effective at damping straining motions as they are at damping vortical motions. This happens because oceanic strain induces a straining wind stress gradient (WSG), which is analogous to ocean vorticity inducing a curl in wind stress. Ocean-induced WSGs alone, whether straining or vortical, always damp ocean currents. However, our theory also reveals that a significant contribution to wind work comes from inherent wind gradients, a main component of which is due to prevailing winds of the general atmospheric circulation. We find that inherent WSGs lead to asymmetric energization of ocean weather based on the polarity of vortical and straining ocean flows.

physics.ao-ph↗

arXiv2024

Calculating Spectra by Sequential High-Pass Filtering

We expand on the method of sequential filtering for calculating spectra of inhomogeneous fields. Sadek & Aluie [Phys. Rev. Fluids, 3, 124610 (2018)] showed that the kernel has to have at least $p$ vanishing moments to extract a power-law spectrum $k^{-α}$ with $α<p+2$ by low-pass filtering. Here, we show that sequential high-pass filtering allows for extracting steeper spectra with $α<2p+3$ using the same $p$-th order kernel. For example, any spectrum of a field that is shallower than $k^{-5}$ can be extracted by sequential high-pass filtering using any 1st order kernel such as a Gaussian or top-hat. Finally, we demonstrate how second-order structure functions fail to capture spectral peaks because they cannot detect scaling that is too shallow.

physics.flu-dyn↗

arXiv2024

Radiation and Heat Transport in Divergent Shock-Bubble Interactions

Shock-bubble interactions (SBI) are important across a wide range of physical systems. In inertial confinement fusion, interactions between laser-driven shocks and micro-voids in both ablators and foam targets generate instabilities that are a major obstacle in achieving ignition. Experiments imaging the collapse of such voids at high energy densities (HED) are constrained by spatial and temporal resolution, making simulations a vital tool in understanding these systems. In this study, we benchmark several radiation and thermal transport models in the xRAGE hydrodynamic code against experimental images of a collapsing mesoscale void during the passage of a 300 GPa shock. We also quantitatively examine the role of transport physics in the evolution of the SBI. This allows us to understand the dynamics of the interaction at timescales shorter than experimental imaging framerates. We find that all radiation models examined reproduce empirical shock velocities within experimental error. Radiation transport is found to reduce shock pressures by providing an additional energy pathway in the ablation region, but this effect is small ($\sim$1\% of total shock pressure). Employing a flux-limited Spitzer model for heat conduction, we find that flux limiters between 0.03 and 0.10 produce agreement with experimental velocities, suggesting that the system is well-within the Spitzer regime. Higher heat conduction is found to lower temperatures in the ablated plasma and to prevent secondary shocks at the ablation front, resulting in weaker primary shocks. Finally, we confirm that the SBI-driven instabilities observed in the HED regime are baroclinically driven, as in the low energy case.

physics.plasm-ph↗

arXiv2023

Global Cascade of Kinetic Energy in the Ocean and the Atmospheric Imprint

We present the first estimate for the ocean's global scale-transfer of kinetic energy (KE), across scales from 10~km to 40000~km. We show the existence of oceanic KE transfer between gyre-scales and mesoscales induced by the atmosphere's Hadley, Ferrel, and polar cells, and intense downscale KE transfer associated with the Inter-Tropical Convergence Zone. We report peak upscale transfer of 300 GigaWatts across mesoscales of 120~km in size, roughly 1/3rd the energy input by winds into the oceanic general circulation. This "cascade" penetrates almost the entire water column, with nearly three quarters of it occurring south of 15$^\circ$S. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag-time of $\mathbf{\approx27~}$days per octave of length-scales such that transfer across 50~km peaks in spring while transfer across 500~km peaks in summer. KE content of those mesoscales follows the same self-similar cycle but peaks $\mathbf{\approx40~}$days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale 4$\times$ larger.

physics.ao-ph↗

arXiv2023

On Galilean Invariance of Mean Kinetic Helicity

While kinetic helicity is not Galilean invariant locally, it is known (K. Moffatt, Journal of Fluid Mechanics, 35, 117 (1969)) that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, \textit{i.e.}, surfaces of zero vorticity flux. We also discuss so-called ``relative'' kinetic helicity, which is Galilean invariant when integrated over any region in the flow.

physics.flu-dyn↗

arXiv2023

Measuring Scale-dependent Shape Anisotropy by Coarse-Graining: Application to Inhomogeneous Rayleigh-Taylor Turbulence

We generalize the `filtering spectrum' [1] to probe scales along different directions by spatial coarse-graining. This multi-dimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multi-dimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of 2D and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately $4:3$ vertical to horizontal aspect ratio, but tends toward isotropy at small scales as expected [2,3,4]. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results in [5]; large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

physics.flu-dyn↗

arXiv2023

Spatio-temporal coarse-graining decomposition of the global ocean geostrophic kinetic energy

We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022) using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales ($>1000~$km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100-500~km) have a root-mean-square (rms) velocity of $\sim15~$cm/s, which increases to $\sim30$-40~cm/s locally in the Gulf Stream and Kuroshio and to $\sim16$-28~cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that $\approx25$-50\% of total geostrophic energy is at scales smaller than 100~km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean component show that most of its energy (up to $70\%$) resides in stationary mesoscales ($<500~$km), highlighting the preponderance of `standing' small-scale structures in the global ocean. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at $\approx200$ km and $\approx2$-3~weeks.

physics.ao-ph↗

arXiv2022

Effective Drift Velocity from Turbulent Transport by Vorticity

We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\ell$ by smaller scale (subscale) turbulence. %subscale flux/stress which appear in the evolution of coarse-grained (resolved) scalars/momentum account for the effect of (subgrid) scales smaller than the coarse-graining length $\ell$. We use the first term in a multiscale gradient expansion due to Eyink \cite{Eyink06a}, which exhibits excellent correlation with the exact subscale physics when the partitioning length $\ell$ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/anti-diffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced non-divergent velocity, $\bv_*$, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, $\OL\bu_\ell$, but by the effective velocity, $\OL\bu_\ell+\bv_*$, the physics of which may improve commonly used LES models.

physics.flu-dyn↗

arXiv2022

Global Energy Spectrum of the General Oceanic Circulation

Since the advent of satellite altimetry, our perception of the oceanic circulation has brought into focus the pervasiveness of mesoscale eddies that have typical scales of tens to hundreds of kilometers [5], are the ocean's analogue of weather systems, and are often thought of as the peak of the ocean's kinetic energy (KE) wavenumber spectrum [7, 19, 23]. Yet, our understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small representative regions (e.g. [16, 14, 4]), typically a few hundred kilometers in size, that cannot capture the vast dynamic range at planetary scales. Here, we present the first truly global wavenumber spectrum of the oceanic circulation from satellite data and high-resolution re-analysis data, using a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three orders of magnitude in length-scale reveal the Antarctic Circumpolar Current (ACC) as the spectral peak of the global extra-tropical ocean, at $\approx 10 \times 10^3~$km. We also find a previously unobserved power-law scaling over scales larger than $10^3~$km. A smaller spectral peak exists at $\approx 300~$km associated with the mesoscales, which, due to their wider spread in wavenumber space, account for more than $50\%$ of the resolved surface KE globally. Length-scales that are twice as large (up to $10^3$~km) exhibit a characteristic lag time of $\approx40~$days in their seasonal cycle, such that in both hemispheres KE at $100~$km peaks in late spring while KE at $10^3~$km peaks in late summer. The spectrum presented here affords us a new window for understanding the multiscale general oceanic circulation within Earth's climate system, including the largest planetary scales.

physics.ao-ph↗

arXiv2021

Scale interactions and anisotropy in Rayleigh-Taylor turbulence

We study energy scale-transfer in Rayleigh-Taylor (RT) flows by coarse-graining in physical space without Fourier transforms, allowing scale analysis along vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $Λ$, due to large-scale pressure gradients acting on small-scales of density and velocity, and deformation work $Π$, due to multi-scale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to RT mixing layer. We find that $Λ$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $Π$ takes over. In 3D, $Π$ continues a persistent cascade to smaller scales, whereas in 2D $Π$ re-channels the energy back to larger scales despite the lack of vorticity conservation in 2D variable density flows. This gives rise to a positive feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the associated potential energy release are enhanced relative to 3D, explaining the oft-observed larger $α$ values in 2D simulations. Despite higher bulk kinetic energy levels in 2D, small inertial scales are weaker than in 3D. Moreover, the net upscale cascade in 2D tends to isotropize the large-scale flow, in stark contrast to 3D. Our findings indicate the absence of net upscale energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and spikes is not due to "mergers" but solely due to baropycnal work $Λ$.

physics.flu-dyn↗

arXiv2021

Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Turbulent viscosity $ν_t$ and resistivity $η_t$ are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number $Pr_t\equiv ν_t/η_t$ has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these ''effective transport'' coefficients acting at different length-scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades [Bian & Aluie 2019]. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of $ν_t$, $η_t$, and $Pr_t$ have power-law scalings in the ''decoupled range.'' We observe that $Pr_t\approx1 \text{~to~}2$ at the smallest inertial-inductive scales, increasing to $\approx 5$ at the largest scales. However, based on physical considerations, our analysis suggests that $Pr_t$ has to become scale-independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid-resolution), and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications to astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large eddy simulation modeling.

physics.flu-dyn↗

arXiv2019

Revisiting the Late-Time Growth of Single-mode Rayleigh-Taylor Instability and the Role of Vorticity

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number ($Re_p$) and Atwood number ($A$) on RTI's late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when $Re_p$ is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high $Re_p$, the bubble's late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher $A$, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor $η=0.45$ to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high $A$. However, we present evidence that if the large $Re_p$ limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller $Re_p$ thresholds.

physics.flu-dyn↗

arXiv2019

Baropycnal Work: A Mechanism for Energy Transfer Across Scales

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.

physics.flu-dyn↗

arXiv2019

Decoupling of the Kinetic and Magnetic Energy Cascades in MHD Turbulence

Magnetic and kinetic energy in ideal incompressible MHD are not global invariants and, therefore, it had been justified to discuss only the cascade of their sum, total energy. We provide a physical argument based on scale-locality of the cascade, along with compelling evidence that at high Reynolds numbers, magnetic and kinetic energy budgets statistically decouple beyond a transitional "conversion" range. This arises because magnetic field-line stretching is a large-scale process which vanishes on average at intermediate and small scales within the inertial-inductive range, thereby allowing each of mean kinetic and magnetic energy to cascade conservatively and at an equal rate. One consequence is that the turbulent magnetic Prandtl number is unity over the "decoupled range" of scales.

astro-ph.SR↗

arXiv2018

Extracting the Spectrum by Spatial Filtering

We show that the spectrum of a flow field can be extracted within a local region by straightforward filtering in physical space. We find that for a flow with a certain level of regularity, the filtering kernel must have a sufficient number of vanishing moments in order for the "filtering spectrum" to be meaningful. Our derivation follows a similar analysis by Perrier et al. 1995 for the wavelet spectrum, where we show that the filtering kernel has to have at least $p$ vanishing moments in order to correctly extract a spectrum $k^{-α}$ with $α< p+2$. For example, any flow with a spectrum shallower than $k^{-3}$ can be extracted by a straightforward average on grid-cells of a stencil. We construct two new "simple stencil" kernels, ${\mathcal M}^{I}$ and ${\mathcal M}^{II}$, with only two and three fixed stencil weight coefficients, respectively, and that have sufficient vanishing moments to allow for extracting spectra steeper than $k^{-3}$. We demonstrate our results using synthetic fields, 2D turbulence from a Direct Numerical Simulation, and 3D turbulence from the JHU Database. 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 in both simulations and experiments when a straightforward Fourier analysis is not justified, such as within coherent flow structures covering non-rectangular regions, in multi-phase flows, or in geophysical flows on Earth's curved surface.

physics.flu-dyn↗

arXiv2018

Convolutions on the Sphere: Commutation with Differential Operators

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the convolution. These properties make the new filtering operation particularly useful to analyzing and modeling nonlinear dynamics in spherical systems, such as in geophysics, astrophysics, and in inertial confinement fusion applications. An essential tool we use is the theory of scalar, vector, and tensor spherical harmonics. We then show that our generalized filtering operation is equivalent to the (traditional) convolution of scalar fields of the Helmholtz decomposition of vectors and tensors.

math-ph↗