arXiv subjects

Katepalli R. Sreenivasan

Publications and source records attributed to Katepalli R. Sreenivasan.

At least 37 records · Page 2Linked to original sources

arXiv2024

Saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D isotropic turbulence

Inertial range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at $\approx 2.1$ for moment orders $p \ge 10$, significantly differing from the longitudinal exponents (which are predicted to saturate at $\approx 7.3$ for $p \ge 30$ from a recent theory). The Lagrangian scaling exponents likewise saturate at $\approx 2$ for $p \ge 8$. The saturation of Lagrangian exponents and transverse Eulerian exponents is related by the same multifractal spectrum by utilizing the well known frozen hypothesis to relate spatial and temporal scales. Furthermore, this spectrum is different from the known spectra for Eulerian longitudinal exponents, suggesting that that Lagrangian intermittency is characterized solely by transverse Eulerian intermittency. We discuss possible implication of this outlook when extending multifractal predictions to the dissipation range, especially for Lagrangian acceleration.

physics.flu-dyn↗

arXiv2024

Average turbulence dynamics from a one-parameter kinetic theory

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from averaging the Klimontovich-type equation for fluid elements satisfying the Navier-Stokes hydrodynamics exactly. The turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell-Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation.

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arXiv2023

Two quantum algorithms for solving the one-dimensional advection-diffusion equation

Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithms (QLSA) based on the Harrow--Hassidim--Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to $N=64$ grid points on the unit interval. Both algorithms are of hybrid nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the sizes of an additional quantum register for the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement and decoherence circuit noise. We reflect the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.

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arXiv2023

Hybrid quantum algorithms for flow problems

For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance quantum simulator which we term QFlowS (Quantum Flow Simulator), designed for fluid flow simulations using QC. Solving nonlinear flows by QC generally proceeds by solving an equivalent infinite dimensional linear system as a result of linear embedding. Thus, we first choose to simulate two well known flows using QFlowS and demonstrate a previously unseen, full gate-level implementation of a hybrid and high precision Quantum Linear Systems Algorithms (QLSA) for simulating such flows at low Reynolds numbers. The utility of this simulator is demonstrated by extracting error estimates and power law scaling that relates $T_{0}$ (a parameter crucial to Hamiltonian simulations) to the condition number $κ$ of the simulation matrix, and allows the prediction of an optimal scaling parameter for accurate eigenvalue estimation. Further, we include two speedup preserving algorithms for (a) the functional form or sparse quantum state preparation, and (b) \textit{in-situ} quantum post-processing tool for computing nonlinear functions of the velocity field. We choose the viscous dissipation rate as an example, for which the end-to-end complexity is shown to be $\mathcal{O}(\textrm{polylog} (N/ε)κ/ε_{QPP})$, where $N$ is the size of the linear system of equations, $ε$ is the the solution error and $ε_{QPP}$ is the error in post processing. This work suggests a path towards quantum simulation of fluid flows, and highlights the special considerations needed at the gate level implementation of QC.

quant-ph↗

arXiv2023

A linear model for inertial modes in a differentially rotating Sun

Inertial wave modes in the Sun are of interest owing to their potential to reveal new insight into the solar interior. These predominantly retrograde-propagating modes in the solar subsurface appear to deviate from the thin-shell Rossby-Haurwitz model at high azimuthal orders. We present new measurements of sectoral equatorial inertial modes at $m>15$ where the modes appear to become progressively less retrograde compared to the canonical Rossby-Haurwitz dispersion relation in a co-rotating frame. We use a spectral eigenvalue solver to compute the spectrum of solar inertial modes in the presence of differential rotation. Focussing specifically on equatorial Rossby modes, we find that the numerically obtained mode frequencies lie along distinct ridges, one of which lies strikingly close to the observed mode frequencies in the Sun. We also find that the $n=0$ ridge is deflected strongly in the retrograde direction. This suggests that the solar measurements may not correspond to the fundamental $n=0$ Rossby-Haurwitz solutions as was initially suspected, but to a those for a higher $n$. The numerically obtained eigenfunctions also appear to sit deep within the convection zone -- unlike those for the $n=0$ modes -- which differs substantially from solar measurements and complicates inference.

astro-ph.SR↗

arXiv2023

Reynolds number asymptotics of wall-turbulence fluctuations

In furtherance of our earlier work (Chen \& Sreenivasan, {\it J. Fluid Mech.} {\bf 908}, 2021, p. R3; {\bf 933}, 2022, p. A20 -- together referred to as CS hereafter), we present a self-consistent Reynolds number asymptotics for wall-normal profiles of variances of streamwise and spanwise velocity fluctuations as well as root-mean-square pressure, across the entire flow region of channel and pipe flows and flat-plate boundary layers. It is first shown that, when normalized by peak values, the Reynolds number dependence and wall-normal variation of all three profiles can be decoupled, in excellent agreement with available data, sharing the common inner expansion of the type $ϕ^+(y^+)=f_0(y^+)+f_1(y^+)/Re^{1/4}_τ$, where $ϕ^+$ is one of the quantities just mentioned, and the functions $f_0$ and $f_1$ depend only on $y^+$. Here, the superscript $+$ indicates normalization by wall variables. Secondly, by matching the above inner expansion and the inviscid outer flow similarity form, a bounded variation $ϕ^+(y^\ast)=α_ϕ-β_ϕy^{\ast{{1}/{4}}}$ is derived beyond the peak where, for each $ϕ^+$, the constants $α_ϕ$ and $β_ϕ$ are independent of $Re_τ$ and $y^\ast$ ($=y^+/Re_τ$, $Re_τ$ being the Reynolds number based on the friction velocity) -- also in excellent agreement with simulations and experimental data. One of the predictions of the analysis is that, for asymptotically high Reynolds numbers, a finite plateau $ϕ^+\approxα_ϕ$ appears in the outer region. This result sheds light on the intriguing issue of the outer shoulder of the variance of the streamwise velocity fluctuation, which should be bounded by the asymptotic plateau of about 10.

physics.flu-dyn↗

arXiv2023

Forecasting small scale dynamics of fluid turbulence using deep neural networks

Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and incorporate Reynolds number dependence explicitly to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers, and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small scale features of turbulence.

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arXiv2023

Quantum Algorithm for Lattice Boltzmann (QALB) Simulation of Incompressible Fluids with a Nonlinear Collision Term

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the framework introduced by Kowalski that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the bosonic Fock space of the bosons. The streaming and collision steps are both achieved via unitary operators. A quantized version of the nonlinear collision term has been implemented, without introducing variables of discrete densities coupled from neighbouring sites, unlike the classical Carleman technique. We use the compact mapping of the bosonic modes to qubits that uses a number of qubits which scales logarithmically with the size of truncated bosonic Fock space. The work can be readily extended to the multitude of multiphysics problems which could adapt the lattice Boltzmann formulation.

quant-ph↗

arXiv2023

Ensemble Fluid Simulations on Quantum Computers

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.

quant-ph↗

arXiv2023

Emergence of universal scaling in isotropic turbulence

Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power-laws in derivative statistics occurs at modest microscale Reynolds numbers of the order of 10, with the corresponding exponents being consistent with those for the inertial range structure functions at very high Reynolds numbers. In this paper we use well-resolved direct numerical simulations of homogeneous and isotropic turbulence to establish this result for a range of initial conditions with different forcing mechanisms. We also show that the moments of transverse velocity gradients possess larger scaling exponents than those of the longitudinal moments, confirming past results that the former are more intermittent than the latter.

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arXiv2023

Turbulent convection at very high Rayleigh numbers and the weakly nonlinear theory

To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point of view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport at high Rayleigh numbers with predictions from Herring's model and, in fact, find excellent agreement. The model has only one unknown parameter compared to the two free parameters present in the lowest order least-squares power-law fit. We discuss why the underlying simplistic physical picture, meant to work at Rayleigh numbers slightly past the critical value of a few thousands, is consistent with the data, when the single free parameter in it is revised, over some eleven decades of the Rayleigh number -- stretching from about a million to about $10^{17}$.

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arXiv2023

Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers

Recently, Shete et al. [Phys. Rev. Fluids 7, 024601 (2022)] explored the characteristics of passive scalars in the presence of a uniform mean gradient, mixed by stationary isotropic turbulence. They concluded that at high Reynolds and Schmidt numbers, the presence of both inertial-convective and viscous-convective ranges, renders the statistics of the scalar and velocity fluctuations to behave similarly. However, their data included Schmidt numbers of 0.1, 0.7, 1.0 and 7.0, only the last of which can (at best) be regarded as moderately high. Additionally, they do not consider already available data in the literature at substantially higher Schmidt number of up to 512. By including these data, we demonstrate here that the differences between velocity and scalar statistics show no vanishing trends with increasing Reynolds and Schmidt numbers, and essential differences remain in tact at all Reynolds and Schmidt numbers.

physics.flu-dyn↗

arXiv2023

Quantum Carleman Lattice Boltzmann Simulation of Fluids

We present a pedagogical introduction to a quantum computing algorithm for the simulation of classical fluids, based on the Carleman linearization of a second-quantized version of lattice kinetic theory. Prospects and limitations for the case of fluid turbulence are discussed and commented on.

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arXiv2022

Lagrangian acceleration in fully developed turbulence and its Eulerian decompositions

We study the properties of various Eulerian contributions to fluid particle acceleration by using well-resolved direct numerical simulations of isotropic turbulence, with the grid resolution as high as $12288^3$ and the Taylor-scale Reynolds number $R_λ$ in the range between 140 and 1300. The variance of convective acceleration, when normalized by Kolmogorov scales, increases linearly with $R_λ$, consistent with simple theoretical arguments, but very strongly differing from phenomenological predictions of Kolmogorov's hypothesis as well as Eulerian multifractal models. The scaling of the local acceleration is also linear $R_λ$ to the leading order, but more complex in detail. The strong cancellation between the local and convective acceleration -- faithful to the random sweeping hypothesis -- results in the variance of the Lagrangian acceleration increasing only as $R_λ^{0.25}$, as recently shown by Buaria \& Sreenivasan [Phys. Rev. Lett. 128, 234502 (2022)]. The acceleration variance is dominated by irrotational pressure gradient contributions, whose variance also follows an $R_λ^{0.25}$ scaling; the solenoidal viscous contributions are relatively small and follow a $R_λ^{0.13}$, consistent with Eulerian multifractal predictions.

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arXiv2022

Asymmetry of velocity increments in turbulence

We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence -- the asymmetry of velocity increments -- with likely implications on important dynamics. This property, ignored by existing small-scale phenomenological models, manifests most prominently in the non-monotonic trend of velocity increment moments (or structure functions) with the moment order, and in differences between ordinary and absolute structure functions for a given separation distance. We show that high-order structure functions arise nearly entirely from the negative side of the probability density of velocity increments, essentially removing the ambiguity between ordinary and absolute moments, and provide a plausible dynamical interpretation of this result.

physics.flu-dyn↗

arXiv2022

Auroras on Mars: from Discovery to New Developments

Auroras are emissions in a planetary atmosphere caused by its interactions with the surrounding plasma environment. They have been observed in most planets and some moons of the solar system. Since their first discovery in 2005, Mars auroras have been studied extensively and is now a rapidly growing area of research. Since Mars lacks an intrinsic global magnetic field, its crustal field is distributed throughout the planet and its interactions with the surrounding plasma environment lead to a number of complex processes resulting in several types of auroras uncommon on Earth. Martian auroras have been classified as diffuse, discrete and proton aurora. With new capability of synoptic observations made possible with the Hope probe, two new types of auroras have been observed. One of them, which occurs on a much larger spatial scale, covering much of the disk, is known as discrete sinuous aurora. The other subcategory is one of proton auroras observed in patches. Further study of these phenomena will provide insights into the interactions between the atmosphere, magnetosphere and the surrounding plasma environment of Mars. We provide a brief review of the work done on the subject in the past 17 years since their discovery, and report new developments based on observations with Hope probe.

astro-ph.EP↗

arXiv2022

Similarities between characteristics of convective turbulence in confined and extended domains

To understand turbulent convection at very high Rayleigh numbers typical of natural phenomena, computational studies in slender cells are an option if the needed resources have to be optimized within available limits. However, the accompanying horizontal confinement affects some properties of the flow. Here, we explore the characteristics of turbulent fluctuations in the velocity and temperature fields in a cylindrical convection cell of aspect ratio 0.1 by varying the Prandtl number $Pr$ between 0.1 and 200 at a fixed Rayleigh number $Ra = 3 \times 10^{10}$, and find that the fluctuations weaken with increasing $Pr$, quantitatively as in aspect ratio 25. The probability density function (PDF) of temperature fluctuations in the bulk region of the slender cell remains mostly Gaussian, but increasing departures occur as $Pr$ increases beyond unity. We assess the intermittency of the velocity field by computing the PDFs of velocity derivatives and of the kinetic energy dissipation rate, and find increasing intermittency as $Pr$ decreases. In the bulk region of convection, a common result applicable to the slender cell, large aspect ratio cells, as well as in 2D convection, is that the turbulent Prandtl number decreases as $Pr^{-1/3}$.

physics.flu-dyn↗

arXiv2022

The saturation of exponents and the asymptotic fourth state of turbulence

A recent discovery about the inertial range of homogeneous and isotropic turbulence is the saturation of the scaling exponents $ζ_n$ for large $n$, defined via structure functions of order $n$ as $S_{n}(r)=\overline{(δ_r u)^{n}}=A(n)r^{ζ_{n}}$. We focus on longitudinal structure functions for $δ_r u$ between two positions that are $r$ apart in the same direction. In a previous paper (Phys.\ Rev.\ Fluids 6, 104604, 2021), we developed a theory for $ζ_n$, which agrees with measurements for all $n$ for which reliable data are available, and shows saturation for large $n$. Here, we derive expressions for the probability density functions of $δ_r u$ for four different states of turbulence, including the asymptotic fourth state corresponding to the saturation of exponents for large $n$. This saturation means that the scale separation is violated in favor of a strongly-coupled quasi-ordered flow structures, which take the form of long and thin (worm-like) structures of length $L$ and thickness $l=O(L/Re)$.

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