arXiv subjects

V. Yakhot

Publications and source records attributed to V. Yakhot.

11 recordsLinked to original sources

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.

physics.flu-dyn↗

arXiv2021

Dynamics of three-dimensional turbulence from Navier-Stokes equations

We accomplish two major tasks. First, we show that the turbulent motion at large scales obeys Gaussian statistics in the interval 0 < Rlambda < 8.8, where Rlambda is the microscale Reynolds number, and that the Gaussian flow breaks down to yield place to anomalous scaling at the universal Reynolds number bounding the inequality above. In the inertial range of turbulence that emerges following the breakdown, the effective Reynolds number based on the turbulent viscosity, Rlambda* assumes this same constant value of about 9. This scenario works also for the emergence of turbulence from an initially non-turbulent state. Second, we derive expressions for the anomalous scaling exponents of structure functions and moments of spatial derivatives, by analyzing the Navier-Stokes equations in the form developed by Hopf. We present a novel procedure to close the Hopf equation, resulting in expressions for zetan in the entire range of allowable moment-order, n, and demonstrate that accounting for the temporal dynamics changes the scaling from normal to anomalous. For large n, the theory predicts the saturation of zetan with n, leading to two inferences: (a) the smallest length scale etan = LRe-1 << LRe-3/4, where Re is the large-scale Reynolds number, and (b) velocity excursions across even the smallest length scales can sometimes be as large as the large scale velocity itself. Theoretical predictions for each of these aspects are shown to be in quantitative agreement with available experimental and numerical data.

physics.flu-dyn↗

arXiv2015

Nanofluidics of Single-crystal Diamond Nanomechanical Resonators

Single-crystal diamond nanomechanical resonators are being developed for countless applications. A number of these applications require that the resonator be operated in a fluid, i.e., a gas or a liquid. Here, we investigate the fluid dynamics of single-crystal diamond nanomechanical resonators in the form of nanocantilevers. First, we measure the pressure-dependent dissipation of diamond nanocantilevers with different linear dimensions and frequencies in three gases, He, N$_2$, and Ar. We observe that a subtle interplay between the length scale and the frequency governs the scaling of the fluidic dissipation. Second, we obtain a comparison of the surface accommodation of different gases on the diamond surface by analyzing the dissipation in the molecular flow regime. Finally, we measure the thermal fluctuations of the nanocantilevers in water, and compare the observed dissipation and frequency shifts with theoretical predictions. These findings set the stage for developing diamond nanomechanical resonators operable in fluids.

physics.flu-dyn↗

arXiv2015

Noisy Transitional Flows in Imperfect Channels

Here, we study noisy transitional flows in imperfect millimeter-scale channels. For probing the flows, we use microcantilever sensors embedded in the channel walls. We perform experiments in two nominally identical channels. The different set of imperfections in the two channels result in two random flows in which high-order moments of near-wall fluctuations differ by orders of magnitude. Surprisingly however, the lowest order statistics in both cases appear qualitatively similar and can be described by a proposed noisy Landau equation for a slow mode. The noise, regardless of its origin, regularizes the Landau singularity of the relaxation time and makes transitions driven by different noise sources appear similar.

physics.flu-dyn↗

arXiv2013

Noninvasive Measurement of the Pressure Distribution in a Deformable Micro-Channel

Direct and noninvasive measurement of the pressure distribution in test sections of a micro-channel is a challenging, if not an impossible, task. Here, we present an analytical method for extracting the pressure distribution in a deformable micro-channel under flow. Our method is based on a measurement of the channel deflection profile as a function of applied \emph{hydrostatic} pressure; this initial measurement generates "constitutive curves" for the deformable channel. The deflection profile under flow is then matched to the constitutive curves, providing the \emph{hydrodynamic} pressure distribution. The method is validated by measurements on planar micro-fluidic channels against analytic and numerical models. The accuracy here is independent of the nature of the wall deformations and is not degraded even in the limit of large deflections, $ζ_{\rm{max}}/2h_{0}= {\cal{O}}(1)$, with $ζ_{\rm{max}}$ and $2h_0$ being the maximum deflection and the unperturbed height of the channel, respectively. We discuss possible applications of the method in characterizing micro-flows, including those in biological systems.

physics.flu-dyn↗

arXiv2012

Crossover from Hydrodynamics to the Kinetic Regime in Confined Nanoflows

We present an experimental study of a confined nanoflow, which is generated by a sphere oscillating in the proximity of a flat solid wall in a simple fluid. Varying the oscillation frequency, the confining length scale and the fluid mean free path over a broad range provides a detailed map of the flow. We use this experimental map to construct a scaling function, which describes the nanoflow in the entire parameter space, including both the hydrodynamic and the kinetic regimes. Our scaling function unifies previous theories based on the slip boundary condition and the effective viscosity.

physics.flu-dyn↗

arXiv2008

A Universality in Oscillating Flows

We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter $ωτ$, where $ω$ is the oscillation (angular) frequency and $τ$ is the fluid relaxation-time; geometry and linear dimension bear no effect on the flow. Experimental energy dissipation data of mechanical resonators in a rarefied gas follow this universality closely in a broad linear dimension ($10^{-6}$ m$< L < 10^{-2}$ m) and frequency ($10^5$ Hz $< ω/2π< 10^8$ Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.

physics.flu-dyn↗

arXiv2007

Computational coarse graining of a randomly forced 1-D Burgers equation

We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, and nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.

physics.comp-ph↗

arXiv2007

High-Frequency Nanofluidics: An Experimental Study using Nanomechanical Resonators

Here we apply nanomechanical resonators to the study of oscillatory fluid dynamics. A high-resonance-frequency nanomechanical resonator generates a rapidly oscillating flow in a surrounding gaseous environment; the nature of the flow is studied through the flow-resonator interaction. Over the broad frequency and pressure range explored, we observe signs of a transition from Newtonian to non-Newtonian flow at $ωτ\approx 1$, where $τ$ is a properly defined fluid relaxation time. The obtained experimental data appears to be in close quantitative agreement with a theory that predicts purely elastic fluid response as $ωτ\to \infty$.

cond-mat.other↗

arXiv2007

"Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators

Using kinetic equation in the relaxation approximation (RTA), we investigate a flow generated by an infinite plate oscillating with frequency $ω$. Geometrical simplicity of the problem allows a solution in the entire range of dimensionless frequency variation $0\leq ωτ\leq \infty$, where $τ$ is a properly defined relaxation time. A transition from viscoelastic behavior of Newtonian fluid ($ωτ\to 0$) to purely elastic dynamics in the limit $ωτ\to \infty$ is discovered. The relation of the derived solutions to microfluidics (high-frequency micro-resonators) is demonstrated on an example of a "plane oscillator .

nlin.CD↗

arXiv1997

Propagation of a Huygens front through turbulent medium

The dynamics of a thin Huygens front propagating through turbulent medium is considered. A rigorous asymptotic expression for the effective velocity $v_{F}$ proportional to the front area is derived. The small-scale fluctuations of the front position are shown to be strongly intermittent. This intermittency plays a crucial role in establishing a steady state magnitude of the front velocity. The results are compared with experimental data.

chao-dyn↗