Emergence of Multiscaling in a Random-Force Stirred Fluid.

We consider the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that, due to multiscaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting a multitude of anomalous scaling exponents.

Generalized Knudsen Number for Unsteady Fluid Flow.

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain.

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, that is, a gas or a liquid. Here, we investigate the fluid dynamics of single-crystal diamond nanomechanical resonators in the form of nanocantilevers.

Reynolds number of transition and self-organized criticality of strong turbulence.

A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers k>Λf, where Λf is a relatively small set of the wave vectors where energy is pumped into fluid by external forces. Iterative averaging over small-scale velocity fluctuations from the interval Λf View Article and Find Full Text PDF

Small-scale universality in fluid turbulence.

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries.

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.

Porous superhydrophobic membranes: hydrodynamic anomaly in oscillating flows.

We have fabricated and characterized a novel superhydrophobic system, a meshlike porous superhydrophobic membrane with solid area fraction Φ(s), which can maintain intimate contact with outside air and water reservoirs simultaneously. Oscillatory hydrodynamic measurements on porous superhydrophobic membranes as a function of Φ(s) reveal surprising effects. The hydrodynamic mass oscillating in phase with the membranes stays constant for 0.

Skin friction in zero-pressure-gradient boundary layers.

A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as Re(δ)→ ∞, the dynamically defined boundary layer thickness δ(x) ∝ x/ln2  Rex and the skin friction λ = 2τ(w)/ρU(0)(2) ∝ 1/ln2  δ(x). Here τ(w) and U0 are the wall shear stress and free stream velocity, respectively.

High-frequency nanofluidics: a universal formulation of the fluid dynamics of MEMS and NEMS.

A solid body undergoing oscillatory motion in a fluid generates an oscillating flow. Oscillating flows in Newtonian fluids were first treated by G.G.

Measurement of local dissipation scales in turbulent pipe flow.

Local dissipation scales are a manifestation of the intermittent small-scale nature of turbulence. We report the first experimental evaluation of the distribution of local dissipation scales in turbulent pipe flows for a range of Reynolds numbers: 2.4x10(4) View Article and Find Full Text PDF

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 omega tau, where omega is the oscillation (angular) frequency and tau is the fluid relaxation time; geometry and linear dimension bear no effect on the flow. Energy dissipation of mechanical resonators in a rarefied gas follows this universality closely in a broad linear dimension (10(-6) m < L < 10(-2) m) and frequency (10(5) Hz < omega/2pi < 10(8) Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.

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 omega tau approximately 1, where tau is a properly defined fluid relaxation time.

Crossover in the enstrophy decay in two-dimensional turbulence in a finite box.

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this Letter uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy Omega, generated by a random Gaussian initial condition, decays as Omega(t) proportional variant t(-gamma) with gamma approximately 0.7-0.

Numerical simulation of the excitation of a Helmholtz resonator by a grazing flow.

The process of noise generation in a flow-excited Helmholtz resonator involves strong interaction between a time-dependent fluid flow and acoustic resonance. Quantitative prediction of this effect, requiring accurate prediction of time-dependent features of a flow over complex three-dimensional bodies, turbulence modeling, compressibility and Mach number effects, is one of the major challenges to computational fluid dynamics. In this paper a numerical procedure based on the lattice kinetic equation, combined with the RNG turbulence model, is applied to describe a well-controlled experiment on acoustic resonance excitation by a grazing flow [Nelson et al.

Extended Boltzmann kinetic equation for turbulent flows.

Complex fluid physics can be modeled using an extended kinetic (Boltzmann) equation in a more efficient way than using the continuum Navier-Stokes equations. Here, we explain this method for modeling fluid turbulence and show its effectiveness with the use of a computationally efficient implementation in terms of a discrete or "lattice" Boltzmann equation.

Two-dimensional turbulence in the inverse cascade range.

Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "normal" Kolmogorov scaling <(deltav)(2n)> proportional r(2n/3) and obey Gaussian statistics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explaining these observations is presented in this paper.

Critical "dimension" in shell model turbulence.

We investigate the Gledzer-Ohkitani-Yamada (GOY) shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an "effective dimension" between d=2 and d=3. We identify a critical point between these two situations where the flux of energy changes sign and the helicity flux diverges.

Mean-field approximation and extended self-similarity in turbulence.

Recent experimental discovery of extended self-similarity (ESS) was one of the most interesting developments, enabling precise determination of the scaling exponents of fully developed turbulence. A sufficient condition for extended self-similarity in a general dynamical system is derived in this paper. It is also shown that if the pressure-gradient contributions are expressed in terms of velocity differences in the mean-field approximation [V.

Symmetry breaking, anomalous scaling, and large-scale flow generation in a convection cell.

We consider a convection process in thin loops of different geometries. At Ra=Ra(')(cr) a first transition leading to the generation of corner vortices is observed. At higher Ra (Ra>Ra(cr)) a coherent large-scale flow, which persists for a very long time, sets up.

Mean-field approximation and a small parameter in turbulence theory.

Numerical and physical experiments on two-dimensional (2D) turbulence show that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space dimensionality d=d(c), at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant.