Nonequilibrium Scaling of the Turbulent-Nonturbulent Interface Speed in Planar Jets.

The length scale which, combined with the fluid's kinematic viscosity ν, defines the local average speed of the turbulent-nonturbulent interface has been postulated to be the smallest (Kolmogorov) length scale η of the turbulence Corrsin and Kistler, [NACA Report No. 1244, 1955, p. 1033.

Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets.

We study the self-similarity and dissipation scalings of a turbulent planar jet and the theoretically implied mean flow scalings. Unlike turbulent wakes where such studies have already been carried out (Dairay 2015 . , 166-198.

Attached flow structure and streamwise energy spectra in a turbulent boundary layer.

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E_{11}(k_{x}) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Re_{τ} considered here which are between 10^{3} and 10^{4}. Instead, we find E_{11}(k_{x})∼k_{x}^{-1-p} where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures.

Statistical independence of the initial conditions in chaotic mixing.

Experimental evidence of the scalar convergence towards a global strange eigenmode independent of the scalar initial condition in chaotic mixing is provided. This convergence, underpinning the independent nature of chaotic mixing in any passive scalar, is presented by scalar fields with different initial conditions casting statistically similar shapes when advected by periodic unsteady flows. As the scalar patterns converge towards a global strange eigenmode, the scalar filaments, locally aligned with the direction of maximum stretching, as described by the Lagrangian stretching theory, stack together in an inhomogeneous pattern at distances smaller than their asymptotic minimum widths.

Unsteady turbulence cascades.

We have run a total of 311 direct numerical simulations (DNSs) of decaying three-dimensional Navier-Stokes turbulence in a periodic box with values of the Taylor length-based Reynolds number up to about 300 and an energy spectrum with a wide wave-number range of close to -5/3 power-law dependence at the higher Reynolds numbers. On the basis of these runs, we have found a critical time when (i) the rate of change of the square of the integral length scale turns from increasing to decreasing, (ii) the ratio of interscale energy flux to high-pass filtered turbulence dissipation changes from decreasing to very slowly increasing in the inertial range, (iii) the signature of large-scale coherent structures disappears in the energy spectrum, and (iv) the scaling of the turbulence dissipation changes from the one recently discovered in DNSs of forced unsteady turbulence and in wind tunnel experiments of turbulent wakes and grid-generated turbulence to the classical scaling proposed by G. I.

Topologies of velocity-field stagnation points generated by a single pair of magnets in free-surface electromagnetic experiments.

The velocity fields generated by a static pair of magnets in free-surface electromagnetically forced flows are analyzed for different magnet attitudes, ionic currents, and brine depths. A wide range of laminar velocity fields is obtained despite the forcing simplicity. The velocity fields are classified according to their temporal mean flow topology, which strongly depends on the forcing geometry but barely on its strength, even through the bifurcation to unsteady regimes.

Axisymmetric turbulent wakes with new nonequilibrium similarity scalings.

The recently discovered nonequilibrium turbulence dissipation law implies the existence of axisymmetric turbulent wake regions where the mean flow velocity deficit decays as the inverse of the distance from the wake-generating body and the wake width grows as the square root of that distance. This behavior is different from any documented boundary-free turbulent shear flow to date. Its existence is confirmed in wind tunnel experiments of wakes generated by plates with irregular edges placed normal to an incoming free stream.

Fractal space-scale unfolding mechanism for energy-efficient turbulent mixing.

Using top-end high fidelity computer simulations we demonstrate the existence of a mechanism present in turbulent flows generated by multiscale or fractal objects and which has its origin in the multiscale or fractal space-scale structure of such turbulent flow generators. As a result of this space-scale unfolding mechanism, fractal grids can enhance scalar transfer and turbulent diffusion by one order of magnitude while at the same time reduce pressure drop by half. This mechanism must be playing a decisive role in environmental, atmospheric, ocean, and river transport processes wherever turbulence originates from multiscale or fractal objects such as trees, forests, mountains, rocky riverbeds, and coral reefs.

Universal dissipation scaling for nonequilibrium turbulence.

It is experimentally shown that the nonclassical high Reynolds number energy dissipation behavior, C(ε)≡εL/u(3)=f(Re(M))/Re(L), observed during the decay of fractal square grid-generated turbulence (where Re(M) is a global inlet Reynolds number and Re(L) is a local turbulence Reynolds number) is also manifested in decaying turbulence originating from various regular grids. For sufficiently high values of the global Reynolds numbers Re(M), f(Re(M))~Re(M).

Rapid growth of cloud droplets by turbulence.

Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain the rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity and small-scale intermittency into account. This is because the range of local Stokes numbers of identical droplets in the turbulent flow field is broad enough even when small-scale intermittency is neglected. This demonstration is given for turbulence which is one order of magnitude less intense than is typical in warm clouds but with a volume fraction which, even though small, is nevertheless large enough for an estimated a priori frequency of collisions to be ten times larger than in warm clouds.

Strong polymer-turbulence interactions in viscoelastic turbulent channel flow.

This paper is focused on the fundamental mechanism(s) of viscoelastic turbulence that leads to polymer-induced turbulent drag reduction phenomenon. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective state-of-the-art numerical method to solve the governing equation for polymers modeled as nonlinear springs, without using any artificial assumptions as usual, was implemented here on a three-dimensional channel flow geometry.

Defining a new class of turbulent flows.

We apply a method based on the theory of Markov processes to fractal-generated turbulence and obtain joint probabilities of velocity increments at several scales. From experimental data we extract a Fokker-Planck equation which describes the interscale dynamics of the turbulence. In stark contrast to all documented boundary-free turbulent flows, the multiscale statistics of velocity increments, the coefficients of the Fokker-Planck equation, and dissipation-range intermittency are all independent of Rλ (the characteristic ratio of inertial to viscous forces in the fluid).

Acceleration-based classification and evolution of fluid flow structures in two-dimensional turbulence.

Zero acceleration points (ZAPs) and flow structures around them are studied in a direct numerical simulation of two-dimensional energy-cascading stationary homogeneous isotropic turbulence with an extended k(-5/3) energy spectrum. A well-defined classification of ZAPs in terms of the acceleration gradient tensor's (∇a) invariants emerges naturally as a result of well-defined properties of and relations between these invariants at ZAPs. About half of all ZAPs are anti-ZAPs [with det(∇a)<0 ] and the number of vortical and straining ZAPs [with det(∇a)>0 ] is about the same.

Stagnation point von Kármán coefficient.

On the basis of various direct numerical simulations (DNS) of turbulent channel flows the following picture is proposed. (i) At a distance y from either wall, the Taylor microscale lambda is proportional to the average distance l(s) between stagnation points of the fluctuating velocity field, i.e.

Evolution of the acceleration field and a reformulation of the sweeping decorrelation hypothesis in two-dimensional turbulence.

From simulations of two-dimensional inverse energy cascading turbulence, we show that points with low acceleration values are predominantly advected by the local fluid velocity. The fluid velocity u in the global frame and the fluid velocity u in the frame moving with a low-acceleration point are approximately statistically independent. This property remains valid in high-acceleration regions but only in the direction of the local acceleration vector.

Depletion of horizontal pair diffusion in strongly stratified turbulence: comparison with plane two-dimensional flows.

In this paper different arguments are put forward to explain why two-particle diffusion is depleted in the direction of stratification of a stably stratified turbulence. Kinematic simulations (KSs) which reproduce that depletion are used to shed light on the responsible mechanisms. The local horizontal divergence is studied and comparisons are made with two-dimensional kinematic simulation.

Tortuosity of unsaturated porous fractal materials.

The tortuosity of a capillary-condensed film of inviscid fluid adsorbed onto fractal substrates as a function of the filling fraction of the fluid has been calculated numerically. This acts as a way of probing the multiscale structure of the objects. It is found that the variation of tortuosity alpha with filling fraction varphi is found to follow a power law of the form alpha approximately varphi- for both deterministic and stochastic fractals.

Sweep-stick mechanism of heavy particle clustering in fluid turbulence.

It is proposed that the inertial range clustering of small heavy particles in fluid turbulence occurs as a result of the sweep-stick mechanism which causes inertial particles to cluster so as to mimic the clusters of points where the fluid acceleration is perpendicular to the direction of highest contraction between neighboring particles. Direct numerical simulations of inertial particles subjected to linear Stokes drag and suspended in homogeneous isotropic turbulence support the validity of the sweep and stick properties on which the sweep-stick mechanism is based, and also support the clustering consequences of this mechanism. It also explains the observed Stokes-number dependence of inertial particle clustering.

Transport properties of saturated and unsaturated porous fractal materials.

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales.

Fast chemical reaction and multiple-scale concentration fields in singular vortices.

Two species involved in a simple, fast reaction tend to become segregated in patches composed of a single of these reactants. These patches are separated by a boundary where the stoichiometric condition is satisfied and the reaction occurs, fed by diffusion. Stirred by advection, this boundary and the concentration fields within the patches may tend to present multiple-scale characteristics.

Multiscale laminar flows with turbulentlike properties.

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multiscale stagnation point topology. This topology is shown to control the evolution of pair separation (Delta) statistics by imposing a turbulentlike locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case Delta(2) approximately t(gamma) is a good approximation with gamma close to 3. Spatially multiscale laminar flows with turbulentlike spectral and stirring properties are a new concept with potential applications in efficient and microfluidic mixing.

Fundamentals of pair diffusion in kinematic simulations of turbulence.

We demonstrate that kinematic simulation (KS) of three-dimensional homogeneous turbulence produces fluid element pair statistics in agreement with the predictions of L F. Richardson [Proc. R.

Turbulent wakes of fractal objects.

Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are studied within inertial and dissipative range scales in an attempt to relate changes in their self-similar behavior to the scaling of the fractal objects.

Acceleration statistics as measures of statistical persistence of streamlines in isotropic turbulence.

We introduce the velocity Vs of stagnation points as a means to characterize and measure statistical persistence of streamlines. Using theoretical arguments, direct numerical simulations (DNS), and kinematic simulations (KS) of three-dimensional isotropic turbulence for different ratios of inner to outer length scales L/eta of the self-similar range, we show that a frame exists where the average Vs = 0 , that the rms values of acceleration, turbulent fluid velocity, and Vs are related by La'/u'2 approximately (V's/u')(L/eta)(2/3+q) , and that V's/u' approximately (L/eta)q with q = -1/3 in Kolmogorov turbulence, q = -1/6 in current DNS, and q = 0 in our KS. The statistical persistence hypothesis is closely related to the Tennekes sweeping hypothesis.

Inertial particle segregation by turbulence.

We study collections of heavy and light small spherical particles initially well mixed with each other, subjected to linear (Stokes) drag force and gravity, and falling through a fluid turbulence. We introduce the segregation power spectrum, which we use to define the segregation length scale. Kinematic simulation predicts that the turbulence can segregate heavy and light falling particles and leads to a well-defined segregation length scale.