Coherence in Turbulence: New Perspective

Статья выдающегося советского, а в течение последних сорока лет американо-израильского физика-теоретика Евгения Левича знаменует новый подход и новое понимание турбулентных процессов. Работа опубликована в журнале Old and New Concepts of Physics, являвшегося прообразом и предшественником журнала Новых Концепций и представлена для привлечения широкого круга профессиональных читателей главным редактором журнала Old and New Concepts of Physics и одним из основателей журнала Newconcepts профессором Эдвардом Капусчиком (Польша). 

COHERENCE IN TURBULENCE

 

 

Abstract

It is claimed that turbulence in uids is inherently coher-

ent phenomenon. The coherence shows up clearly as strongly

correlated helicity uctuations of opposite sign. The helic-

ity uctuations have cellular structure forming clusters that

are actually observed as vorticity bands and coherent struc-

tures in laboratory turbulence, direct numerical simulations

and most obviously in atmospheric turbulence. The clusters

are named BCC - Beltrami Cellular Clusters - because of the

observed nearly total alignment of the velocity and vorticity

elds in each particular cell, and hence nearly maximal possi-

ble helicity in each cell; although when averaged over all the

cells the residual mean helicity in general is small and does

not play active dynamical role. The Beltrami like

are short-lived and stabilize only in small and generally con-

tiguous sub-domains that are tending to a (multi)fractal in the

asymptotic limit of large Reynolds numbers, Re ! 1. For the

model of homogeneous isotropic turbulence the theory predicts

the leading fractal dimension of BCC to be: DF = 2:5:

particular BCC is responsible for generating the Kolmogorov

5=3 power law energy spectrum.

The most obvious role that BCC play dynamically is that

the nonlinear interactions in them are relatively reduced, due

to strong spatial alignment between the velocity eld v(r; t)

and the vorticity eld !(r; t) = curlv(r; t); while the physical

quantities typically best characterizing turbulence intermit-

tency, such as entrophy, vorticity stretching and generation,

and energy dissipation are maximized in and near them. The

theory quantitatively relates the reduction of nonlinear inter-

actions to the BCC fractal dimension DF and subsequent

turbulence intermittency.

It is further asserted that BCC is a fundamental feature of

all turbulent ows, e.g., wall bounded turbulent ows, atmo-

spheric and oceanic ows, and their leading fractal dimension

remains invariant and universal in these ows. In particu-

lar, theoretical and numerical evidence is given indicating that

BCC in turbulent channel/pipe ows have the depth at the

walls proportional to the square root of the Reynolds number

in wall units, Ly /p

Re , which is equivalent to the fractal dimension in normal to the walls y direction Dy

F = 0; 5;

and the total dimension DF = Dx;z

F + Dy

F = 2 + 0:5 = 2:5:

Similar BCC structure and the same fractal dimension are

suggested for geophysical turbulence, in near agreement with

the recent comprehensive analysis of experimental and obser-

vational data. It is asserted that the atmospheric and oceanic

events, e.g., tropical hurricanes, tornadoes and other mesoscale

phenomena, and probably ocean currents are manifestations of

BCC and their environs.

Generally BCC should be rather seen as the turbulence

core, while the whole surrounding 3D ow as being created

and sustained by the intense vorticity of BCC by means of

induction, in a manner similar to that for an electric current

generating magnetic eld.

It is further argued that BCC is not only a theoretical

concept important for fundamental grasp on turbulence, but

may be a practical asset furnishing tools for turbulence man-

agement in regular uids and plasmas.

The concept of helical uctuations in turbulence goes 25

years back in time, and while never totally abandoned nev-

ertheless has been residing on the fringes of research activity.

 

 

Experiment and numerical simulations had not been able to ei-

ther validate or repudiate decisively the concept. However, re-

cent large scale direct numerical simulations and proliferation

of experimental and observational data showed convincingly

how ubiquitous is the phenomenon of helicity uctuations in

various turbulent ows, from hurricanes and tornadoes to tur-

bulent jets to solar wind plasma turbulence to turbulent

in compressible uids. This allowed a fresh look at the concept

and led to a quantitative theory exposed in this paper.

The paper concludes with a brief discussion of possible sim-

ilarities between turbulence and certain other complex non-

equilibrium systems generating smart intrinsic coherence in

the course of dissipative dynamical evolution.

 

Concepts of Physics, Vol. VI, No. 3 (2009) 241

Eugene Levich