The Enigma of Turbulence – Part I


which description would you choose describe turbulence best:

Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity… Lewis Fry Richardson

  • Turbulence is a phenomenon which sets in in a viscous fluid for values of viscosity, hence its purest, limiting form may be interpreted as asymptotic, limiting behavior of viscous fluid as its coefficient approaches zero… Neumann
  • Turbulence is a manifestation of the spatial and temporal chaotic behaviour of fluid flows at large Reynolds numbers, of a strong ly nonlinear dissipative system with an enormous large number of degrees of freedom described by th Navier-Stokes equations.

Or perhaps none is sufficient to say one of the above as conclusive description of the quantitative features manifested in the turbulence phenomenon.

The first bold quest to describe turbulence by means of convenient understanding where those conducted in the seminal work of Tenneks and Lumley, and to do so in a qualitative manner.

A First Course in Turbulence (MIT Press)

So let us begin:

  • Intristic spatial-temporal seemingly random irregularity:Turbulence is without a doubt chaotic. One of the most important features the is self -stochatization. Meaning there is no need for an external random forcing in the fluid domain its self or at its boundaries and no initial condition is of necessity as far as the reynolds number – a dimensionless number reflecting on how well momentum is diffused relative to the flow velocity (in the cross-stream direction) and on the thickness of a boundary layer relative to the body which is “large enough”.
    An interesting question raised by J. K. McDonough is how such behaviour arises from a set of deterministic equations as NSE. The answer lies in the equation being extremely sensitive in initial, boundary conditions or external noise. Turbulence acts as the ultimate non-linear oscillator and an amplifier with an enormous gain.
  • Wide range of strongly interacting scales:
    In atmospheric flows, relevent scales range from hundreds of kilometers to sizes comparable with less than a millimeter. Putting this on somewhat of a mathematical ground this translates to about 10^30 excited degrees of freedom is which are strongly interacting. This fact is extremely interesting, again contributing a J. M. Mcdonough standpoint that the statistical description is by no means statistical theorization (consider this strong point when conducting CFD by statistical measures such as RANS and LES).
    The strong interaction between som many scales resulting from non-linearity (linear systems with as many scales possible do not excite each other).kolmogorov scales                                                 Wide range of interacting scales
  • Unpredictability:
    Chaos is chaos. Two initially nearly (but not precisely, let us say to a difference sizable of the order of 10^-30 mm)become unrecognizable different on a time scale of engineering or even academic interest. One realization is strongly different from the other (consider this fact as quantitive trying to validate a DNS by one realization. Strongly chaotic systems like turbulence are extremely sensitive to small disturbances. The interesting concept which qualitatively wins the day is that different realizations of the same turbulent flows have the same statistical properties.
    That is almost al statistical properties carry that special and beloved feature, which actually means that statistical features of different realizations of the same turbulent flows are insensitive to disturbances – they are statistically stable.
    Mind you not, this feature is only statistical (CFD statistical methods rely on this for “simulating reality”).
    This means that turbulent flows carry both predictable and unpredictable features. different pairs of realizations have the same statistical features. The qualitative route wins again.
  • Turbulent flows are highly dissipative:
    It is a well-known fact that a source of energy is an inseparable ingredient to maintain turbulence, and the energy is supplied mostly by the large scales while the dissipation occurs at the small ones. statistically irreversible process is happening – turbulent flows are directed only in one way in time.
  • Turbulent flows are three-dimensional and rotational
    The  “random” fields of vorticity (curl of the velocity vector) own predominant vortex stretching. This actually means continuous positive production of enstrophy by nonlinear inertial processes, that dissipate by viscosity. A feature exhibited is positive production of strain due to amplification of the gradients of the velocity fields (as both strain and rotation are an extraction from the velocity gradient tensor). The direct three-dimensional rotational nature is a qualitative feature extracted from realization of DNS (especially by visualisation of the Q factor).

Turbulent Boundary Layer DNS (APS Gallery Submission)

  • Strongly diffusive :
    Strongly and enhanced transport processes are exhibited in turbulent flows. Besides momentum and energy these are the passive objects (scalars like particles, heat and moisture and vectors liken gradients of passive scalars and magnetic fields).
    The enhancement of diffusive effects is not actually a particular property of turbulence as every random field, even Lagrangian chaotic laminar flows exhibit enhanced transport of passive objects.
    Particle image velocimetry (PIV) combined or better yet 3DPTV (stand corrected by one of my mentors in a comment below) with an Eulerian/Lagrangian DNS are the future arsenal of weaponry to explore quantitative manifestation of the well exhibited qualitative feature.


particle image velocimetry

To Conclude, these widely known qualitative features of all turbulence flows are the same in essence. By that we may keep talking about the concept of qualitative universality.


We shall close with one of the videos I found as a pearl:

5 thoughts on “The Enigma of Turbulence – Part I

  1. Just a remark about PIV – it’s a great tool, but limited for the highly three-dimensional turbulent flows. I recommend to mention 3D-PTV as an alternative that better suits turbulent flow studies. It provides both Lagrangian and through interpolation Eulerian information (note that the opposite transfer from Eulerian to Lagrangian is not possible) and it can now run on pretty fast hardware and large CMOS cameras very effectively.

  2. Pingback: Let’s Talk Turbulence – Part II – CFD ISRAEL – TENZOR blog – Autohrized Channel Partner – ANSYS

  3. Pingback: Direct Numerical Simulation Part III – The Reynolds Number Limitation – CFD ISRAEL – TENZOR blog – Autohrized Channel Partner – ANSYS

  4. Pingback: Define Turbulence… PART I – CFD ISRAEL – TENZOR blog – Autohrized Channel Partner – ANSYS

Leave a Reply