turbulence

      a flow regime

stochastic
      rapid variation of

            pressure & velocity

      (dimensionless)

      unsteady
                 vortices
      on many scales



interact with each other

      energy cascades

             from large scale structures

                        to smaller

via inertia

      solutions are unstable


                    dependence on initial

      & boundary

                        conditions

      makes fluid

                    flow
irregular



      in time and in space

      Kolmogorov

                    proposed the first

                          statistical theory

relating to turbulence:

                     the cascade

                     through microscales

and self-similarities

are broken

      inhering to

on other levels:


mesocyclones within

      a convective storm

                    ionized crowns

                                   of hail and lightning.

             As a result,

                                   the Kolmogorov microscales

              were named after him, still,

              the complete description

of turbulence remains one of the

              unsolved problems

                               in physics.