Intermittency, dissipation anomaly and closure in 3D turbulence

7 problems

• Origin of anomalous scaling exponents in three-dimensional turbulence

  Open

  In turbulence, velocity differences between two points grow with their separation, and the simplest theory (Kolmogorov 1941) predicts how; measurements show rare violent events that break this prediction more and more strongly for higher statistical moments. Nobody can yet calculate the observed deviations from the equations of fluid motion.

• Decay exponent of freely decaying homogeneous isotropic turbulence

  Contested

  When stirring stops, turbulence in a box dies away with its energy falling as a power of time. Measured powers differ by up to a factor of two between experiments, and theory gives competing values that depend on how the largest swirls were set up.

• Do high-order structure-function exponents saturate at large order?

  Partially resolved

  The statistics of the most extreme velocity differences appear to stop becoming more extreme beyond a certain order, as if the flow had a limiting roughness. Whether this saturation is real, and the same for differences measured along and across the separation, is not established.

• Controlled closure calculation of the Kolmogorov constant

  Open

  The energy spectrum of turbulence has a known shape with one dimensionless prefactor, the Kolmogorov constant, measured near 1.6. No calculation from the equations of motion produces this number with an error that the method itself controls.

• Do Lagrangian intermittency exponents follow from Eulerian ones?

  Partially resolved

  The velocity of a single fluid particle followed in time shows rare violent jumps, just as velocity differences between two points in space do. Whether the jumps along a particle path are fully predictable from the spatial ones, at all flow speeds and statistical orders, is not established.

• Does small-scale anisotropy of a mixed scalar vanish at high Reynolds number?

  Open

  When turbulence stirs a dye or temperature that varies steadily in one direction, the small-scale ripples of the dye keep a preferred direction even at the highest speeds tested. This contradicts the textbook expectation that small scales forget large-scale directions, and whether the memory ever disappears is unknown.

• Is the dissipation anomaly strong or weak in wall-free turbulence?

  Contested

  Experiments suggest that turbulent energy loss stays finite even as the fluid viscosity is made vanishingly small, a property called the dissipation anomaly. Recent large simulations without walls hint that the effect may instead fade very slowly as the flow speed grows.