Citations

Hydrodynamic instability, energy deficit during transition

  • Es wird oft angemerkt, dass Turbulenz nichts mit einer strömungsmechanischen Instabilität zu tun hat (H. Oertel, jr. in Prandtl’s Textbook, 13. edition)
  • During transition to turbulence, the flow resistance increases by a factor 3-10. The input of mechanical power into the experiment has to be increased by that magnitude. Without that additional energy input no transition takes place (H.P. Drescher).
  • Any transition has to be “forced”. The critical Reynolds number could be adjusted anywhere in the range of 2000-13000 (F. Durst, B. Ünsal).
  • When turbulent transition occurs, the pressure drop changes and the unit automatically adjusts immediately to take this increased pressure drop into account to yield a pipe flow with a constant mass flow rate (F. Durst, B. Ünsal).
  • Klassische Lehrbücher der theoretischen Physik behandeln das Kontinuum in der Regel, ohne auf die thermischen Effekte einzugehen (J. Meixner).
  • Remark on discussions with A. Sommerfeldt: “Dem Verständnis der Turbulenz war er (A. Sommerfeldt) nicht nähergekommen“ (Th. v. Kármán).

Non-local physical character of turbulence

  • There is the “fundamental paradox” of turbulence modelling, between the local character of the partial differential equations and the non-local physical nature of turbulence (Ph. R. Spalart).
  • The historical statements of Prandtl, v. Kármàn, Taylor (mixing length, turbulent boundary layer, similarity, logarithmic flow profile) are non-local and not at all based on the Navier-Stokes equations (H.P. Drescher).
  • “A certain analogy to the kinetic theory of gases” in Prandtl’s mixing length hypothesis (H. Schlichting).
  • The kinematic component of non-steady motion play a much greater role than one could have previously supposed based on the closed treatment of the corresponding system of equations (C.E.A. Meier).
  • The (logarithmic) law of the wall is one of the most famous empirically derived relationships in turbulent flows (D. C. Wilcox).
  • The experimental turbulent Couette flow profile cannot be described by the Navier-Stokes equations (H.P. Drescher).

Direct numerical simulation (DNS)

  • Not all simulations based on the Navier-Stokes equations are “direct”. Because of artificial modifications, incomplete resolution, or non-physical boundary conditions a simulation not directly corresponds to a realisable turbulent flow (St. B. Pope).
  • The same set of DNS studies has in fact failed to closely confirm the logarithmic law for velocity (Ph. R. Spalart).
  • There is no pretence that DNS can provide a brute-force method of solving engineering problems: It clearly cannot. Instead, it is regarded as a scientific tool (P.A. Davidson).
  • There is a mismatch between DNS and the objective of determining the mean velocity and energy containing motions in a turbulent flow (St. B. Pope).
  • Flows with high Reynolds numbers still remain inaccessible for direct simulation (E. Krause).