Engineering topics

Waleffe, Fabian A.

Publications and source records attributed to Waleffe, Fabian A..

3 records

NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗

NASA NTRS1993

Regeneration of near-wall turbulence structures

An examination of the regeneration mechanisms of near-wall turbulence and an attempt to investigate the critical Reynolds number conjecture of Waleffe & Kim is presented. The basis is an extension of the 'minimal channel' approach of Jimenez and Moin which emphasizes the near-wall region and further reduces the complexity of the turbulent flow. Reduction of the flow Reynolds number to the minimum value which will allow turbulence to be sustained has the effect of reducing the ratio of the largest scales to the smallest scales or, equivalently, of causing the near-wall region to fill more of the area between the channel walls. In addition, since each wall may have an active near-wall region, half of the channel is always somewhat redundant. If a plane Couette flow is instead chosen as the base flow, this redundancy is eliminated: the mean shear of a plane Couette flow has a single sign, and at low Reynolds numbers, the two wall regions share a single set of structures. A minimal flow with these modifications possesses, by construction, the strongest constraints which allow sustained turbulence, producing a greatly simplified flow in which the regeneration process can be examined.

Hamilton, James M.↗

NASA NTRS1991

On the origin of the streak spacing in turbulent shear flows

It is shown that the ideas of selective amplification and direct resonance, based on linear theory, can not provide an explanation for the well-defined streak spacing of about 100 wall units (referred to as 100(+) hereafter) in wall-bounded turbulent shear flows. In addition, for the direct resonance theory, the streaks are created by the non-linear self-interaction of the vertical velocity rather than of the directly forced vertical vorticity. In view of the failure of these approaches, it is then proposed that the selection mechanism must be inherently non-linear and correspond to a self-sustaining mechanism. The 100(+) value should thus be considered as a critical Reynolds number for that mechanism. Indeed, in the case of Poiseuille flow, this 100(+) criterion for transition to turbulence corresponds to the usually quoted value of 1000 based on the half-width and the centerline velocity. In Couette flow, it corresponds to a critical Reynolds number of about 400 based on the half width and half velocity difference.

Waleffe, Fabian A.↗