Catálogo de publicaciones - libros

After a brief summary of experimental results focussed on plane Couette flow and contrasting the low-Reynolds numbers transition between laminar flow and the turbulent spot regime, with its high-Reynolds counterpart between homogeneous turbulence and turbulent stripes, we introduce a hierarchy of models from models designed to answer the most basic questions to models more adapted to the study of specific topics.

Among conceptual models we distinguish between low-dimensional deterministic dynamical systems apt to analyze problems linked to attractor coexistence and basin boundaries, stochastic models more appropriate to studying the role of noise in the natural transition, and models derived from statistical mechanics focussed on the “macroscopic” growth of turbulent patches in the triggered transition. Semi-realistic models separating cross-stream and in-plane variables are designed in view of concrete analysis of processes at a more “microscopic” scale, related to pattern formation and space-time chaos studies.

We discuss the theoretical, numerical and experimental evidence for the formation of a chaotic saddle in the transition region to turbulence in pipe flow and plane Couette flow.

We analyse the bifurcation sequence of typical simple plane shear flows numerically by using a bifurcation analysis and also a DNS technique, considering flows with and without a system rotation about a spanwise axis. Our analysis is applied to (1) plane Couette flow, (2) plane Poiseuille flow, and (3) flow with a cubic velocity profile.

Direct numerical simulation of a turbulent channel flow in a periodic domain of relatively wide spanwise extent, but minimal streamwise length, is carried out at Reynolds numbers = 137 and 349. The large-scale structures previously observed in studies of turbulent channel flow using huge computational domains are also shown to exist even in the streamwise-minimal channel of the present work. In the system, it is also clearly observed how the large-scale structures and the near-wall structures affect each other. While the collective behavior of near-wall structures enhance a large-scale structure, the resulting large-scale structure in turn activates the generation and drift of the latter. Hence near-wall and large-scale structures interact in a co-supporting cycle. The preliminary numerical results suggesting the existence of traveling wave solutions that correspond to large-scale structures are reported.

The self-sustaining process is a fundamental and generic three-dimensional nonlinear process in shear flows. It is responsible for the existence of non-trivial traveling wave and time-periodic states. These states come in pairs, an upper branch and a lower branch. The limited data available to date suggest that the upper branch states provide a good first approximation to the statistics of turbulent flows. The upper branches may thus be understood as the “backbone” of the turbulent attractor while the lower branches might form the backbone of the boundary separating the basin of attraction of the laminar state from that of the turbulent state. Evidence is presented that the lower branch states tend to purely streaky flows, in which the streamwise velocity has an essential spanwise modulation, as the Reynolds number tends to infinity. The streamwise rolls sustaining the streaks and the streamwise undulation sustaining the rolls, both scale like in amplitude, just enough to overcome viscous dissipation. It is argued that this scaling is directly related to the observed transition threshold. These results also indicate that the exact coherent structures never bifurcate from the laminar flow, not even at infinity. The scale of the key elements, streaks, rolls and streamwise undulation, remain of the order of the channel size. However, the higher -harmonics show a slower decay with than naively expected. The results indicate the presence of a warped critical layer.

Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to simulations of channel flows pioneered by Jiménez and Moin. In our case computational domains are of minimal size in only two directions. The third direction is taken to be large. Furthermore, the long direction can be tilted at any prescribed angle to the streamwise direction. We report on different patterned states observed as a function of Reynolds number, imposed tilt, and length of the long direction. We compare our findings to observations in large aspect-ratio experiments.

The effects of global flow rotation and curvature on the subcritical transition to turbulence in shear flows are examined. The relevant time-scales of the problem are identified by a decomposition of the flow into a laminar and a deviation from laminar parts, which is performed for rotating plane Couette and Taylor—Couette flows. The usefulness and relevance of this procedure are discussed at the same time. By comparing the self-sustaining process time-scale to the time-scales previously identified, an interpretation is brought to light for the behavior of the transition Reynolds number with the rotation number and relative gap width in the whole neighborhood (in parameter space) of the non-rotating plane Couette flow covered by the available data.

We propose to examine the effects of restricting the interaction between nearwall turbulence and the outer flow on the structure and dynamics of the empirical eigenfunctions functions determined using the proper orthogonal decomposition (POD). This research is motivated by the fact that standard POD-based low-dimensional models for the near-wall region have been derived for empirical eigenfunctions computed for an unbiased channel flow. However, under the present truncation of the flow dynamics, the POD basis may be significantly affected so that the common assumption that effective reduced-order models can be constructed from the POD basis of an unaltered flow may be suspect. This issue is explored for plane, incompressible, turbulent channel flow at Reynolds number, = 180. Based on direct numerical simulations, POD basis functions are constructed for an unbiased and four truncated minimal channel flows. The POD eigenfunctions which characterize these modified flows are associated to a travelling-wave solution which undergoes a series of bifurcation until settling into a turbulent regime. A POD-based two-mode model is also derived for the near-wall layer and is evaluated. It is shown that travelling-wave solutions appear as a backbone to the low-dimensional dynamics of the autonomous near-wall region.

A numerical simulation of the early nonlinear stages of transition in a pipe flow, for which the base profile presents a small defect, reveals the formation of coherent states reminiscent of the recently found non-linear travelling waves.

System rotation may have either stabilizing or destabilizing effects on shear flows depending on the direction of rotation vector as compared to the vorticity vector of mean flow. This study describes experimental results of laminar, transitional and turbulent plane Couette flow with both stabilizing and destabilizing system rotation. For laminar flow with destabilizing rotation roll cells appear in the flow which may undergo several different types of secondary instabilities, especially interesting is a repeating pattern of wavy structures followed by breakdown, thereafter roll cells reappear in a cyclic pattern. For higher Reynolds number roll cells appear also in a turbulent environment. It is also shown how stabilizing rotation may quench the turbulence completely.