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Review Articles

# Transition in Wall-Bounded Flows

[+] Author and Article Information
C. B. Lee

State Key Laboratory for Turbulence Research and Complex Systems, Peking University, Beijing 100871, China

J. Z. Wu

State Key Laboratory for Turbulence Research and Complex Systems, Peking University, Beijing 100871, China; University of Tennessee Space Institute, Tullahoma, TN 37388

http://www.tu-chemnitz.de/physik/KSND/abb/node6.html.

Appl. Mech. Rev 61(3), 030802 (May 06, 2008) (21 pages) doi:10.1115/1.2909605 History: Published May 06, 2008

## Abstract

In this paper, we present direct comparisons of experimental results on transition in wall-bounded flows obtained by flow visualizations, hot-film measurement, and particle-image velocimetry, along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications. Despite somewhat different initial disturbance conditions used in experiments, the flow structures were found to be practically the same. The following observed flow structures are considered to be of fundamental importance in understanding transitional wall-bounded flows: the three-dimensional nonlinear wave packets called solitonlike coherent structures (SCSs) in boundary layer and pipe flows, the $Λ$-vortex, the secondary vortex loops, and the chain of ring vortices. The dynamic processes of the formation of these structures and transition as newly discovered by recent experiments include the following: (1) The sequential interaction processes between the $Λ$-vortex and the secondary vortex loops, which control the manner by which the chain of ring vortices is periodically introduced from the wall region into the outer region of the boundary layer. (2) The generation of high-frequency vortices, which is one of the key issues for understanding both transitional and developed turbulent boundary layers (as well as other flows), of which several explanations have been proposed but a particularly clear interpretation can be provided by the experimental discovery of secondary vortex loops. The ignorance of secondary vortex loops would make the dynamic processes and flow structures in a transitional boundary layer inconsistent with previous discoveries. (3) The dominant role of SCSs in all turbulent bursting, which is considered as the key mechanism of turbulent production in a low Reynolds-number turbulent boundary layer. Of direct relevance to bursting is the low-speed streaks, whose formation mechanism and link to the flow structures in wall-bounded flows can be answered more clearly than before in terms of the SCS dynamics. The observed SCSs and secondary vortex loops not only enable revisiting the classic story of wall-bounded flow transition, but also open a new avenue to reconstruct the possible universal scenario for wall-bounded flow transition.

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## Figures

Figure 4

The streamwise evolution of disturbance velocity amplitude A of a SCS. U0 is the freestream velocity.

Figure 10

Secondary vortex (SCV↑) formation. ((a)–(d)) Part of the first closed vortex called Λ-vortex, i.e., the Λ-vortex and a SCS appear (SCS↑). ((e)–(h)) The right-hand side of the secondary closed vortex appears and then separates from the SCS. At the same time, the Λ-vortex is stretched (FCV↑). The time interval between successive pictures is 1∕12s. This figure is 1∕2 of the actual size and the flow is from left to right. The hydrogen-bubble wire was located parallel to the plate and normal to the flow direction. The wire position was x=300mm from the leading edge and y=1.25mm from the wall.

Figure 11

Visualization of the SCSs

Figure 17

Cartoon of chain of ring vortices generation from the direct interaction of the secondary closed vortex and the Λ-vortex. 1–4 represent the four ring vortices in a chain.

Figure 1

Side view of the formation of the kink structure (Arrow A) (corresponding to SCSs lately) and the head part of the Λ-vortex (Arrow B) by means of hydrogen-bubble visualization (7)

Figure 2

Instantaneous velocity profiles observed at the “peak position” at z=0mm and x=350mm when a nonlinear wave passes away. (a) Inferred from hydrogen-bubble time line (7). (b) Measured by hot wire (29).

Figure 3

Plan view of the young SCS to a low-speed streak. A Λ-vortex appears in the position of B.

Figure 5

Visualization of the formation of the SCS and the well-known Λ-vortex. In these pictures, the wire was located parallel to the plate and normal to the flow direction with the flow from left to right in the pictures. The wire was positioned at y=0.75mm. The time interval between successive pictures was 1∕12s. (a)–(f) show the SCS (CSS↑). The formation of the Λ-vortex is clearly visualized in (e)–(h) (Λ↑)(30).

Figure 6

Side view of the formation of the Λ-vortex (Arrow A) after the generation of the SCS (Arrow B) (28)

Figure 7

Two spikes in one period (y from 1.22mmto2.22mm). The spikes are generated by the SCS in the near-wall region, and by the Λ-vortex in the outer layer (29)

Figure 8

Turbulent spot. Arrow A points out the young SCS and Arrow B for the old stage of the SCS and its bounded vortex (Arrow C). In fact, it is no so easy to distinguish the SCS in a turbulent spot. In the bottom side of the spot, the flow looks like a laminar one; a young SCS (A↓) can been observed. In the center of the turbulent spot, there are several turbulent production channels and several SCSs (B↓), and their bounded vortices appear. It is also a strong evidence to show that the SCSs appear much earlier than its bounded vortex

Figure 9

The generation of secondary vortices via surface interaction for a symmetric hairpin vortex (51)

Figure 12

Oscilloscope traces of velocity disturbances in both the x- and y-directions at various distances from the wall at x=450mm. T represents the period of the T-S waves (0.5s).

Figure 13

(a) Plan view of a solitonlike coherent structure (SCS↑) and its surrounding vortex called the secondary closed vortex (inside the red circle). (b) Variation of ωz over one period. The positive and negative values of ωz indicate the vortex region corresponding to the left side (inside the red circle) and the right side (Arrow R), respectively, of the secondary closed vortex in (a).

Figure 14

Plan view of the chain of ring vortices (↑) associated with a Λ-vortex (A↑) (the wire was at x=360mm and y=1.75mm). 1∕2 scale of the actual sizes for all photos. The first ring vortex propagated downstream (1↑) while the other three (2↑, 3↑, and 4↑) appeared at nearly the same time. The time interval between successive pictures was 1∕24s. Figure 1 shows the first ring vortex. Figures  16161616 show the other three ring vortices.

Figure 15

Generation of the first ring vortex (1↑) by the interaction between the secondary closed vortex (SCV↑) and the Λ-vortex (Λ↑). The hydrogen-bubble wire is at x=250mm and y=1mm from the leading edge of the flat plate with the time intervals between successive pictures of 1∕12s. 9∕10 scale of the actual sizes of the photos.

Figure 16

Formation of the second (2↑), third (3↑), and fourth (4↑) ring vortices in a chain of ring vortices (26). The hydrogen-bubble wire was at x=350mm and y=1.5mm. The time interval between successive pictures was 1∕24s. 1∕2 scale from the actual sizes of the photos. (a) shows the filaments of the Λ-vortex moving into the center of the secondary closed vortex (SCV↑) and the two symmetric filaments with two narrow necks formed at the center of the secondary closed vortex. (c) shows the breaking and reconnection of the two symmetric filaments at their narrow necks within the secondary closed vortex; the third ring vortex is also clearly seen. In (e) and (f), the fourth ring vortex appears. The filament on its left side comes from the secondary closed vortex and that on its right from the symmetric filaments of the Λ-vortex. (h)–(k) show the formation of the second ring vortex. The filaments of this vortex come from both the secondary closed vortex and the two symmetric filaments. All three ring vortices appear clearly in (i) (j) (k). Two streamwise vortices (SW↑) appear on the two sides of these three vortices, which are the well-known structures also known as low-speed streaks. The filaments of the streamwise vortex come from both the secondary closed vortex and the Λ-vortex.

Figure 18

Breakdown of the first ring vortex in a transitional boundary layer. In (A)–(E), one sees the breakdown of the near-wall part of the vortex. The first ring vortex appears in A. Arrows indicate the position of the breakdown in the near-wall region of the boundary layer. In (a) (b)–(e), one sees breakdown of the first ring vortex in the outer region of the boundary layer. (a) The vortex in the outer layer starts to break (1↑), and the vortex in the near-wall region had already broken (W↑). In (c)–(e), the arrows show the points of the breakdown. In (e), the chain of ring vortices appears (1↑, 2↑, 3↑, and 4↑).

Figure 19

Time traces starting from the four-spike stage to the multiple spike stage and their corresponding spectra. The Tollmien–Schlichting wave frequency was 2Hz. Lines 1, 2, 3, and 4 on the right side of the figure are the spectra at x=500mm, 600mm, 650mm, and 700mm.

Figure 20

Breakdown of a low-speed streak at x=600mm(L↑). ((a)–(c)) A regular low-speed streak. ((d)–(f)) A wavy low-speed streak. (g) Start of breakdown of a low-speed streak. ((h)–(l)) Breakdown process associated with the appearance of the chain of ring vortices (HFV↑) in the peak position. (l) The arrow points to the breakdown of the low-speed streak. The hydrogen-bubble wire was at x=550mm and y=0.75mm. The time interval between successive pictures was 1∕12s. 1∕2 scale from the actual photo sizes.

Figure 21

The paths from receptivity to transition (13)

Figure 22

Growth of SCS slug. Shaded region is a real SCS and the mean fluid speed is approximately midway between the speeds of the rear and the front of a SCS.

Figure 23

Left column: a few typical hydrogen-bubble photos of complex flow structures illuminated by laser sheet at different horizontal heights. The SCS (SCS↑), the secondary closed vortex (SV↑), Λ-vortex (Λ↑), and the first ring vortex (FRV↑) are shown. Right column: a three-dimensional structure reconstructed from the photos on the left column, with the corresponding laser sheets locations marked and high-density hydrogen-bubble traces sketched thereon.

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