Mean dynamics and transition to turbulence in oscillatory channel flow

Abstract

The mean dynamics in oscillatory channel flow is examined to investigate the dynamical mechanisms underlying the transition to turbulence in oscillatory wall-bounded flow. The analyses employ direct numerical simulation data acquired at three Stokes Reynolds numbers: $Re_{s}=648$, 801 and 1009, where the lower $Re_{s}$ flow is transitional over the entire cycle and the two higher $Re_{s}$ flows exhibit flow characteristics similar to steady turbulent wall-bounded flow during part of the cycle. The flow evolution over a half-period of oscillation for all three $Re_{s}$ is as follows: near-wall streamwise velocity streaks develop during the early accelerating portion of the cycle; then at some later point in the cycle that depends on $Re_{s}$, the near-wall streaks breakdown (demarking the onset of the nonlinear development stage), and the near-wall Reynolds stress grows explosively; the Reynolds stress remains elevated for part of the cycle before diminishing (yet remaining finite) during the late decelerating portion of the cycle. This process is then repeated indefinitely. The present findings demonstrate that transition to turbulence occurs when the nonlinear development stage begins during the accelerating portion of the cycle. This crucially leads to the diminishing importance of the centreline momentum source, the emergence of a locally accelerating/decelerating internal layer centred about the edge of the Stokes layer and the wall-normal rearrangement of the mean forces prior to the start of the decelerating portion of the cycle. The rearrangement of mean forces culminates in a four layer structure in the mean balance of forces. This is significant on a number of accounts since empirical and theoretical evidence suggests that the formation of a four layer structure is an important characteristic of a self-similar hierarchal structure that underlies logarithmic dependence of the mean velocity profile in steady turbulent wall-bounded flows (Klewicki et al., J. Fluid Mech., vol. 638, 2009, pp. 73–93). When the nonlinear development stage begins during the decelerating portion of the cycle (i.e. at $Re_{s}=648$), a four layer structure is not observed in the mean balance of forces and the flow remains weakly transitional over the entire cycle.

Mean flow structure and velocity–bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: direct numerical simulations

“…However, the von Kármán constant κ and the intersect A s of those profiles do not seem to agree with those of the equilibrium logarithmic profile of the unidirectional zero-pressure gradient boundary-layer flows (ZPGBL) (Krug, Philip & Marusic 2017;Jiménez 2018). This is also consistent with some of the observations in recent DNS studies by Ebadi et al (2019) for oscillatory channel flows and the large eddy simulation (LES) analysis by Kaptein et al (2020) for oscillatory boundary layers, both of whom reported a range of slopes and intersects for the mean velocity profiles for oscillatory boundary layers that differ from those of equilibrium ZPGBL. We believe that this lack of equilibrium conditions is also relevant to the inconsistencies found in the literature regarding the presence of a phase lag between the bed-shear stress and the free-stream velocity.…”

“…After a close inspection of the ensemble-averaged bed-shear stress measurement by Hino et al (1976) it is easy to conclude that they had also observed negative phase differences for a flow of Re δ = 876 (see p. 373, figure 10 in their work). Similarly, observations have been made in the literature both experimentally (Jensen et al 1989;Carstensen et al 2010) and numerically (Spalart & Baldwin 1989;Ozdemir et al 2014;Bettencourt & Dias 2018;Ebadi et al 2019). A more extended presentation and summary of these works can be found in Mier et al (2021).…”

Turbulent–turbulent transient concept in pulsating flows

“…This evolution would bear some similarity to momentum balance evolution identified by Guerrero et al (2021) for non-periodic acceleration. Furthermore, the early decelerating regime of Ebadi et al (2019) was characterised by a shift in VF from a momentum sink to a momentum source, which is also observed in ramp-down decelerating flows (Guerrero et al 2023).…”

“…In such cases, this led to an explosive growth of turbulence which continued during the early deceleration period. Ebadi et al (2019) explored the temporal evolution of the momentum balance in intermittently turbulent oscillating flows. Once the onset of transition occurred, the turbulent inertia (TI) grew rapidly, in conjunction with a rapid increase in the rate of energy transfer to the wall-normal and spanwise turbulent motions.…”

Mean flow structure and velocity–bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: experimental observations

“…Many studies are available in the literature that deal with the bottom boundary layer. On the experimental side, the pioneering works of Hino, Sawamoto & Takasu (1976), Hino et al (1983), Jensen, Sumer & Fredsøe (1989), Akhavan, Kamm & Shapiro (1991 a ), Sarpkaya (1993), Carstensen, Sumer & Fredsøe (2010) and van der A, Scandura & O'Donoghue (2018) among others, summarize current knowledge regarding the oscillatory boundary layer structure and possible flow regimes in oscillatory flow over flat, smooth beds; while on the numerical side, high-fidelity direct numerical simulation (DNS) and large-eddy simulation works have investigated the same family of flows, which has enhanced our current understanding in terms of flow structure (Spalart & Baldwin 1989; Vittori & Verzicco 1998; Salon, Armenio & Crise 2007; Pedocchi, Cantero & García 2011; Ozdemir, Hsu & Balachandar 2014; Scandura, Faraci & Foti 2016; Bettencourt & Dias 2018; Ebadi et al 2019), stability analysis (e.g. Akhavan, Kamm & Shapiro 1991 b ) and coherent structures (Costamagna, Vittori & Blondeaux 2003; Mazzuoli, Vittori & Blondeaux 2011).…”