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Register a new userHybrid POD-FFT analysis of nonlinear evolving coherent structures of DNS wavepacket in laminar-turbulent transition
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This paper concerns the study of direct numerical simulation (DNS) data of a wavepacket in laminar turbulent transition in a Blasius boundary layer. The decomposition of this wavepacket into a set of modes (a basis that spans an approximate solution space) can be achieved in a wide variety of ways. Two well-known tools are the fast Fourier transform (FFT) and the proper orthogonal decomposition (POD). To synergize the strengths of both methods, a hybrid POD-FFT is pioneered, using the FFT as a tool for interpreting the POD modes. The POD-FFT automatically identifies well-known fundamental, subharmonic and Klebanoff modes in the flow, even though it is blind to the underlying physics. Moreover, the POD-FFT further separates the subharmonic content of the wavepacket into three fairly distinct parts: a positively detuned mode resembling a Lambda-vortex, a Craik-type tuned mode and a Herbert-type positive-negative detuned mode pair, in decreasing order of energy. This distinction is less widely recognized, but it provides a possible explanation for the slightly positively detuned subharmonic mode often observed in previous experiments and simulations.
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Turbulence structure in the quasi-linear restricted nonlinear (RNL) model is analyzed and compared with DNS of turbulent Poiseuille flow at Reynolds number R=1650. The turbulence structure is obtained by POD analysis of the two components of the flow partition used in formulating the RNL model: the streamwise-mean flow and the associated perturbations. The dominant structures are found to be similar in RNL simulations and DNS despite the neglect of perturbation-perturbation nonlinearity in the RNL formulation. POD analysis of the streamwise-mean flow indicates that the dominant structure in both RNL and DNS is a coherent roll-streak structure in which the roll is collocated with the streak in a manner configured to reinforce the streak by the lift-up process. This mechanism of roll-streak maintenance accords with analytical predictions made using the second order statistical state dynamics (SSD) model, referred to as S3T, which shares with RNL the dynamical restriction of neglecting the perturbation-perturbation nonlinearity. POD analysis of perturbations from the streamwise-mean streak reveals that similar structures characterize these perturbations in both RNL and DNS. The perturbation to the low-speed streak POD are shown to have the form of oblique waves collocated with the streak that can be identified with optimally growing structures on the streak. Given that the mechanism sustaining turbulence in RNL has been analytically characterized, this close correspondence between the streamwise-mean and perturbation structures in RNL and DNS supports the conclusion that the self-sustaining mechanism in DNS is the same as that in RNL.
This study concerns wavepackets in laminar turbulent transition in a Blasius boundary layer. While initial amplitude and frequency have well-recognized roles in the transition process, the current study on the combined effects of amplitude, frequency, and bandwidth on the propagation of wavepackets is believed to be new. Because of the complexity of the system, these joint variations in multiple parameters could give rise to effects not seen through the variation of any single parameter. Direct numerical simulations (DNS) are utilized in a full factorial (fully crossed) design to investigate both individual and joint effects of variation in the simulation parameters, with a special focus on three distinct variants of wavepacket transition {textemdash} the reverse Craik triad formation sequence, concurrent N-type and K-type transition and abrupt shifts in dominant frequency. From our factorial study, we can summarize the key transition trends of wavepackets as follows: 1. Broad bandwidth wavepackets predominantly transit to turbulence via the N-route. This tendency remains strong even as the frequency width is reduced. 2. Narrow bandwidth wavetrains exhibit predominantly K-type transition. The front broadband part of an emerging wavetrain may experience N-type transition, but this wavefront should not be considered as a part of truly narrow-bandwidth wavepackets. 3. K-type transition is the most likely for wavepackets that are initiated with high energy/amplitude and/or with the peak frequency at the lower branch of the neutral stability curve.
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold Rt above which turbulence is uniform (featureless) and a lower threshold Rg below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, alternatively laminar and turbulent, and oriented obliquely with respect to the general flow direction. The final decay of the bands at Rg points to the relevance of directed percolation and criticality in the sense of statistical-physics phase transitions. The nature of the transition at Rt where bands form is still somewhat mysterious and does not easily fit the scheme holding for pattern-forming instabilities at increasing control parameter on a laminar background. In contrast, the bands arise at Rt out of a uniform turbulent background at a decreasing control parameter. Ingredients of a possible theory of laminar-turbulent patterning are discussed.
The aim of the present work is to investigate the role of coherent structures in the generation of the secondary flow in a turbulent square duct. The coherent structures are defined as connected regions of flow where the product of the instantaneous fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Duran et al. (J. Fluid Mech., vol. 694, 2012, pp. 100-130). We consider both the direct contribution of the structures to the mean in-plane velocity components and their geometrical properties. The instantaneous phenomena taking place in the turbulent duct are compared with turbulent channel flow at Reynolds numbers of $Re_tau=180$ and $360$, based on friction velocity at the center-plane and channel half height. In the core region of the duct, the fractional contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. On the other hand, in the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity, which is less relevant than that of the complementary portion of the flow not included in such objects. Our results show however that strong Reynolds shear-stress events, despite the differences observed between channel and duct, do not contribute directly to the secondary motion, and thus other phenomena need to be considered instead.
In this visualisation, the transition from laminar to turbulent flow is characterised by the intermittent ejection of wall fluid into the outer stream. The normalised thickness of the viscous flow layer reaches an asymptotic value but the physical thickness drops exponentially after transition. The critical transition pipe Reynolds number can be obtained simply by equating it with the asymptotic value of the normalised thickness of viscous flow layer. Key words: Transition, critical stability Reynolds number, critical transition Reynolds number, non-Newtonian pipe flow
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