Rare-event detection in a backward-facing-step flow using live optical-flow velocimetry: observation of an upstream jet burst

TL;DR

This work addresses rare-event detection in a separated BFS flow by employing long-duration Live Optical Flow Velocimetry (L-OFV) to monitor 2D velocity fields in real time. A data-driven protocol uses localized probes and a circular image buffer to trigger live recording when extreme events occur, enabling the capture of pre/post event dynamics. The study reports the first direct experimental observation of an upstream-directed jet burst in BFS flow at $Re_h\approx2100$, initiated by the collapse of a merged Kelvin–Helmholtz vortex and sustained by counter-rotating vortices, with concomitant heavy-tailed statistics and simultaneous surges in fluctuating kinetic energy and enstrophy. This demonstrates the viability of L-OFV for experimental rare-event analysis in separated shear layers and provides a concrete mechanism for upstream jet bursting, while noting the need for more events to quantify incidence across Reynolds numbers and configurations.

Abstract

Rare and extreme events in turbulent flows play a critical role in transport, mixing and transition, yet are notoriously difficult to capture experimentally. Here we report, to our knowledge, the first direct experimental detection of an upstream-directed jet burst in a backward-facing step (BFS) flow at $Re_h=2100$, using long-duration Live Optical Flow Velocimetry (L-OFV). Continuous monitoring over 1.5 h enabled a data-driven definition of extremes as rare velocity probes excursions deep into the observed distribution's tails; in practice, large negative events ($u: Z < -6$, $v: Z < -5$ at $(x,y) = (2h,h / 2)$, where $|Z| > > 0$ stands for large deviations from the mean value) triggered the live capture of surrounding velocity fields. The recording is triggered when the probes surpass the defined threshold, using live analysis of the velocity fields. The detected event features a jet-like intrusion into the recirculation region initiated by the collapse of a merged Kelvin-Helmholtz vortex and sustained by counter-rotating vortices, and is accompanied with heavy-tailed probe statistics and simultaneous amplification of fluctuating kinetic energy and enstrophy. While a single event was recorded, underscoring its rarity, the results establish L-OFV as a viable platform for rare-event detection in separated shear layers and document a previously unreported mechanism of upstream jet bursting in BFS flow.

Figures (15)

• Figure 1: 3D sketch of the BFS model used in the experiments, showing the measurement plane located at the center of the yz plane.
• Figure 2: a) Sketch showing the main instabilities and main structures generated downstream the step edge. b) Instantaneous $u(x, y)$ (upper picture) and $v(x, y)$ (lower picture) velocity fields measured in the vertical symmetry plane ($z/h=0$), downstream of the BFS, at $Re_h=2100$. $x=0$ is taken at the step edge, while $y=0$ is defined at the horizontal wall downstream the step.
• Figure 3: Instantaneous velocity field magnitude in the vertical symmetry plane ($z/h=0$), downstream of the BFS, at $Re_h=2100$. Velocity probes are located at the mid-height of the step ($y/h=0.5$) and at five streamwise positions (from $x/h=2$ to $x/h=10$).
• Figure 4: Time series and PDF of the streamwise component $u(t)$ of the velocity measured by probes located at $y/h = 0.5$ and in various streamwise positions, ranging from $x/h = 2$ (a), $x/h = 4$ (b), $x/h = 6$ (c), $x/h = 8$ (d), $x/h = 10$ (e). Measurement of 1.5 hours at 100 Hz.
• Figure 5: Time series and PDF of the wall-normal component $v(t)$ of the velocity measured by probes located at $y/h = 0.5$ and in various streamwise positions, ranging from $x/h = 2$ (a), $x/h = 4$ (b), $x/h = 6$ (c), $x/h = 8$ (d), $x/h = 10$ (e). Measurements were carried out over 1.5 hours at 100 $Hz$. On the right side of the time-series, their PDF are plotted.