Fully Turbulent Wakes at Low Reynolds Numbers: the Case of the Thin Flat Plate

TL;DR

This study demonstrates that the wake behind a thin flat plate becomes fully turbulent by $Re=400$, evidenced by DNS results that align with higher-$Re$ experimental data in mean fields, Reynolds stresses, energy budgets, and broad, Kolmogorov-like spectra. Using both spectral-element DNS and finite-volume simulations, along with two PIV experiments, the authors show sustained multi-scale turbulence and intermittency absent at $Re=150$, revealing a transition path fundamentally different from circular or square cylinder wakes. The work highlights how pressure fluctuations and vorticity transport near the shear layer influence early turbulence, challenging canonical transition scenarios and informing low-$Re$ wake modeling for thin-plate geometries. Overall, the findings establish a robust computational-experimental framework for diagnosing turbulence in highly symmetric, 2D-like wakes and underscore the practical importance of geometry-driven transition mechanisms in wake dynamics.

Abstract

We consider the wake flow past a thin two-dimensional flat plate normal to the uniform stream and demonstrate that this flow is turbulent already at a relatively low Reynolds number of $Re = 400$. This is achieved by performing a careful comparison of the results of a DNS of this flow with experimental measurements of wake flows in the same geometric configuration at the Reynolds numbers of $Re=12500, 19700$. This comparison reveals that the distribution of several key quantities, including the mean velocity, Reynolds stresses and different effects contributing to the transport of the turbulent kinetic energy, are, up to measurement uncertainty, the same in these flows. Moreover, the wake flow at $Re = 400$ also features energy spectra characteristic of turbulent flows with intermittency detected in the distributions of the fluctuating strain and rotation rates. In contrast, these features are absent from the results of the DNS of the wake flow at $Re = 150$ where the distribution of the key quantities is also fundamentally different. These results show that the path to transition to turbulence in the wake past a thin flat plate is different from that in the wakes of canonical (i.e., circular or square) cylinders. We also identify possible physical mechanisms that may be responsible for these differences.

Figures (22)

• Figure 1: Schematic of the computational domain in the $x$--$y$ plane.
• Figure 2: Isometric view of the computational domain.
• Figure 3: Centreline profiles of the time-averaged quantities (a) $U$ (solid lines) and $P$ (dashed lines), (b) $\overline{u^{\prime 2}}$, (c) $\overline{v^{\prime 2}}$ and (d) $\overline{w^{\prime 2}}$ in the simulations performed on different meshes, cf. Table \ref{['tab:constud']}: P5_2 ( ); P7_2 ( ); DNS400 ( ); DNS400V ( ).
• Figure 4: Mean streamlines (top half planes) and velocity vector fields (bottom half planes) on the symmetry plane $y=0$ for (a) DNS150, (b) DNS400, (c) EX12K and (d) EX20K. Flat plates are depicted in all figures with streamwise thicknesses to scale. Streamlines are iso-contours of the stream function $\Psi = \int_0^y u \hbox{d}y$.
• Figure 5: Centreline profiles of the mean streamwise velocity $U(x,0,0)$. Legend: DNS150 ( ); DNS400 ( ); EX12K ($\bigcirc$); EX20K ($\bigtriangledown$).