A Thin Plate Wakes Turbulence Early express
A thin plate stands across a flow of water or air. Behind it, a wake forms — a region where the flow becomes tangled and mixed. Usually, such a wake becomes turbulent when the flow speed is high enough, quantified by the Reynolds number. For circular and square obstacles, turbulence in the wake appears at Reynolds numbers on the order of several thousand. But for a flat plate, things are different.
The authors computed the flow past a plate at a Reynolds number of 400 and compared it with wind tunnel measurements at Reynolds numbers of 12500 and 19700. Key quantities (mean velocity, Reynolds stresses, and turbulent kinetic energy transport) matched within experimental uncertainty. Moreover, the simulation at 400 exhibited energy spectra and intermittency characteristic of fully developed turbulence. At a Reynolds number of 150, none of this is present: the distributions are completely different, and there is no turbulence.
The difference in wake behavior stems from how the plate sheds vortices. For a thin plate, sharp edges force the flow to separate immediately, forming a vortex street even at low speeds. For a circular cylinder, separation is gradual, and turbulence develops later. This finding helps improve calculations of flow around thin structures, from wings to bridge railings.
Original abstract
as written by the authors arXiv:2601.17341
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.
At a Reynolds number of 400, water in a 1 cm diameter pipe must flow at just 4 cm/s for the wake behind a thin plate to become turbulent.