# Universal continuous transition to turbulence in a planar shear flow

## TL;DR

This study investigates the transition to turbulence in a planar shear flow, demonstrating a continuous onset and universal behavior consistent with directed percolation universality class, using large-scale simulations.

## Contribution

It introduces a truncated mode simulation approach enabling larger system sizes and provides evidence for universal continuous transition to turbulence in planar shear flow.

## Key findings

- Turbulence fraction increases continuously above a critical Reynolds number.
- Turbulent structures follow power-law scalings of directed percolation.
- Simulation approach allows larger system sizes than previous studies.

## Abstract

We examine the onset of turbulence in Waleffe flow -- the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four modes, we are able to simulate system sizes an order of magnitude larger than any previously simulated, and thereby to attack the question of universality for a planar shear flow. We demonstrate that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number and that statistics of the turbulent structures exhibit the power-law scalings of the (2+1)-D directed percolation universality class.