Turbulent Flows

Turbulent flow arises when inertial forces overwhelm viscous damping and small perturbations grow into chaotic, three-dimensional eddies that span a broad range of scales. Characterised by irregular fluctuations in velocity, pressure and scalar fields, turbulence enhances mixing, diffusion and energy dissipation. The onset of turbulence is commonly described by the Reynolds number, Re = UL/ν, which compares inertial to viscous forces for characteristic velocity U, lengthscale L and kinematic viscosity ν. Above a critical Re, instabilities in shear layers or boundary layers birth vortical structures that stretch, fold and break down in an energy cascade: large eddies transfer kinetic energy to smaller motions until viscous dissipation prevails at the finest scales. In practical flows—pipes and channels, jets and plumes, atmospheric and oceanic currents—turbulence governs momentum and heat transfer, noise generation and drag. Wall-bounded turbulence exhibits a near-wall viscous sublayer, a buffer region and an overlying logarithmic layer where mean velocity follows u⁺ = (1/κ) ln y⁺ + B. Free turbulence, as in jets and mixing layers, displays self-similar behaviour after initial instabilities. The universality and predictability of turbulent flows remain a central challenge owing to their nonlinear, multiscale nature and sensitivity to boundary conditions.

Research from Nature Portfolio

Recent studies have employed explainable deep-learning methods to interrogate wall-bounded turbulence. By training convolutional networks on high-resolution channel-flow data, researchers have attributed predictive importance to individual coherent structures and revealed that the most dynamically influential regions are not necessarily those with the highest contribution to Reynolds shear stress. This insight paves the way for targeted flow-control strategies that suppress key structures rather than relying solely on mean-stress metrics. Another advance has uncovered an energy-efficient drag-reduction mechanism at high friction Reynolds numbers. In addition to the established small-scale eddy actuation via spanwise surface oscillation—which yields up to 25 % drag reduction but incurs prohibitive power costs—a novel pathway actuates at the frequency of large-scale outer eddies. This latter approach achieves double-digit drag reduction at ultra-high Reynolds numbers with a fraction of the power input, pointing towards scalable turbulence control for transport and energy devices.

Turbulent Flows publication trend

The graph below shows the total number of articles in turbulent flows across all publications each year (not limited to Nature Index journals).

Technical terms

Reynolds number: Dimensionless ratio of inertial to viscous forces, Re = UL/ν, governing transition to turbulence.

Energy cascade: Sequential transfer of kinetic energy from large to small eddies until viscous dissipation at the Kolmogorov scale.

Viscous sublayer: The near-wall region (y⁺ < 5) in turbulent boundary layers where viscous stresses dominate and u⁺ ≃ y⁺.

Logarithmic layer: The overlap region (30 ≲ y⁺ ≲ 0.1 Re_τ) where the mean velocity follows u⁺ = (1/κ) ln y⁺ + B.

Entrainment: Incorporation of ambient fluid into a jet or plume by turbulent mixing at the flow interface.

Direct numerical simulation (DNS): Fully resolved solution of the Navier–Stokes equations without turbulence modeling.

Virtual origin: The effective upstream location from which a self-similar plume or jet appears to originate.

References

1. Introduction to Turbulent Flows.
2. Identifying regions of importance in wall-bounded turbulence through explainable deep learning. Nature Communications (2024).
3. An energy-efficient pathway to turbulent drag reduction. Nature Communications (2021).
4. A review on turbulent flow over rough surfaces: Fundamentals and theories. International Journal of Thermofluids (2021).
5. Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number. Journal of Fluid Mechanics (2022).
6. Analytical solutions and virtual origin corrections for forced, pure and lazy turbulent plumes based on a universal entrainment function. Journal of Fluid Mechanics (2020).