Far field of turbulent spots

TL;DR

This paper investigates the far-field velocity structure of turbulent spots in shear flows, revealing algebraic decay patterns governed by system symmetries, and proposes a multipolar expansion model for the far field.

Contribution

It provides a numerical analysis of the far field of turbulent spots across different shear flow scenarios, highlighting decay laws and symmetry-dependent flow structures.

Findings

Velocity fields decay algebraically, not exponentially.

Decay exponents depend on system symmetries, not Reynolds number.

Far field modeled as multipolar expansion, dominated by quadrupolar or dipolar components.

Abstract

The proliferation of turbulence in subcritical wall-bounded shear flows involves spatially localised coherent structures. Turbulent spots correspond to finite-time nonlinear responses to pointwise disturbances and are regarded as seeds of turbulence during transition. The rapid spatial decay of the turbulent fluctuations away from a spot is accompanied by large-scale flows with a robust structuration. The far field velocity field of these spots is investigated numerically using spectral methods in large domains in four different flow scenarios (plane Couette, plane Poiseuille, Couette-Poiseuille and a sinusoidal shear flow). At odds with former expectations, the planar components of the velocity field decay algebraically. These decay exponents depend only on the symmetries of the system, which here depend on the presence of an applied gradient, and not on the Reynolds number. This suggests an effective two-dimensional multipolar expansion for the far field, dominated by a quadrupolar flow component or, for asymmetric flow fields, by a dipolar flow component.