Research

Universality class of turbulent transitions in stably stratified flows

Published in In Preparation, 2026

In geophysical shear flows, ocean thermoclines, atmospheric boundary layers, stable density stratification suppresses vertical motion and competes with shear-driven turbulence, controlling whether turbulence is sustained or collapses to a laminar state. The laminar-turbulent transition in unstratified shear flow is now understood as a directed percolation (DP) phase transition: the turbulent fraction vanishes continuously at a critical Reynolds number with universal scaling exponents. Whether stratification shifts this critical point, modifies the exponents, or drives the transition into a different universality class entirely is an open question with both fundamental and geophysical significance.

May’s Complexity-Stability Hypothesis in Neural Networks

Published in In Preparation, 2026

May’s 1972 theorem establishes that sufficiently complex random systems are generically unstable, yet evolved ecosystems systematically violate this prediction through structural mechanisms that natural selection has had billions of years to build. This project investigates whether neural networks, as another class of optimized systems, develop analogous stabilizing structure, or remain in the random-matrix regime, and what properties of the optimization process determine the difference.

Tricritical Directed Percolation Controls the Laminar-Turbulent Transition in Pipes with Body Forces

Published in Physical Review Letters, 2025

Transition to turbulence in shear flows has been established to be a non-equilibrium phase transition. Body forces can make the transition discontinuous. Observed phenomenology can be explained by a new tricritical point near transition, enriching the phase diagram of transitional turbulence.

Recommended citation: Guru K. Jayasingh and Nigel Goldenfeld, Tricritical directed percolation controls the laminar–turbulent transition in pipes with body forces, Phys. Rev. Lett. 135, 104001 (2025). doi:10.1103/PhysRevLett.135.104001 https://doi.org/10.1103/46g3-n7cx