Spatial marching with subgrid-scale local exact coherent structures in non-uniformly curved channel flow

TL;DR

This paper introduces a new multi-scale spatial marching method that couples boundary region equations with local exact coherent structures to analyze complex shear flows, demonstrated on curved channel flows with sustained traveling waves and self-sustained states.

Contribution

The paper presents a novel multi-scale spatial marching framework that integrates boundary region equations with local exact coherent structures for analyzing non-uniformly curved shear flows.

Findings

The method estimates momentum transport and flow structure influenced by inlet conditions.

It demonstrates the formation of subcritical self-sustained states in decreasing curvature flows.

The approach aligns with high-Reynolds-number asymptotic theory.

Abstract

We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that capture small-scale dynamics. This framework is consistent with high-Reynolds-number asymptotic theory and offers a promising approach to construct time periodic finite amplitude solutions in a broad class of spatially developing shear flows. As a first application, we consider a non-uniformly curved channel flow, assuming that a finite-amplitude travelling wave solution of plane Poiseuille flow is sustained at the inlet. The method allows for the estimation of momentum transport and highlights the impact of the inlet condition on both the transport properties and the overall flow structure. We then consider a case with gradually decreasing curvature, starting with Dean vortices at the inlet. In this setting, small external oscillatory disturbances can give rise to subcritical self-sustained states that persist even after the curvature vanishes.