Amplification of localized body forces in channel flows of viscoelastic fluids

TL;DR

This paper investigates how localized body forces are amplified in channel flows of viscoelastic fluids, revealing mechanisms that could trigger elastic turbulence, with implications for experimental studies and flow control.

Contribution

It provides the first analysis of localized body force amplification in viscoelastic channel flows using linearized equations, identifying key flow structures and energy dynamics.

Findings

Localized forces near the wall cause maximum amplification.

Spanwise forces most significantly impact the streamwise velocity.

Vortical structures develop away from impulsive excitation sources in viscoelastic fluids.

Abstract

The study of nonmodal amplification of distributed body forces in channel flows of viscoelastic fluids has provided useful insights into the mechanisms that may govern the initial stages of transition to elastic turbulence. However, distributed body forces are not easy to implement in experiments and so there is a need to examine amplification of localized body forces. In this work, we use the linearized governing equations to examine such amplification in Poiseuille flow of FENE-CR fluids. We first identify the wall-normal location at which the impulsive excitations experience the largest amplification and then analyze the kinetic energy of the fluctuations and the resulting flow structures. For both a Newtonian fluid at high Reynolds numbers and a viscoelastic fluid at low Reynolds numbers, the largest amplification occurs for disturbances that are located near the channel wall. Our analysis of the energy evolution shows that a localized body force in the spanwise direction has the largest impact and that the streamwise velocity component is most affected. For viscoelastic fluids we observe the development of vortical structures away from the source of impulsive excitation. This feature is less prominent in Newtonian fluids and it may provide a mechanism for triggering the initial stages of transition to elastic turbulence.