Transient growth calculations obtained directly from the Orr-Sommerfeld matrices

TL;DR

This paper presents an algorithm to compute transient amplification in two-phase flow using Orr-Sommerfeld matrices and validates it through direct numerical simulations, highlighting the dominance of modal growth in strongly supercritical cases.

Contribution

The paper introduces a novel algorithm for direct computation of transient growth from Orr-Sommerfeld matrices and compares linear theory with numerical simulations in two-phase flow.

Findings

Transient growth calculations align with direct numerical simulations.

Modal growth dominates transient growth in strongly supercritical conditions.

The algorithm provides a direct method for analyzing transient amplification in linear stability theory.

Abstract

We introduce and validate an algorithm to compute transient amplication factors for the Orr-Sommerfeld-Squire linear theory for parallel two-phase flow. We further introduce direct numerical simulation as a way of comparing the linear theory with early-stage wave growth in simulations. The simulation results are drawn from a strongly supercritical parameter case wherein the modal growth rates are strong. In this case, the modal growth dominates the transient growth