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Title

Resolvent analysis of turbulent flows: Extensions, improvements and applications

Creator

Lopez-Doriga Costales, Barbara

Date

2024

Description

This thesis presents several advances in both physics-based and data-driven modeling of turbulent fluid flows. In particular, the present...
Show moreThis thesis presents several advances in both physics-based and data-driven modeling of turbulent fluid flows. In particular, the present thesis focuses on resolvent analysis, a physics-based framework that identifies the coherent structures that are most amplified by the Navier-Stokes equations when they are linearized about a known turbulent mean flow via a singular value decomposition (SVD) of a discretized operator. This method has proven to effectively capture energetically-relevant features observed in various flows. However, it has some shortcomings that the present work intends to alleviate. First, the original formulation of resolvent analysis is restricted to statistically-stationary or time-periodic mean flows. To expand the applicability of this framework, this thesis presents a spatiotemporal variant of resolvent analysis that is able to account for time-varying systems. Moreover, sparsity (which manifests in localization) is also incorporated to the analysis through the addition of an l1-norm penalization term to the optimization associated with the SVD. This allows for the identification of energetically-relevant coherent structures that correspond to spatio-temporally localized amplification mechanisms, for flows with either a time-varying or stationary mean. The high computational cost associated with the discretization and analysis of a large discretized of the mean-linearized Navier-Stokes operator represents the second drawback of resolvent analysis. As a second contribution, this thesis provides an analytic form of resolvent analysis for planar flows based on wavepacket pseudomode theory, avoiding the numerical computations required in the original framework. The third contribution focuses on the characterization of the energetically-dominant coherent structures that arise in turbulent flow traveling through straight ducts with square and rectangular cross-sections. First, resolvent analysis is applied to predict the coherent structures that arise in this flow, and to study the sensitivity of this methodology to the secondary mean flow components that display a distinct pattern near the duct corners. Next, a data-driven causality analysis is performed to understand the physical mechanisms involved in the evolution of coherent structures near the duct corners. To do this, a nonlinear Granger causality analysis method is developed and applied to proper orthogonal decomposition coefficients of direct numerical simulation data, revealing that the structures associated with the secondary velocity components are behind the formation and translation of the near-wall and near-corner streamwise structures. A general discussion and future prospects are discussed at the end of this thesis.
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