Buoyancy force driven mixing in environmental flows: Theory, observations and numerical modeling

Mixing theory is one of the fundamental works in environmental flows. Turbulent mixing-layer theories from classic fluid mechanics are commonly used to describe the mixing dynamics, where certain basic assumptions have been made to simplify the problem, such as neglecting weakly varying fluid densities. While these assumptions worked well for high Mach number flows, which are the targeted problems in the classic fluid mechanics community, in environmental flows, buoyancy forces caused by density differences between two mixing fluids can generate density currents at the mixing layer interface, changing the flow dynamics, hence cannot be neglected. In this dissertation, the limitations of classic turbulent mixing-layer theory are discussed; a generalized conceptual model for mixing dynamics is proposed based on observational data, which includes the classic model as a special case; a generalized mixing-layer theory is also proposed by including buoyancy forces into the derivation of classic mixing layer theory; multiple numerical models are built and used to validate the proposed conceptual model and generalized mixing-layer theory. Observations: The buoyancy-force impacted mixing layer widely exists in environmental flows. Across the world's rivers, they have been observed in numerous field campaigns and can be identified in high-resolution remote sensing images. The data obtained using multiple methods and different measurement technologies are compiled at the confluence of Chicago Sanitary and Ship Canal (CSSC) with the Cal-Sag Canal, Illinois, to analyze different mixing patterns. A 4-type mixing conceptual model that is capable of describing the transition of flow dynamics from classic mixing to buoyancy-force driven mixing is proposed based on the field observations. Theory: The observational data showed that the impact of buoyancy forces could not be described by the classic turbulent mixing-layer theoretical framework because of the formation of sub-surface density currents. By introducing the wave representation of the sub-surface currents, a new theoretical framework is proposed using a 5-step theoretical approach. Generalized environmental fluid mechanics theories are proposed for each step. A new dimensionless Froude number is proposed to describe the surface mixing interface (SMI). Turbulent mixing layer theory is generalized using the projection of the velocity field onto the SMI. The speed and amplitude of internal waves of the density currents are also analyzed to provide a complete mathematical view of the buoyancy-force driven mixing flow dynamics. Numerical model: RANS model using FEM code OpenTelemac and Direct Numerical Simulation model using SEM code Nek5000, have been built to validate the proposed conceptual models and new theories. Based on these modeling results, three critical Richardson numbers are suggested to quantitatively describe the transitional conditions from classic mixing to buoyancy-force driven mixing. Secondary flows were found to have an impact on the mixing efficiency and they can be enhanced or reversed in direction depending on the mixing flow angles. Both parameter and constant values found in the proposed mixing theories are determined using the modeling results, as well. Theories and models advanced in this study can potentially provide a new way to interpret remote sensing observational data. Their application to the formation of turbidity currents at a river mouth, which is a special case of this framework, is also discussed thus paving the way for future research.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Wang, Dongchen

Contributors dc:contributor

• Garcia, Marcelo H.
• Parker, Gary
• Best, Jim
• Fischer, Paul
• Valocchi, Albert
• Tinoco, Rafael O.

• Buoyancy Force Driven Mixing Layer
• Density Currents
• River Confluence
• Generalized Turbulent Mixing Layer Theory
• Environmental Fluid Mechanics
• Remote Sensing

Statement dc:rights

• Copyright 2023 Dongchen Wang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120491

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120491