Doctoral Defense - Ankit K Gautam

The Department of Mechanical Engineering

Michigan State University

Ph.D. Dissertation Defense

October 3, 2025 at 11:00am EST

Remote via Zoom
Contact the Department or Advisor for Zoom Information

 

ABSTRACT

MIXING DYNAMICS OF INHOMOGENEOUS ANISOTROPIC TURBULENCE: AN EXPERIMENTAL STUDY OF SINGLE-STREAM SHEAR LAYERS

By: Ankit Gautam

Advisor: Dr. Ricardo Mejia

 

Free shear layers, or turbulent mixing layers, are inherently inhomogeneous and anisotropic, representative of real-world flows, and fundamental to understanding turbulence in both natural and engineering systems. This dissertation focuses on the single-stream shear layer (SSSL)—a configuration that, despite its importance, dynamic similarity to many real-world flows, and distinct behavior from the more extensively studied two-stream shear layer (TSSL), remains comparatively underexplored, especially through high-resolution full-field measurements. To address this gap, a custom high-Reynolds-number water tunnel is built, to generate a controlled SSSL, complemented by advanced flow diagnostics that enable three-dimensional tracking of fluid particle trajectories over time. These measurements provide a detailed perspective on the temporal
evolution of coherent motions and the turbulent mixing dynamics within, from flow separation through the onset of self-similarity, forming the core philosophy of this work.
The captured particle trajectory data are assimilated to reconstruct velocity fields from sparse, scattered track data, enabling a detailed characterization of statistical turbulence descriptors, including turbulent kinetic energy budget terms. The analysis yields high-fidelity measurements of SSSL growth rates, mixing dynamics and turbulent energy distribution within the coherent motions. A key discrepancy in reported growth rates from the literature emerges, which this work reconciles by proposing an empirical scaling law based on the initial boundary-layer (BL) Reynolds number, validated using high-speed 2D-PIV flow field measurements across a range of Reynolds numbers. This scaling unifies the growth behavior of both SSSLs and TSSLs, establishing the BL Reynolds number as the primary governing parameter. Moreover, the work raises critical questions about the broader role of BL Reynolds number and other key BL flow parameters in controlling growth and determining the onset of self-similarity in free shear layers. Complementing the Eulerian analyses, a comprehensive Lagrangian statistical analysis is conducted by leveraging the particle trajectories. The analysis involving assessment of particle dispersion behavior, conditioned on its origin location, seem to be tied with local mean and fluctuation velocity scales. Probability density functions for velocity increments, strain rate and enstrophy capture signatures of both internal intermittency in the core and external intermittency near the turbulent/non-turbulent interface. Furthermore, the velocity gradient tensor (VGT) estimated along the particle trajectories enable the investigation into the evolution dynamics of VGT invariants. In summary, the work reveals how dispersion, intermittency, and small-scale turbulence differ between the core region, which behaves nearly homogeneously, and the turbulent/non-turbulent interface near the SSSL edge, where external intermittency dominates.

Beyond these experimental insights, this work briefly delves into a data-driven modeling approach by applying Mori–Zwanzig modal decomposition (MZMD) to the velocity flow fields. Unlike other dimensionality-reduction methods such as dynamic mode decomposition, MZMD incorporates memory effects, allowing the model to capture nonlinear periodic motions characteristic of large spanwise coherent motions more accurately. The dissertation also contributes practical advances, including the development of ultra-low-cost fluorescent tracer particles suitable for liquid flow velocimetry, a single-camera imaging strategy to economize experimental campaigns for simultaneous velocity and scalar measurements, and recommendations for multi-fluid mixing flow measurements. Collectively, these methodological, physical, and modeling contributions advance both the understanding of turbulent mixing dynamics and the experimental and computational tools available for studying complex shear flows.