Turbulent Behavior of the Generalized Surface Quasi-Geostrophic (gSQG) Equations
Investigation of the energy spectrum and enstrophy flux in gSQG turbulence.
Study of the relationships between characteristic wavenumbers in gSQG.
Analysis of the dissipation law in two-dimensional turbulence.
On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations (submitted).
Preprint available at: https://arxiv.org/abs/2510.15077
Data Assimilation for the 2D Dissipative Surface Quasi-Geostrophic (SQG) Equation
Establishes convergence results for a nudging-based data assimilation scheme applied to the SQG equation.
Tests exponential decay of the error between the assimilated solution and the true solution under suitable conditions on the nudging parameter \mu and spatial resolution h.
Provides bounds linking the assimilation parameters to physical quantities such as dissipation rate and forcing amplitude.
Computational Fluid Dynamics (CFD) Based Fan Performance Modeling
Developed a fan performance model using Reynolds-Averaged Navier–Stokes (RANS) simulations with a standard k-\epsilon turbulence model and enhanced wall treatment.
Simulated 27 fan geometries varying radius ratio R_o/R_i, blade count, and blade angle under multiple flow rate conditions.
Validated CFD predictions against experimental measurements, showing close agreement in trend and magnitude of pressure–flow curves.
Incorporated curve-fitted CFD results and analytical relationships into an optimization framework capable of predicting performance for arbitrary fan geometries.
Quantified power components, separating pressure head power from brake power, enabling more accurate efficiency assessment.
Publication: Xiao, J., Uvodich, K., Fu, C., Youn, E., Ryan, F., Samarakoon, A., & Haran, K. (2025). Modeling and Optimization of Self-pumping Air-cooled Thermal Management System for a High Specific Power Outer Runner Electric Motor. In International Electric Machines and Drives Conference, IEMDC 2025 (pp. 164-169). (International Electric Machines and Drives Conference, IEMDC 2025). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IEMDC60492.2025.1106111
The passive scalar equation behaves like a gSQG model with parameter α = 2 and no external forcing.
Prior work (DEIJ 2022; lgindi-Liss 2024) shows anomalous dissipation can occur when the velocity field is sufficiently rough.
Using the NSE solution as the divergence-free velocity field, we observe no anomalous dissipation since the flow is smooth.
When the velocity’s Fourier coefficients are modified to make the field rougher (based on its energy spectrum), anomalous dissipation appears.
The modified field vvv retains the dynamics of the NSE velocity while introducing the roughness needed for dissipation anomalies.
In our results (Figure Below), the original velocity produces no dissipation anomaly, while the modified velocity does.