UC Santa Barbara

Turbulence contains vortices with a broad range of spatial and temporal scales, which dominate the safety and performance of systems like turbomachinery and aerospace vehicles. The expensive efforts needed to resolve all vortices in these flows have led to the development of hybrid algorithms, where vortical regions are treated differently. In this study, we first illustrate the physical meaning of the dominant structures extracted through proper orthogonal decomposition (POD) and Koopman mode decomposition (KMD). We then verify that KMD recovers linear stability eigenvalues and eigenmodes associated with the inviscid merger of two co-rotating vortices. Thereafter, Koopman analysis results are provided to quantitatively and qualitatively assess the viscous interactions of co-rotating vortices. The onset of symmetry-breaking is found weakly sensitive to Reynolds number, but highly sensitive to small details in initial conditions. We build on our results to seek a data-driven model that balances efficiency and accuracy. We record total circulation, enstrophy, and angular impulse and solve their theoretical evolution equations to automate the selection of the model parameter values. We provide a test of algorithmic performance in simulating vortex merging. We first test the robustness of selecting each of the above three flow quantities to enforce accuracy. We then verify that KMD eigenvalues recover the correct time scales of the flow systems. Finally, we analyze the model performance by simulating the merger of uniform, patch-like co-rotating vortex pairs under different Reynolds numbers. This approach has the potential to be beneficial for simulating flows comprising fine vortical features in large domains.

In this study, we also delve into the topic of superhydrophobic drag reduction at high Reynolds numbers, utilizing adaptive octree discretizations in distributed environments to conduct simulations that are both accurate and computationally feasible. This work builds upon the parallel level-set schemes developed by Mirzadeh et al., employing {\tt p4est} and extending the research presented in Egan et al.. Superhydrophobic surfaces (SHS) have shown high drag reductions in turbulent flows. However, simulating the high gas fractions and high Reynolds numbers typical of naval applications poses a challenge due to the sharp gradients that arise near the transitions between no-slip regions and gas-liquid interfaces. To address this, we leverage high-performance multicore systems and scalable linear solvers to simulate SHS structures, enabling a relatively rapid exploration of the parameter space up to gas fractions of 93.75\%. We introduce momentum flow lines to map the pathways taken by the streamwise momentum as it is transported from the channel interior towards the walls, aiding in the understanding of the flow dynamics. This study reveals how flow properties, including Reynolds stresses and vortical structures, are influenced by gas fraction and Reynolds number. These insights can contribute to the development of refined models that are valid across different flow regimes.