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Shilpa Khatri
Assistant Professor, Applied Mathematics, UC Merced
Ph.D., Courant Institute of Mathematical Sciences

Fluid-Structure Interactions and Multiphase Flow
numerical methods and simulations in conjunction with modeling, experiments, and analysis

I am a numerical analyst and an applied mathematician and have been using my skills to answer open questions about marine phenomena in fluid flow. To understand how nutrients, organisms, and pollutants interact in the ocean, we ask what are the fluid forces acting on these and what are the resulting dynamics. For these complex coupled problems, numerical methods often still need to be developed. My research involves designing mathematical models and numerical and analytical methods for fluid-structure interactions and multiphase flow while comparing with experiments. Below is my previous and current research in which mathematical models and tools have been developed to answer interdisciplinary questions.

Settling and Rising in Density Stratified Fluids

  I. Settling of Porous Particles

Les Houches 2013 (pdf)
ICTAM 2012 (pdf)

R. Camassa, C. Falcon, S. Khatri, R. McLaughlin, B. White, and S. Yu, A predictive theory for a porous sphere settling through stratified fluids, in preparation.

R. Camassa, S. Khatri, R. M. McLaughlin, J. C. Prairie, B. L. White, and S. Yu, Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids, Physics of Fluids, 25:081701, 2013. (pdf) (link)

J. C. Prairie, K. Ziervogel, C. Arnosti, R. Camassa, C. Falcon, S. Khatri, R. McLaughlin, B. L. White, and S. Yu, Delayed settling of marine snow at sharp density transitions driven by fluid entrainment and diffusion-limited retention, Marine Ecology Progress Series, 487:185-200, 2013. (pdf) (link)

  II. Settling of Dense-Core Miscible Vortex Rings

APS DFD 2011 (mov)

R. Camassa, S. Khatri, R. McLaughlin, K. Mertens, D. Nenon, C. Smith, and C. Viotti, Numerical simulations and experimental measurements of dense-core vortex rings in a sharply stratified environment, Computational Science & Discovery, 6:014001, 2013. (pdf) (link)

  III. Rising of Oil Droplets

A Numerical Method to Model Surfactants In Multiphase Flow

Soluble Surfactants Simulation:
Drop in Shear Flow
S. Khatri and A.-K. Tornberg, An embedded boundary method for soluble surfactants with interface tracking for two phase flows, Journal of Computational Physics, 256:768-790, 2014. (pdf) (link)

S. Khatri and A.-K. Tornberg, A numerical method for two phase flows with insoluble surfactants, Computers & Fluids, 49:150-165, 2011. (pdf) (link)

S. Khatri and A.-K. Tornberg, A numerical method for soluble surfactants on moving interfaces, Proceedings in Applied Mathematics and Mechanics, Special Issue: Sixth International Congress on Industrial and Applied Mathematics and GAMM Annual Meeting, 7:1024509-1024510, 2007. (pdf) (link)

S. Khatri, A Numerical Method for Two Phase Flows with Insoluble and Soluble Surfactants, Doctorate thesis, Courant Institute of Mathematical Sciences, New York University, 2009. (pdf)

Odorant Molecule Capture by Marine and Terrestial Crabs

S. Khatri, L. Waldrop, and L. Miller, Odorant molecule capture by marine and terrestial crabs, in preparation.

Surface Stress Induced Entrainment in Stratified Fluids

Experiment (m4v)
S. Khatri, Surface Stress Induced Entrainment in Stratified Fluids, Honors thesis, Dept. of Mathematics, University of North Carolina at Chapel Hill, 2003. (pdf)