I specialize in turbulent flows, variational methods, analysis of partial differential equations, and computational techniques. I am interested in problems at the intersection of physical and mathematical fluid dynamics, especially those that require the exchange of ideas and benefit both fields. My recent works have explored a range of flow designs, from heat and momentum transport in turbulent flows to problems related to nonuniqueness in fluid PDEs.

I completed my Ph.D. in Applied Mathematics at the University of California, Santa Cruz, surrounded by the stunning views of the Pacific Ocean and the majestic redwoods. My thesis was titled Bulk Properties and Flow Structure in Turbulent Flows. Prior to that, I earned my Master’s in Mechanical Engineering from the Indian Institute of Science and Bachelor's from the Indian Institute of Technology Jodhpur.

Publications

(15) Kumar, A. (with F. Weber), Optimal mixing of a divergence-free passive vector,  (in preparation).

(14) Kumar, A. (with M. Colombo and R. Colombo), A convex integration scheme for the continuity equation past the Sobolev embedding threshold, 2025  (submitted).
● arXiv: 2504.03578

(13) Kumar, A., Almost anomalous dissipation in advection-diffusion of a divergence-free passive vector, 2024, (submitted).
● arXiv: 2409.15000

(12) Kumar, A. (with E. Bruè and M. Colombo), Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity, 2024,  (submitted).
● arXiv: 2408.07934

(11) Kumar, A. (with E. Bruè and M. Colombo), Sharp nonuniqueness in the transport equation with Sobolev velocity field, 2024,  (submitted).
● arXiv: 2405.01670

(10) Kumar, A., Nonuniqueness of trajectories on a set of full measure for Sobolev vector fields, 2023,  Archive for Rational Mechanics and Analysis, Volume 248, article no. 114, 1-26, 2024.
● arXiv: 2301.05185 ● DOI:10.1007/s00205-024-02063-y

(9) Kumar, A., Three dimensional branching pipe flows for optimal scalar transport between walls, 2024,  Nonlinearity,  Volume 37, 115011, pp. 1-55.
● arXiv: 2205.03367 ● DOI:10.1088/1361-6544/ad789e

(8)  Kumar, A., Geometrical dependence of optimal bounds in Taylor–Couette flow, Journal of Fluid Mechanics,Volume 948, pp. A11:
1-40, 2022.
● arXiv: 2201.06214 ● DOI:10.1017/jfm.2022.662

(7)  Kumar, A., Arslan, A., Fantuzzi, G., Craske, J., Wynn, A., Analytical bounds on the heat transport in internally heated convection, Journal of Fluid Mechanics, Volume 938, pp. A26: 1-21, 2022.
● arXiv: 2110.10344 ● DOI:10.1017/jfm.2022.170 

(6)  Kumar, A., Rehman, N.M.A., Giri, P., Shukla, R.K., An asymptotic theory for the high-Reynolds-number flow past a shear-free circular cylinder, Journal of Fluid Mechanics, Volume 920, pp. A44: 1-32, 2021.
● arXiv:1711.04278 ● DOI:10.1017/jfm.2021.446

(5)  Kumar, A., Pressure-driven flows in helical pipes: bounds on flow rate and friction factor, Journal of Fluid Mechanics, Volume 904, pp. A5: 1-27, 2020
● arXiv:2009.01322 ● DOI:10.1017/jfm.2020.655

(4)  Kumar, A., Garaud, P., Bounds on the drag coefficient for a flat plate in a uniform flow, Journal of Fluid Mechanics, Volume 900, pp. A6: 1-24, 2020.
● DOI:10.1017/jfm.2020.477

(3)  Garaud, P., Kumar, A., Sridhar, J., The Interaction between Shear and Fingering (Thermohaline) Convection, The Astrophysical Journal, Vol. 879, No. 1, pp. 1-16, 2019.
● arXiv:1905.07636 ● DOI:10.3847/1538-4357/ab232f 

(2)  Rehman, N.M.A., Kumar, A., Shukla, R.K., Influence of hydrodynamic slip on convective transport in flow past a circular cylinder, Theoretical and Computational Fluid Dynamics, Vol. 31, No. 3, pp. 251-280, 2017.
● DOI:10.1007/s00162-017-0421-5

Ph.D. Thesis

(1) Kumar, A., Bulk properties and flow structures in turbulent flows.
● link: escholarship.org/uc/item/47k237g4

Talks

(42) Invited Talk: Forum for Early Career Scientists, APS Global Physics Summit, CA, March, 2025.

(41) Online Turbulence Seminar, March, 2025 (online).

(40) Winter School: Boundary and Singularity in Fluid Mechanics, Simons Center for Geometry and Physics, Stony Brook, NY, January, 2025.

(39) Andreas Acrivos Award, Invited Talk, APS DFD 77th Annual Meeting, Salt Lake City, Utah, November, 2024.

(38) APS DFD 77th Annual Meeting, Salt Lake City, Utah, November, 2024.

(37) PDE and Applied Math Seminar, UC Davis, CA, October, 2024 (online).  

(36) SIAM Northern and Central California Annual Meeting, UC Merced, October, 2024.  

(35) TIFR-Centre for Applicable Mathematics, India, October, 2024 (online).

(34) Analysis and PDE seminar, UC Berkeley, CA, September, 2024.

(33) Analysis and PDE seminar, Caltech, CA, September, 2024.

(32) Invited lecture at the 3rd ISTA Summer School in Analysis and Mathematical Physics, Austria, June, 2024.
● Slides:https://summerschool-analysis.pages.ist.ac.at/wp-content/uploads/sites/141/2024/06/Kumar.pdf

(31) Analysis seminar, University of California San Diego, CA, May, 2024.

(30) Applied analysis and probability seminar, The Pennsylvania State University, PA, April, 2024.

(29) Center for nonlinear analysis seminar, Carnegie Mellon University, PA, April, 2024.
● Video:https://mm.math.cmu.edu/recordings/cna/Anuj_Kumar.mp4

(28) Seminar Analysis and Mathematical Physics, Universität Basel, Switzerland, April, 2024.

(27) Analysis seminar, ETH Zürich, Switzerland, March, 2024.

(26) Analysis seminar, EPFL, Switzerland, March, 2024.

(25) Università degli Studi di Milano, Italy, March, 2024.

(24) Math Monday, MUSA, UC Berkeley, CA, March, 2024.

(23) Nonlinear Physics Seminar, UC Berkeley, CA, February, 2024.

(22) Applied Math Seminar, University of Victoria, Canada, January, 2024.

(21) Department of Decision Sciences, Università Bocconi, Italy, November, 2023.

(20) Harmonic Analysis and Differential Equations Seminar, UC Berkeley, CA, October, 2023.

(19) Enjoying Probability and Fluids in Lausanne, EPFL, Switzerland, September, 2023. 

(18) Exotic Solutions and Well Posedness in ODE's and PDE's, The Riemann Prize ceremony, RISM, Italy, July, 2023.
● Video:https://www.youtube.com/watch?v=pVFX3qHdmCc&t=11305s

(17) Junior Analysis Seminar, Imperial College London, UK, March, 2023.

(16) Applied Mathematics Seminar, UC Berkeley, CA, January, 2023.

(15) Geophysical and Environmental Processes Seminar, University of Cambridge, UK, October, 2022, (online).

(14) Applied Mathematics Colloquium, Columbia University, NY, October, 2022.

(13) Analysis of Fluids and Related Topics Seminar, Princeton University, NJ, September, 2022.

(12) Numerical Methods for PDEs Seminar, Massachusetts Institute of Technology, MA, September, 2022.

(11) GFD Seminar, Woods Hole Oceanographic Institution, MA, July 2022.

(10) Environmental Fluid Dynamics Group, Rice University, TX, June 2022, (online).

(9)  Small scale dynamics in fluid motion workshop, Simons Center for Geometry and Physics, Stony Brook, NY, June, 2022.
● Video:https://scgp.stonybrook.edu/video_portal/video.php?id=5307

(8)  Aerodynamics and Control Seminar, Imperial College London, UK, May, 2022.
● Video:https://cassyni.com/events/FAKhU8y5KsJ4JS9fSe2pmK

(7)  Analysis and Applied Mathematics Seminar, University of Illinois Chicago, IL, February, 2022.

(6)  GAFD Seminar, UC Santa Cruz, CA, February, 2022.

(5)  APS DFD 74th Annual Meeting, November, 2021.

(4)  Charlie at GFD: An Appreciation, August, 2021 (online).

(3)  APS DFD 73rd Annual Meeting, November, 2020 (online).

(2)  APS DFD 72nd Annual Meeting, Seattle, Washington, November, 2019.

(1)  GAFD Seminar, UC Santa Cruz, CA, October, 2019.

Teaching

Instructor, UC Berkeley

Spring 2025: Second Course in Analysis (MATH 105) 

Spring 2025: Introduction to Real Analysis (MATH 104) 

Fall 2024: Mathematical Methods for Optimization (MATH 170) 

Spring 2024: Introduction to Real Analysis (MATH 104), 2 sections

Fall 2023: Mathematical Methods for Optimization (MATH 170)

Teaching Assistant, UC Santa Cruz

Spring 2022: An Introduction to High Performance Computing (AM250)

Winter 2022: Computational Methods and Applications (AM147)

Fall 2021: Fluid Mechanics (AM107/AM217)

Spring 2021: An Introduction to High Performance Computing (AM250)

Winter 2021: Computational Methods and Applications (AM147)

Fall 2020: Fluid Mechanics (AM107/AM217)

Spring 2020: Stochastic Differential Equations (AM216)

Spring 2020: Numerical Methods for the Solution of Differential Equations (AM213b)

Winter 2020: Computational Methods and Applications (AM147)

Awards and Achievements

Andreas Acrivos Dissertation Award in Fluid Dynamics, American Physical Society (2024)

David Crighton Fellowship, University of Cambridge (2022) 

Chancellor's Dissertation-Year Fellowship, UC Santa Cruz (2022) 

Graduate Dean's Travel Grant (2022)

Jack Baskin and Peggy Downes Baskin Fellowship, UC Santa Cruz (declined) (2020)

Geophysical Fluid Dynamics Fellowship program, Woods Hole Oceanographic Institution (2019) 

 Dean's and Regents' Fellowship, UC Santa Cruz  (2018)

Master of Engineering with distinction, Indian Institute of Science (2016) 

Ministry of Human Resource Development (MHRD) Fellowship (2014)

All India Rank 12 (out of 185,578) in Graduate Aptitude Test in Engineering (2014)