1. W. Ran. Modeling and analysis of parallel and spatially-evolving wall-bounded shear flows. PhD thesis, University of Southern California, 2020. Keyword(s): Boundary layers, Boundary layer receptivity, Control-oriented modeling, Distributed systems, Drag reduction, Energy amplification, Floquet theory, Flow modeling and control, Free-stream turbulence, Low-complexity modeling, Navier-Stokes equations, Parabolized Floquet equations, Parabolized stability equations, Riblets, Sensor-free flow control, Spatially-evolving flows, Spatially-periodic systems, Spatio-temporal frequency responses, Stochastically-forced Navier-Stokes equations, Transition to turbulence, Turbulence modeling. [bibtex-entry]

1. W. Ran, A. Zare, M. J. P. Hack, and M. R. Jovanovic. Modeling mode interactions in boundary layer flows via Parabolized Floquet Equations. Phys. Rev. Fluids, 4(2):023901 (22 pages), February 2019. Keyword(s): Boundary layers, Control-oriented modeling, Distributed systems, Floquet theory, H-type transition, Laminar streaks, Parabolized Floquet equations, Parabolized stability equations, Periodic systems, Transition to turbulence. [bibtex-entry]

1. W. Ran, A. Zare, M. J. P. Hack, and M. R. Jovanovic. Low-complexity modeling of mode interactions in boundary layer flows. In Proceedings of the 2018 American Control Conference, Milwaukee, WI, pages 134-139, 2018. Note: (Invited paper). Keyword(s): Boundary layers, Control-oriented modeling, Distributed systems, Floquet theory, Parabolized stability equations, Spatially-periodic systems, Transition to turbulence. [bibtex-entry]



2. W. Ran, A. Zare, M. J. P. Hack, and M. R. Jovanovic. Low-complexity stochastic modeling of spatially-evolving flows. In Proceedings of the 2017 American Control Conference, Seattle, WA, pages 3815-3820, 2017. Note: (Invited paper). Keyword(s): Flow modeling and control, Low-complexity modeling, Parabolized stability equations, Spatially-evolving flows, Transition to turbulence, Turbulence modeling. [bibtex-entry]



3. W. Ran, A. Zare, M. J. P. Hack, and M. R. Jovanovic. Low-complexity stochastic modeling of spatially-evolving flows. In Proceedings of the 2016 Summer Program, Center for Turbulence Research, Stanford University/NASA, pages 285-294, 2016. Keyword(s): Flow modeling and control, Low-complexity modeling, Parabolized stability equations, Spatially-evolving flows, Transition to turbulence, Turbulence modeling. [bibtex-entry]

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