Professor of Mathematics
Department of Mathematics & Statistics
My research has been primarily on the theory and computation of fluid turbulence, with a special interest in numerical methods based on the wavelet transform.
There are numerous problems that remain unresolved in the theory
of turbulence, despite more than 100 years of research on the
subject. A complete and precise theory of turbulence would be
useful in areas as diverse as aerodynamics, combustion, urban
pollution modelling, weather prediction and climate
modelling. Although we are still far from being able to
formulate such a theory, much progress has been made in the
last few decades. The aim of my research is to combine
several recent discoveries in order to develop a new
approach to turbulence modelling. These discoveries include
wavelet transforms (which are used to compress data and
solve partial differential equations), penalisation methods
(which can be used with any numerical method to simulate complex
geometries, such as an airplane), and coherent vortices (flow
structures that control turbulence dynamics). The general theme of
this work has been the interaction between coherent structures
(such as vortices or shocks) and the random background in
turbulence. This new approach should allow high Reynolds
number (high speed, large size) flows to be calculated in
realistic engineering or geophysical configurations.
Pudritz, R.E. & Kevlahan, N.K.-R. 2013 Shock interactions, turbulence and the origin of the stellar mass spectrum. Phil. Trans. R. Soc. A 2013 371, 20120248 doi:10.1098/rsta.2012.0248
Dubos, T. & Kevlahan, N.K.-R. 2013 A conservative adaptive wavelet method for the shallow-water equations on staggered grids. Q. J. R. Meteorol. Soc. 139, 1997-2020 doi:10.1002/qj.2097
Farazmand, M.M., Kevlahan, N.K.-R. & Protas, P. 2011 Controlling the dual cascade of two-dimensional turbulence. J. Fluid Mech. 668, 202-222.
Mehra, M. & Kevlahan, N.K.-R. 2008 An adaptive wavelet collocation method for the solution of partial differential equations on the sphere. J. Comput. Phys. 227, 5610-5632.
Kevlahan, N.K.-R. 2007 Three-dimensional Floquet stability analysis of the wake in cylinder arrays. J. Fluid Mech. 592, 79-88.
Vasilyev, O.V., de Stefano, G., Goldstein, D. & Kevlahan, N.K.-R. 2008 Lagrangian dynamic SGS model for Stochastic Coherent Adaptive Large Eddy Simulation J. Turbulence 9, Art. No. N11.
Kevlahan, N.K.-R. & Vasilyev, O.V. 2005 An adaptive wavelet collocation method for fluid-structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26(6), 1894-1915.
CMLA, Ecole Normale
Superieure de Cachan, France
LMD, Ecole Normale Superieure, Paris, France
DAMTP, University of Cambridge, United Kingdom
Physics, University of British Columbia, Canada
office: Hamilton Hall - HH324