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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.

Dubrulle, B., Laval, J.-P. & Nazarenko, S. & Kevlahan, N. 2001 Derivation of equilibrium profiles in plane parallel flows from a dynamical subgrid Model. Phys. Fluids 13, 2045-2064.

Farge, M., Schneider, K. & Kevlahan, N. 1999 Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis. Phys. Fluids 11, 2187-2201.

Kevlahan, N. K.-R. 1996 The propagation of weak shocks in non-uniform flows. J. Fluid Mech. 327, 161-197.

Math 1AA3 - Calculus II
Inquiry 1SC3 - First year science inquiry
Math 2T03 - Numerical Analysis I
Math 3C03 - Mathematical Physics I
Math 3D03 - Mathematical Physics II
Math 3Q03 - Numerical interpolation and approximation
Math 4Q03 - Numerical Methods for Ordinary and Partial Differential Equations
Math 744 - Asymptotic Analysis
Math 745, CES 715 and 716 - Introduction to mathematical and computational fluid dynamics

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

email:  kevlahan@mcmaster.ca
office: Hamilton Hall - HH324