Vincent Duchêne | Mathematically Modeling the Behavior of the Ocean

Vincent Duchêne Ju Tang Chu and Wu Ping Chu Foundation Assistant Professor of Applied Mathematics

This profile is included in the publication Excellentia, which features current research of Columbia Engineering faculty members.                                     Photo by Eileen Barroso

The ocean is a vast frontier that has fascinated mankind for centuries. But as much as we think we know about it, much more is mysterious. Consider the phenomena of internal waves. When two or more layers of ocean water—like fresh and salt water, or warm and cold water—rest one on top of the other without mixing, waves form between the two layers. This wave energy forms and dissipates, affecting everything from ships and submarines, drilling rigs and undersea cables, and the ecosystem of the ocean.

Studying waves on the surface of the ocean—where their formation and dissipation can be easily observed—is one thing. Trying to understand what happens below depths at the interfaces of water layers is almost impossible because measurement techniques are limited and available data are sparse.

By developing mathematical models to study the propagation of internal waves, scientists can numerically compute and study the behavior of hidden waves in relation to different parameters like depth and fluids densities. By applying that knowledge to oceanic fluid mechanics, new models can be constructed to improve our understanding of the effects of these waves and the energy they generate.

With that understanding, the design of marine structures and ships can be improved and the results of how pollutants mix and percolate to the depths of the ocean can be better monitored.

Vincent Duchêne develops mathematical models that seek to explain oceanographic challenges, especially those regarding the behavior of density-stratified flows constituted of two immiscible fluids influenced by gravity. He has been successful in producing and rigorously justifying models related to the dead water phenomena by reproducing the phenomena’s key aspects which include generation of transverse internal waves at the rear of a body while moving at the surface of stratified flows and the positive drag on a body when an internal elevation wave is located at its stern. These models allow scientists to study the behavior of internal waves in relation to different parameters like the depth of the layers, densities of the fluids, and velocity of a ship.

Duchêne’s other research interests include understanding problems related to the propagation of light through photonic crystals and partial differential equations with particular emphasis on hyperbolic equations.

Ancien élève, École Normale Supérieure de Lyon (France), 2007; M.S.C., Université Bordeaux 1 (France), 2008; Ph.D., Université Pierre et Marie Curie (Paris VI), 2011