My primary area of research is on nonlinear internal waves in the ocean and in lakes. This work uses both theoretical and computational methods. Other research interests include other types of nonlinear waves in both fluids and other physical systems such as nonlinear optics. I am also interested in many other aspects of fluid dynamics including hydrodynamic instabilities, large scale ocean circulation, and a variety of stratified flow phenomena.
Internal waves occur in density stratified fluids when gravitational restoring forces act on vertically displaced fluid. They are common in both the ocean and atmosphere where they are primarily generated by flow over rough topography, from vertical motions associated with horizontal convergence (e.g., wind forcing at the ocean surface) or from vertical convection. In stratified lakes internal waves are generated by wind forcing. Computer animations of a variety of internal wave phenomena can be seen here: internal wave animations.Most of this simulations were generated from the two-dimensional non-hydrostatic numerical model igw that I developed.
Much of my research is on large amplitude, short-period, horizontally propagating internal waves in the ocean. These waves include undular bores and internal solitary waves which are common features in stratified coastal regions of the world's oceans where they can be tens of meters in amplitude and have wave lengths of hundreds of meters to several kilometers.
The most important generation mechanism of internal solitary waves in the ocean is tidal flow across large topographic features such as the shelf break, sills and bank edges. The flow near the topographic feature can be highly nonlinear and turbulent, including such features as hydraulic jumps. To date, there are no satisfactory theories which will predict the quantitative properties of the waves which are ultimately formed by this mechanism, although once formed, the properties and evolution of internal waves of moderate amplitude have been described with considerable success by weakly-nonlinear evolution equations such as the Korteweg-de Vries (KdV) equation for waves in shallow-water.
Internal waves in stratified lakes are generated when winds push warm surface water to one end of the lake resulting in a tilted thermocline (called the metalimnion lakes ). When the wind relaxes basin scale internal waves are formed as the thermocline adjusts. Nonlinearity can cause these basin scale waves to steepen and form high frequency internal waves.
Like the generation, the ultimate fate of these waves and their impact on their environment is not well understood. Rapidly shoaling waves increase in amplitude and may overturn. The location and distribution of such breaking is poorly understood. Wave breaking results in the vertical mixing of the water which has many important implications including, for example, vertical mixing of nutrients.
Internal waves transport energy, momentum and mass and can play an important role in mixing processes. Large surface currents associated with large waves of depression can substantially modify the surface wave field, an effect which can be observed via remote sensing techniques. Particularly large waves have been known to transport ocean vessels several kilometres. They are a concern to oil companies due to their impact on drilling operations. Scouring of the bottom by internal waves has caused problems by uncovering pipelines. Biologists are interested in the role these waves play in the transport of organisms. These properties, along with their common occurrence, make them an important physical phenomenon.
The goal of my research is to better understand the wave generation process and to understand what effects the waves have on their environment. I am increasingly interested in investigated mixing processes associated with internal waves. My research is very numerically oriented and theoretical in nature. High resolution numerical simulations, using a fully-nonlinear, nonhydrostatic numerical model, are being done to study a variety of processes related to internal waves. These include such things as wave generation by tidal flow of topographic features such as bank edges and sills, the evolution of shoaling solitary waves and tidal flow over a sill. Mathematical models, such as those based on weakly-nonlinear theory, are also used to study problems related to internal solitary waves. These provides a framework for interpreting and understanding the results of numerical simulations.
My research is funded by NSERC's Research Grant program
This page last updated Oct 23, 2003