Kevin Lamb's research

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 kilometres.

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.

Current projects include:

1. Nonlinear dispersive waves

   Nonlinear dispersive waves occur in a variety of forms. Internal gravity waves and surface water waves are two examples. They also occur in plasmas, nonlinear optics and many other physical systems.

2. Physical limnology

   I am involved in an interdisciplinary project aimed at understanding hypoxia in Lake Erie. Part of this project is aimed at understanding the internal wave field in the lake. This includes the basin scale waves into which most of the energy is injected and the nonlinear transfer of energy to smaller scale waves which break in the region where the metalimnion intersects the lake bottom. We will be studying the mixing and sediment resuspension associated with these breaking waves and the effects of these processes on bio-geochemical processes, including hypoxia. This three-year project is funded by an NSERC Strategic Grant in collaboration with Joe Ackerman (Department of Integrative Biology, University of Guelph), Leon Boegman (Civil Engineering, Queen's University) and Ralph Smith (Biology Department, University of Waterloo).

3. The development of parameterizations of high-frequency, non-hydrostatic internal waves

   Most large scale ocean circulation models use the hydrostatic approximation which is appropriate for modelling phenomena whose horizontal length scale is long compared with the vertical length scale. The use of the hydrostatic approximation is popular because it simplifies numerical models resulting in much shorter model run times. Hydrostatic models cannot model solitary internal waves and other high-frequency waves because the hydrostatic approximation excludes these dispersive waves. Non-hydrostatic models run on large domains have a difficult time modelling these waves because they can be difficult to resolve.

4. Tidal flow over a sill

   Shear instabilities in the subcritical response; boundary layer separation and its effects on internal wave generation.

5. Shoaling internal solitary wave

   Internal solitary waves are common occurrences in oceans and lakes. When propagate into shallower water they deform and can overturn and break resulting in mixing and sediment resuspension.All aspects of shoaling waves are of interest.

6. Shear instabilities in internal solitary waves

   A recent publication (Lamb and Farmer, 2011) described the results of two-dimensional simulations of shear instabilities in internal solitary waves. These simulations were coupled with observations taken on the Oregon Shelf. Current research is focussed on better understanding these instabilities in idealized situations. Both two- and three-dimensional simulations are being done.

7. Internal solitary waves with cores

   This has been an ongoing project which has resulted in several papers. Future work will focus on three dimensional numerical simulations and comparisons with laboratory experiments.

8. The effects of internal solitary wave trains on ocean acoustics

   The ultimate goal of this project is to understand how internal solitary wave trains effect acoustic propagation in the ocean. In order to do this it is necessary to understand the characteristics of internal wave trains that are generated by tidal flow over topography so this project includes studies of the internal wave generation process as well as acoustic propagation. This work is done with collaborators at the Naval Research Laboratory in the U.S.

My research is funded by NSERC's Research Grant program