Covering both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. Its presentation is suitable for advanced undergraduate and graduate students in fluid mechanics, as well as for practising scientists, engineers, and researchers. Using laboratory experiments and illustrations to further understanding, the author explores topics ranging from the classical hydraulics of single-layer flow to more complex situations involving stratified flows over two- and three-dimensional topography, including complex terrain. A particular focus is placed on applications to the atmosphere and ocean, including discussions of downslope windstorms, and of oceanic flow over continental shelves and slopes. This new edition has been restructured to make it more digestible, and updated to cover significant developments in areas such as exchange flows, gravity currents, waves in stratified fluids, stability, and applications to the atmosphere and ocean.

This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere. The first topic examines the conditions that lead to very large internal waves trapped over topography in a fluid with a pycnocline stratification. This type of stratification is connected to ocean or lake settings. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows under two conditions: a vertically varying background current under the Boussinesq approximation and a constant background current under non-Boussinesq conditions. A numerical method is developed to solve these equations for an efficient exploration of parameter space. Very large waves are found over depression topography when the background flow speed is close to a limiting value. Variations in the background current are examined, as well as comparisons between Boussinesq and non-Boussinesq results. The second topic aims to extend the above subject by considering unsteady, viscous flows. Once again, supercritical flow over topography in a pycnocline stratification generates internal waves. These internal waves interact with the viscous bottom boundary layer to produce bottom boundary instabilities. The three-dimensional aspects of these instabilities are studied under changes in viscosity. The boundary layer instabilities have important implications for sediment transport in the coastal oceans or lakes. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. Modifications to the stratification and topography are applied. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases. This structure may have important implications for dust transport in the atmosphere. In addition, Martian atmospheric parameters are used to study the flow properties under Mars-like conditions.