Explore the nature of density-stratified flow over and around topography, including applications to the flow of the atmosphere and ocean.

The dynamics of flows in density-stratified fluids are an important topic for scientific enquiry. Flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. Both the ocean and atmosphere are characterized by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. This volume provides a state-of-the-art account of stratified flows as they are relevant to the ocean and atmosphere, with a primary focus on meso-scale phenomena; that is, phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth's rotation on the other, can be regarded as of less importance. Environmental Stratified Flows is essential to researchers in the field of oceanography, coastal and marine engineering, and environmental fluid dynamics.

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.

This study focused on understanding how advection of density within the bottom boundary layer influence the three-dimensional structure, evolution, and dynamics of both the bottom boundary layer and the overlying (interior) flow. Simple theories were developed and then tested and extended using both a numerical model and analysis of oceanic observations. Results indicate the simple theories are relevant to the ocean and that the bottom boundary layer plays an important role in the behavior of ocean currents, even when the boundary layer is thin compared to the current depth.

This book covers the theory of stratified flows, from basic concepts to recent developments in environmental fluid mechanics. State-of-the-art numerical techniques suited for stratified flows are given, along with results of recent research in the areas of environmental stratified flows. The book offers a unified view of stratified turbulent flows, from small-scale mixing to large-scale environmental phenomena, including detailed discussion on interaction between turbulence and internal gravity waves.

Stratified flow over topography is examined in the context of its establishment from rest. A key element of numerical and steady state analytical solutions for large amplitude topographic flow is the splitting of streamlines which then enclose a trapped wedge of mixed fluid above the rapidly moving deeper layer. Measurements have been acquired which show that this wedge arises from small scale instabilities and mixing formed initially by the acceleration of subcritical stratified flow over the obstacle crest. The volume of trapped fluid progressively increases with time, permitting the primary flow to descend beneath it over the lee face of the obstacle. Throughout the evolution of this flow, small scale instability and consequent entrainment is the mechanism responsible for producing the weakly stratified wedge, thus allowing establishment of the downslope flow to take place. Velocity structure of instabilities within the entrainment zone is observed and the associated entrainment rate determined. The entrainment is sufficient to produce a slow downstream motion within the upper layer and a density step between the layers that decreases with downstream distance. The resulting internal hydraulic response is explained in terms of a theory which accommodates the spatially variable density difference across the sheared interface. The measurements described here were acquired in a coastal inlet subject to gradually changing tidal currents. It is proposed that the observed mechanism for flow establishment also has application to atmospheric flow over mountains.