Gravity current propagation through density stratified media with applications to transport in the built environment and pollution dispersion in nature

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Gravity currents are primarily horizontal flows that are driven by differences of fluid density and appear over a broad range of time- and length-scales in the natural and built environment. Examples include an airborne chemical agent that flows through a network of subway tunnels, smokestack effluent that propagates along an atmospheric inversion or the counter-flowing drafts of warm and cold air that result when a door to a solarium is suddenly opened. Whereas the flow of gravity currents through a uniform ambient is well-described by experimentally-validated models, far less is known concerning gravity current flow through a stratified ambient, for example one consisting of a dense lower and light upper layer. This lack of understanding represents a serious shortcoming: the atmosphere, most bodies of water and even voluminous building zones typically exhibit some appreciable vertical stratification and this has the effect of altering the dynamics of the flow. For instance, a gravity current propagating through a stratified medium often excites interfacial waves and these can, in turn, extract momentum from the advancing gravity current. Thus a strong feedback may arise so that the gravity current generates waves, which modulate the advance of the current, which changes the pattern of wave excitation and so on. Disentangling the above details is a long-term objective that would constitute a substantial scientific achievement with equally significant practical ramifications in terms of determining patterns of pollution dispersion, optimizing heat exchange in buildings, etc. The goals of the present research are more targeted. They consist of exploring, using theoretical, experimental and numerical techniques, the above dynamics in two specific scenarios. First, I will study axisymmetric gravity currents flowing through a two-layer ambient. This mimics the flow of a river plume into the sea or a draft of warm or cold air into an open-plan, naturally-ventilated building. As compared to the rectilinear analogue problem, here the gravity current height must continually decrease suggesting that the front cannot for long propagate at constant speed. However, preliminary laboratory experiments exhibit surprisingly rich and sometimes counterintuitive behavior depending on the particulars of the initial and source conditions. It remains to complete a more comprehensive sweep of the parameter space then to validate experimental results using appropriate theoretical and numerical models. Next, I will return to rectilinear coordinates and examine the role of bottom topography in modifying the advance of a bottom- or top-propagating gravity current, again through a density-stratified medium. Earlier research with a uniform ambient shows that obstacles exhibit a retarding influence. Conversely, in the absence of topography there are well-documented scenarios in which gravity current fluid can travel long distances at constant speed. Determining which of the above effects predominates under which particular conditions is an important task that will provide invaluable information in assessing dispersion patterns related, for example, to an accidental or malicious release of dense gas over uneven terrain. Model predictions and measured data from the above investigations may be adapted into algorithms that lack sufficient resolution to fully describe flow details at all spatial scales. Instead, parameterizations of the interactions between the advancing gravity current and ambient interfacial waves are required. To this effect, the prime objective of the current proposal is to collect, interpret and synthesize data in a way that is meaningful to other researchers, industry practitioners, regulators and policy makers.