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Gravity-Driven Intrusions in Stratified Fluids

  • Author(s): Maurer, Benjamin D.
  • et al.
Abstract

All natural fluids stratify. Stable stratifications, in which isobars and isopycnals are parallel, are capable of supporting internal wave motion. Unstable stratification, in which density and pressure gradients are not aligned, results in gravity-driven flow. Gravity currents are a subset of these flows in which horizontal density gradients sharpen and propagate horizontally, transporting mass, momentum, and energy. If the density of the gravity current is within the density extrema of the stably stratified ambient fluid, it propagates as an intrusion at an intermediate height. Through laboratory experiments and numerical simulations, this dissertation explores the influence of stratification on the dynamics of gravity-driven intrusions.

Intrusions require stable stratification in the ambient fluid, which is capable of transporting momentum and energy away from the current in the form of internal waves. We investigate the constant velocity propagation of well-mixed intrusions propagating into a linearly stratified ambient fluid. Varying the level of neutral buoyancy, we quantify the corresponding variation in structure, momentum, and energy of the upstream wave field.

Adjacent stable stratifications of differing vertical density structure necessarily entail horizontal density gradients. These gradients determine the hydrostatic pressure differences driving the ensuing gravity current. We examine the mid-depth, constant velocity propagation of one linearly stratified fluid into another more strongly linearly stratified fluid. Working from the available potential energy of the system and measurements of the intrusion thickness, we develop an energy model to describe the speed of the intrusion in terms of the ratio of the two buoyancy frequencies.

Distinct from adjacent linear stratifications, adjacent discrete stratifications may create flow consisting of interleaving intrusions. Single intrusions into a twolayer ambient fluid are well understood. Limiting our study to an idealized system of multiple intrusions, we attempt to extend the two-layer model to describe the interleaving process. We show that this simple extension fails when the average densities of the two stratifications are unequal, and suggest that this failure is due to the coupling of interfacial waves across constant density layers.

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