Session ZC27: Geophysical Fluid Dynamics: General

Experimental evidence of algebraic relaxation time in particle settling under gravity in Stokes flow

Particles settling under gravity through a fluid are common in geophysics and the environment, e.g., plankton in the ocean and droplets in clouds. The Maxey-Riley equation models the dynamics of such small inertial particles when spherical and in the unsteady Stokes regime. It is standard practice to neglect the Basset-Boussinesq history force in this equation and deduce an exponentially fast relaxation of the particle to its terminal velocity. However, a few theoretical studies, including Basset (1910), cautioned that the history force could result in qualitatively different behavior. In fact, the particle relaxes to its terminal velocity algebraically slowly, asymptotically at the rate t^{-1/2}, i.e., with an algebraic relaxation rate of -0.5, not exponentially fast. We conducted experiments to validate the theoretical predictions. By employing high-speed imaging, we analyzed the trajectories of stainless-steel spherical particles settling in Silicone oil in a controlled Stokes regime. Furthermore, we explored the wake structures surrounding the particles using flow visualization. The experiments show an algebraic relaxation rate, verifying the theory. To the best of our knowledge, these experiments provide the first confirmation of the theoretical relaxation rate.   

Extended Shallow Water Models for Steady-State Gravity Currents

Turbidity currents have been observed to propagate for very long distances, longer than one would expect based on the current knowledge of mixing and evolution of gravity currents. Recent DNS simulations suggest that when in steady state the gravity current presents a much more stable interface, potentially reducing the mixing with ambient waters and hence being able to survive and propagate for longer distances. We report experiments that investigate gravity currents that have reached a statistically steady state and compare the results to DNS and extended shallow water models that track the profile evolution.   

Using clusters of instantaneous vortices to quantify secondary circulation sub-cells in open channel bends with and without a submerged transverse jet

Large eddy simulations of an open channel bend with and without a submerged transverse jet upstream of the bend are conducted. Sub-cells of secondary circulation are identified using clusters of instantaneous vortices, which allows for better resolution of sub-cell development than can be achieved with mean flow alone. The method allows us to pinpoint the development location of sub-cells to positions at the outer bank, which can be understood using conceptual models of vorticity production based on flow acceleration at wall boundaries. The sub-cell circulation quantification allows for interactions between developing sub-cells and established circulation cells to become clear. This is demonstrated through the interaction of developing sub-cells and jet vortices, by introducing a transverse jet from the outer bank wall upstream of the channel bend. The presence of the jet counter-rotating vortex pair at the beginning of the bend redistributes the bend secondary circulation between sub-cells but does not change the total amount of secondary circulation. The principle of using clusters of instantaneous vortices to track developing cells and their interactions with already-established cells has many further applications, from studying secondary circulation development in channels with previous bends to identifying locations where circulation first develops in bends with bathymetry.   

A two-layer eddy viscosity model to predict the near-bed hydrodynamic in vegetated flows

Flow-vegetation interaction in aquatic vegetation canopies affects various ecosystem services. The hydrodynamics within the bottom boundary layer in vegetated channels governs sediment transport, sediment-oxygen exchange, pollutant dispersion etc. However, the dynamics of the vegetated boundary layer is still poorly understood due to the challenges associated with direct flow measurement within the boundary layer. In this work we perform wall resolving Large Eddy Simulations (LES) to explore the boundary layer dynamics in flow through a dense (solid volume fraction, Φ = 0.09) array of rigid emergent cylinders for varying Reynolds Numbers (Re ∈ [8,20]x10⁴). The mean flow statistics far from the bed exhibit a self-similar behavior with Re. However, the flow within the boundary layer shows significant dependence on Re, which leads to variations in near-bed flow statistics. To elucidate the effect of Re on near-bed hydrodynamics, we perform quadrant analysis to identify the contribution of intense events to the generation of Reynolds stresses. We quantify the near-bed Reynolds Stress to develop a novel two-layer eddy viscosity model for vegetated flows for varying Re. This has numerous applications including, but not limited to, stream restoration, sediment transport, blue carbon, and microplastic transport.   

A geometric mechanism behind sharp crests and scallops in erosion by dissolution

When water flows over soluble rocks such as limestone, salt or gypsum, the feedback between the topography and the flow can lead to the formation of remarkable patterns. One of the most common is known as scallops, and consists of cups-like concavities surrounded by very sharp crests. They can be found typically on the walls of caves carved by underground rivers. Yet very similar patterns form by melting or sublimation of ice, or by ablation on meteorites. The similarity between these patterns, despite the wide range of materials and hydrodynamic conditions, suggests a common and general mechanism.

By comparing field measurements, numerical models and experiments, we propose a geometric approach to explain the generic emergence of scallops. We first characterize the morphology of scallops found on the walls of a limestone cave, and demonstrate the presence of crests which can be seen as singular structures. Then, we discuss the results of numerical models of interface propagation. They allow us to interpret the appearance of crests and the formation of cellular structures as a direct consequence of the fact that the erosion velocity is always directed along the normal to the interface. Finally, we carry out a simple experiment in which patterns are created by dissolution, on the surface of a block of salt, by a solutal Rayleigh-Bénard instability. In accordance with our model, we report the emergence of a cellular pattern of concavities surrounded by sharp crests, very reminiscent of natural scallops.