Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session R23: Geophysical Fluid Dynamics: General Topics |
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Chair: Matthew Moore, Florida State University Room: 2001 |
Tuesday, November 25, 2014 1:05PM - 1:18PM |
R23.00001: Tsunami propagation using a consistent acoustic-gravity wave formulation Stefan Llewellyn Smith Recent tsunamis such as the 2004 Sumatra tsunami, the 2010 Chile tsunami and the 2011 Tohoku tsunami have led to considerable loss of life and economic repercussions. The existing literature on tsunamis covers the full problem of tsunami generation, propagation and runup, with the goals of tsunami warning and preparedness being a major topic. The simpler question of tsunami propagation in the open ocean still raises a number of questions. Tsunamis propagate at the shallow water wave speed, which in a typical ocean is hundreds of meters per second. Compressibility effects are potentially important, in particular when it comes to the first arrival time and behavior of the leading front of the disturbance. Previous work has examined the effect of compressibility using a formulation based on the hypothesis that the fluid motion is barotropic, Consequently the fluid motion remains irrotational at all times if it is started from rest. We reconsider the effect of compressibility in tsunami propagation without using the assumption of barotropic flow. For a model problem with constant sound speed and buoyancy frequency, the causal Green's function is calculated and the solution to the initial-value problem with specified displacement at the lower boundary is then examined. The effect of r [Preview Abstract] |
Tuesday, November 25, 2014 1:18PM - 1:31PM |
R23.00002: Modelling channelization under ice shelves Michael Dallaston, Ian Hewitt Ice-ocean interactions represent one of the greatest sources of uncertainty in climate model predictions, particularly sea-level rise. It has recently been observed that the undersides of many ice shelves have large incised channels, which has implications for ice sheet stability and mass balance. We describe a mathematical model that captures the growth of these channels from initial perturbations in ice thickness or meltwater flux at the grounding line. Our aim is to use this model to help understand aspects of recently reported observations and numerical experiments. One key finding is that the deformation of ice alone does not prevent the arbitrarily large growth of small wavelength channels, and so dissipative effects (e.g. eddy diffusion) within the ocean/meltwater layer must play a large role in the selection of channel spacing. [Preview Abstract] |
Tuesday, November 25, 2014 1:31PM - 1:44PM |
R23.00003: Equilibrium morphology of laminar rivers Eric Lajeunesse, Gregoire Seizilles, Olivier Devauchelle The flow of a viscous fluid over a bed of plastic sediment spontaneously generates single-thread channels. With time, these analogues of alluvial rivers reach a reproducible steady state, exhibiting a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combination of gravity and flow-induced stress maintains the bed surface at the threshold of motion.\footnote{Seizilles et al., \textbf{Phy. Rev. E.} 87, 052204} If the river transports sediments, gravity pulls the moving grains towards the center of the channel.\footnote{Parker \textbf{J. Fluid Mech.} 89, 127-146} Because of bed roughness, these moving grains follow a random walk in the transverse direction.\footnote{Seizilles et al., \textbf{Phys. Fluids} 26, 013302} Consequently, sediments diffuse towards the less active areas of the bed, thus counteracting gravity by continuously rebuilding the river banks. As the sediment discharge increases, this balance requires a wider and narrower channel, until the river becomes unstable. Based on these experimental observation, we propose a theory explaining how the channel selects its size and slope for given flow and sediment discharges. [Preview Abstract] |
Tuesday, November 25, 2014 1:44PM - 1:57PM |
R23.00004: ABSTRACT WITHDRAWN |
Tuesday, November 25, 2014 1:57PM - 2:10PM |
R23.00005: Sculpting of a dissolvable body by flowing water Jinzi Mac Huang, M. Nicholas J. Moore, Leif Ristroph Fluid flows strongly influence the dissolution of materials in geological contexts and in chemical and pharmaceutical applications. We approach flow-driven dissolution as a moving boundary problem and conduct experiments on hard candy bodies immersed within fast flowing water. We discover that different initial shapes are sculpted into a similar final form before ultimately vanishing, suggesting convergence to a stable shape-flow state. A model linking the flow and solute concentration suggests an explanation for this state and offers scaling laws for quantities such as the volume decay rate in time. As a whimsical application, we also show how this model can be used to address the long-standing question, ``How many licks does it take to get to the center of lollipop?'' [Preview Abstract] |
Tuesday, November 25, 2014 2:10PM - 2:23PM |
R23.00006: A Riemann-Hilbert problem for the shape of a body dissolving in flow Nick Moore, Jinzi Mac Huang, Leif Ristroph As is familiar to anyone who has stirred sugar into coffee, fluid flow can enhance the dissolution of solid material. This effect plays an important role in contexts as varied as landscape formation and drug delivery within the body, but such processes are not well understood due to the interaction between evolving surfaces and flow. By performing experiments with hard-candy bodies dissolving in fast flowing water, we find that different initial geometries converge to the same final shape as they vanish. By modeling both the separated flow around the body and the molecular diffusion of material within the boundary layer, we obtain a Riemann-Hilbert problem for the terminal shape. The solution predicts a front surface of nearly constant curvature, in agreement with experimental measurements. Once formed, this geometry dissolves self-similarly in time and vanishes with a power-law predicted by the model. [Preview Abstract] |
Tuesday, November 25, 2014 2:23PM - 2:36PM |
R23.00007: Dynamics of an unconfined aquifer Adrien Gu\'erin, Olivier Devauchelle, Eric Lajeunesse Rainwater infiltrates into the ground to join a groundwater reservoir, where it flows slowly towards a river. We use a tank filled with glass beads to simulate this process in a simplified laboratory experiment. A sprinkler pipe simulates rain, which infiltrates into the porous material. Groundwater exits this laboratory aquifer through one side of the tank. The resulting water discharge increases rapidly during rainfall, and decays slowly after the rain has stopped. A theory based on Darcy's law and the shallow water approximation reveals two asymptotic regimes. At the beginning of a rain event, the water discharge increases linearly with time, with a slope proportional to the rainfall rate at the power of $3/2$. Long after the rain has stopped, it decreases as the inverse time squared, as predicted by Polubarinova-Kochina (1962). These predictions compare well against our experimental data. These asymptotic regimes depend on the geometric configuration of the flow. However, field measurements from two distinct catchments exhibit the same asymptotic behaviours as our experiment. This observation suggests that these results could be extended to a broader class of groundwater flows. [Preview Abstract] |
Tuesday, November 25, 2014 2:36PM - 2:49PM |
R23.00008: The relationship between hydraulic transmissibility factor and consolidation coefficient for the saturated geo-granular medium Zhifang Zhou The values of transmissibility factor coefficient and consolidation coefficient are generally considered as equal due to the clearly resemble between seepage-deformation control equations and consolidation equations in form for the saturated geo-granular medium. Therefore, the transmissibility factor obtained by in-situ seepage experiments is always used in soil consolidation caused ground settlement prediction, and consolidation coefficient is also widely used in seepage caused ground settlement problems. However, only a limited amount of information is available about the inter-relationship between these two parameters. In this work, we present an analytical method to analyze the differences and relations between hydraulic conductivity and consolidation coefficient. Two different kinds of representative elementary volume (REV) would be proposed based on the physical model of seepage and consolidation. It is found the transmissibility factor and consolidation coefficients are two different parameters with different values, but can be connected by a certain model. Our results indicate consolidation coefficient is 1/(1-n) bigger than conductivity coefficient, where n is porosity of geo-granular medium. [Preview Abstract] |
Tuesday, November 25, 2014 2:49PM - 3:02PM |
R23.00009: Data-driven LES of turbulence and solute transport in a natural stream Ali Khosronejad, Jessica Kozarek, Amy Hansen, Kristopher Guentzel, Miki Hondzo, Peter Wilcock, Michele Guala, Jacques Finlay, Fotis Sotiropoulos We develop and validate a coupled 3D numerical model for carrying out high-resolution large-eddy simulations of turbulence and solute transport for a conservative tracer in a natural stream, the Eagle Creek, located $\sim$ 30 miles south of Minneapolis, Minnesota. We employ the Curvilinear Immersed Boundary method along with a convection-diffusion module to simulate the transient transport of momentum and contaminant concentrations. The detailed geometry of the stream, which is about 135m long, 2.5m wide, and 0.2cm deep is surveyed and used as the simulation domain. The geometry and position of large woody debris in the channel were included in the simulation to account for their effect on the transport of momentum and concentration. The numerical simulation is carried out on a grid with 25 million nodes under two tracer injection conditions, including a pulse and a plateau release. Comprehensive field measurement data is used to validate the flow and concentration field. It is shown that the simulations can accurately capture the spatial and temporal characteristics of the solute transport processes observed in the field and resolve the underlying physical phenomena at unprecedented resolution. [Preview Abstract] |
Tuesday, November 25, 2014 3:02PM - 3:15PM |
R23.00010: Inferring degree of mixing from sparse finite-time measurements of Lagrangian paths using braid dynamics Marko Budisic, Jean-Luc Thiffeault Detailed oceanic measurements, e.g., of temperature and salinity, are often taken by floats, sensors advected by oceans' currents. In addition to physical variables, floats record their own positions, resulting in abundance of data sets of float trajectories. Unfortunately, recent analysis techniques based on knowledge of velocity fields require much denser sampling of velocities than obtained by floats. We discuss braid dynamics, an approach that requires only Lagrangian paths as inputs and is therefore well-suited for analysis of float data. Braid analysis was previously successfully used to design paths of mechanical stirrers to optimize mixing in industrial applications. The difficulty with applying the technique to oceanic flows is that there are no known distinguished ``stirrers'' that induce the flow in the oceans. Consequently, instead of a single braid to be analyzed, a range of different braids can be generated by the same oceanic flow. The following questions arise: What kinds of braids can be sampled from a flow? Can a ``typical'' sampled braid be used to estimate actual mixing timescales? How do number and length of float paths affect the quality of the estimates? We present results based on theoretical and numerical analyses. [Preview Abstract] |
Tuesday, November 25, 2014 3:15PM - 3:28PM |
R23.00011: Simultaneous tracking of particles and reaction fronts in mixing Jesse Cramer, Douglas Kelley In mixing problems, the effects of advection are often studied and relatively well understood. However, many real-life mixing problems---e.g. plankton bloom growth, the spread of oil spills---deal with a combination of advection, reaction, and diffusion. How does advection help---or hinder---the rate of reaction and propagation of the reaction fronts? We present an experimental method for producing consistent advection-reaction data sets via the Belousov-Zhabotinsky reaction, and post-processing methods for simultaneously tracking particles (for advection) and tracking wave fronts (for reaction). By adjusting the rate of advection, we determine how advection affects the rate and location of the reaction. [Preview Abstract] |
Tuesday, November 25, 2014 3:28PM - 3:41PM |
R23.00012: Hydromagnetic Dynamics and Magnetic Field Enhancement in a Turbulent Spherical Couette Experiment D.S. Stone, Q. Liu, D.S. Zimmerman, S.A. Triana, H.C. Nataf, D.P. Lathrop The University of Maryland Three Meter Geodynamo, a spherical Couette experiment filled with liquid sodium and geometrically similar to the earth's core, is used to study hydrodynamic and hydromagnetic phenomena in rapidly rotating turbulence. Turbulent flow is driven in the sodium by differential rotation of the inner and outer spherical shells, while an external coil applies a magnetic field in order to study hydromagnetic effects relevant to the earth's outer core such as dynamo action. An array of 31 external Hall sensors measures the Gauss coefficients of the resulting magnetic field. The flow state is strongly dependent on Rossby number $Ro=(\Omega_{I} -\Omega_{O} )/\Omega_{O} $, where $\Omega_{I} $ and $\Omega_{O} $ are the inner and outer sphere rotation frequencies. The flow state is inferred from the torque required to drive the inner sphere and the generation of internal toroidal magnetic field through the $\Omega $-effect, which is measured by a Hall probe inserted into the sodium. A self-sustaining dynamo has not yet been observed at rotation speeds up to about half of the design maximum. However, continuous dipole amplification up to 12{\%} of a small applied field has been observed at $Ro=-17.7$ while bursts of dipole field have been observed up to 15{\%} of a large external applied field at $Ro=+6.0$ and up to 20{\%} of a small applied field at $Ro=+2.15$. [Preview Abstract] |
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