Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session G32: Geophysical Fluid Dynamics: GeneralGeophysical
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Chair: Marius Ungarish, Technion, Haifa Room: 104 |
Monday, November 20, 2017 10:35AM - 10:48AM |
G32.00001: Gravity current into an ambient fluid with an open surface Marius Ungarish Consider the steady-state gravity current of height $h$ and density $\rho_1$ that propagates into an ambient motionless fluid of height $H$ and density $\rho_2$ with an upper surface open to the atmosphere (open channel) at high Reynolds number. The current propagates with speed $U$ and causes a depth decrease $\chi$ of the top surface. This is a significant extension of Benjamin's (1968) seminal solution for the fixed-top channel $\chi = 0$. Here the determination of $\chi$ is a part of the problem. The dimensionless parameters of the problem are $a=h/H$ and $r = \rho_2/\rho_1$. We show that a control-volume analysis determines $\tilde{\chi} = \chi/H$ and $Fr = U/(g' h)^{1/2}$ as functions of $a,r$, where $g' = (r^{-1}-1)g$ is the reduced gravity. The system satisfies balance of volume and momentum (explicitly), and vorticity (implicitly). We present solutions. The predicted flows are in general dissipative, and thus physically valid only for $a \le a_{\max}(r) \approx 0.5 r$ where non-negative dissipation appears. The open-surface $Fr(a,r)$ is smaller than Benjamin's $Fr_b(a)$, but the reduction is not dramatic, typically a few percent. In the Boussinesq $r \approx 1$ case, $\tilde{\chi} \ll 1$ while $Fr$ and dissipation are close to Benjamin's values. [Preview Abstract] |
Monday, November 20, 2017 10:48AM - 11:01AM |
G32.00002: Inertial gravity currents from edge drainage Mostafa Momen, Zhong Zheng, Elie Bou-Zeid, Howard Stone Gravity currents are formed due to a density gradient in the horizontal direction between the current and an ambient fluid. In this work, we present theoretical, numerical, and experimental studies of the release of a finite volume of fluid instantaneously from the edge of a rectangular domain for high-Reynolds-number flows. The setup is relevant in geophysical and engineering applications such as open channels, and dam-break problems. For the cases we considered, the results indicate that about half of the initial volume exits during an early adjustment period. Then, the inertial gravity current reaches a self-similar phase during which about 40{\%} of its volume drains and its height decreases as $\tau^{\mathrm{-2}}$, where $\tau $ is a dimensionless time that is derived with the typical gravity wave speed and the horizontal length of the domain. Based on scaling arguments, we reduce the shallow-water PDEs into two nonlinear ODEs, which are then solved analytically. The new self-similar solutions are in good agreement with the performed experiments and direct numerical simulations for various geometries and fluid densities. This study provides new insights into the dynamical behavior of edge drainage flows, particularly during the inertial regime. [Preview Abstract] |
Monday, November 20, 2017 11:01AM - 11:14AM |
G32.00003: Intrusive gravity currents in linearly stratified ambients Amin Khodkar, Khaoula El Allam, Eckart Meiburg We extend the vorticity-based modeling approach for stratified flows to intrusions advancing into linear stratifications. Consistent with previous experimental and numerical observations, the vorticity model confirms the formation of equilibrium intrusions when the intrusion density equals the mean density of the ambient fluid, and non-equilibrium intrusions with upstream propagating internal gravity waves when this condition does not hold. We show that the two limits of bottom- and top-propagating gravity currents are non-smooth, so that the current model degenerates under these conditions. Predictions by the model agree closely with two-dimensional DNS simulations and earlier experimental results, specifically with regard to the propagation speed of near-equilibrium intrusions. In addition, the present vorticity model is able to capture the dynamics of internal gravity waves. Since the vorticity approach does not require any empirical energy-related assumptions, the energetics of the flow can be assessed \textit{a posteriori}. [Preview Abstract] |
Monday, November 20, 2017 11:14AM - 11:27AM |
G32.00004: Large-Eddy-Simulation of a flow over a submerged rigid canopy Alessandro Monti, Mohammad Omidyeganeh, Alfredo Pinelli We have performed a wall-resolved Large-Eddy-Simulation of flow over a shallow submerged rigid canopy ($H/h=4$; $H$ and $h$ are the open channel and the canopy heights respectively) in a transitional/dense regime (Nepf ARFM 44, 2011), at low Reynolds number ($Re_b=U_{bulk} H/\nu = 6000$). An immersed boundary method (Favier et al. JCP 261, 2013) has been adopted to represent filamentous rigid elements of the canopy. The presence of the permeable and porous canopy induces a typical inflection point in the mean velocity profile, depicting two separated and developed layers, outer boundary layer and in-canopy uniform flow. The aim of the work is to explore and unravel the mechanisms of the interaction between the fluid flow and the rigid canopy by identifying the physical parameters that govern the mixing mechanisms within the different flow layers and by exploring the impact of the sweep/ejection events at the canopy edge. The results show that the flow is characterised by large scale stream- and span-wise vortices and regions of different dynamics that affect also the filamentous layer, hence the mixing mechanisms. [Preview Abstract] |
Monday, November 20, 2017 11:27AM - 11:40AM |
G32.00005: Coalescence of Fluid-Driven Fractures Niall O'Keeffe, Zhong Zheng, Herbert Huppert, Paul Linden We present an experimental study on the coalescence of two in-plane fluid-driven penny-shaped fractures in a brittle elastic medium. Initially, two fluid-driven fractures propagate independently of each other in the same plane. Then when the radial extent of each fracture reaches a certain distance the fractures begin to interact and coalesce. This coalescence forms a bridge between the fractures and then, in an intermediate period following the contact of the two fractures, most growth is observed to focus along this bridge, perpendicular to the line connecting the injection sources. We analyse the growth and shape of this bridge at various stages after coalescence and the transitions between different stages of growth. We also investigate the influence of the injection rate, the distance between two injection points, the viscosity of the fluid and the Young's modulus of the elastic medium on the coalescence of the fractures. [Preview Abstract] |
Monday, November 20, 2017 11:40AM - 11:53AM |
G32.00006: Fluid-driven cracks and backflow in a multi-crack system Samuel Smiddy, Ching-Yao Lai, Howard Stone We design a~two-crack experiment~to study~the effects of natural fractures on hydraulic fractures. Instead of~a single layer elastic matrix, we~inject liquid into a~multi-layered elastic matrix.~A similar system has been used to study~geological processes such as dike-sill formations. ~In our experiments, pressurized fluid fractures the matrix and pressures are quantified based on laser imaging of particle displacement.~ First, we report the opening of the cracks and subsequently, the direction of the fluid reverses upon release of~injection~pressure, driven by the elastic relaxation of the gelatin.~The volume remaining in the gelatin matrix is measured as a function of time for different gelatin Young's moduli and fluid viscosities. We explain our results with scaling arguments. [Preview Abstract] |
Monday, November 20, 2017 11:53AM - 12:06PM |
G32.00007: Ionospheric Data Assimilation and Targeted Observation Strategies: Proof of Concept Analysis in a Geomagnetic Storm Event Eric Kostelich, Juan Durazo, Alex Mahalov The dynamics of the ionosphere involve complex interactions between the atmosphere, solar wind, cosmic radiation, and Earth's magnetic field. Geomagnetic storms arising from solar activity can perturb these dynamics sufficiently to disrupt radio and satellite communications. Efforts to predict ``space weather,'' including ionospheric dynamics, require the development of a data assimilation system that combines observing systems with appropriate forecast models. This talk will outline a proof-of-concept targeted observation strategy, consisting of the Local Ensemble Transform Kalman Filter, coupled with the Thermosphere Ionosphere Electrodynamics Global Circulation Model, to select optimal locations where additional observations can be made to improve short-term ionospheric forecasts. Initial results using data and forecasts from the geomagnetic storm of 26--27 September 2011 will be described. [Preview Abstract] |
Monday, November 20, 2017 12:06PM - 12:19PM |
G32.00008: Solute transport by flow yields geometric shocks in shape evolution Jinzi (Mac) Huang, Megan Davies Wykes, George Hajjar, Leif Ristroph, Michael Shelley Geological processes such as erosion and dissolution of surfaces often lead to striking shapes with strikingly sharp features. We present observations of such features forming in dissolution under gravity. In our experiment, a dissolving body with initially smooth surface evolves into an increasingly sharp needle shape. A mathematical model of its shape dynamics, derived from a boundary layer theory, predicts that a geometric shock forms at the tip of dissolved body, with the tip curvature becoming infinite in finite time. We further discuss the model's application to similar processes, such as flow driven erosion which can yield corners. [Preview Abstract] |
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