Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L10: General Fluid Dynamics I |
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Chair: Jean Hertzberg, University of Colorado Room: 313 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L10.00001: ABSTRACT WITHDRAWN |
Monday, November 21, 2011 3:48PM - 4:01PM |
L10.00002: The origin of the self-organization of the 2D Euler fluid flows Florin Spineanu, Madalina Vlad The 2D ideal incompressible fluid is usually described in terms of streamfunction, velocity and vorticity. An equivalent model consists of a discrete set of point-like vortices interacting in plane by a long-range potential. The essential property of the latter model is that it re-formulates the description in terms of matter, field and interaction. We first extend the model to reflect the parity-invariance and show that returning to continuum it leads to a field-theoretical formulation, with a Lagrangian density for a nonlinear scalar (matter) field, a gauge field and their minimal interaction. A fundamental property of the 2D Euler fluid is revealed in this way: the extremum of the action functional shows Self-Duality, a property known to generate coherent structures (almost all known solitons and instantons in the natural systems). We derive analytically the sinh-Poisson equation, governing the stationary states at relaxation.The presence of the Chern- Simons part in the Lagrangian explains why in 3D the fluid will never relax to a stationary coherent flow. Connections with 4D fermion systems (Nambu-Jona-Lasinio) and with surfaces of constant mean curvature (CMC) will be presented. Stability of certain regular flows results from the property of non-self- intersection of CMC surfaces embedded in 3D space. [Preview Abstract] |
Monday, November 21, 2011 4:01PM - 4:14PM |
L10.00003: On Liouville's theorem in fluid mechanics P.J. Morrison, F. Bouchet, S. Thalabard, O.V. Zaboronski Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g.\ Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L10.00004: A ``reciprocal'' theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number Jacques Magnaudet We derive a theorem paralleling Lorentz's reciprocal theorem and providing general expressions for the force and torque acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible flow at arbitrary Reynolds number. This theorem follows the approach initiated by Quartapelle and Napolitano (1983) by making use of auxiliary solenoidal irrotational velocity fields. It allows any component of the force and torque to be evaluated solely in terms of velocity and vorticity, irrespective of its orientation with respect to the relative velocity between the body and fluid. When the body moves in a time-dependent linear flow, this theorem reveals the various couplings between the body translation and rotation and the strain rate and vorticity of the carrying flow. We show that the predictions obtained with this approach encompass all those previously obtained in the inviscid limit. We also show how it can be used to evaluate explicitly the drag and lift components of the force acting on high-Reynolds-number bubbles moving in inhomogeneous flows. [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L10.00005: Spatiotemporal cascades of the Poiseuille-Hagen flow in invariant elliptic structures Victor Miroshnikov Spatiotemporal cascades of the transitional Poiseuille-Hagen flow are considered in elliptic structures, which are invariant with respect to differential and nonlinear algebraic operations. Differentiation and algebra of the invariant structures and decomposition of smooth velocity profiles in the invariant structures are treated both theoretically and symbolically. Reduction of the invariant elliptic structures to invariant trigonometric structures and invariant hyperbolic structures is also considered. By using the invariant structures, the displayed and hidden perturbations of the basic Poiseuille-Hagen flow are represented as dual perturbations, while the series solution for the perturbed flow converges uniformly. The cascade solution for the Poiseuille-Hagen flow is constructed in a multiscale form, which explicitly shows the effect of various factors at multiple scales. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L10.00006: An Exact Solution of the 3D Navier-Stokes Equation Amador Muriel We use a time evolution equation for the single particle distribution function (Muriel, Physica D, 1997) to generate the time evolution of the velocity fields. These velocity fields are then substituted into the Navier-Stokes equation to calculate the pressure gradients. The pressure gradients are then integrated over space to generate pressure tensors. In addition, we calculate the energy fields, showing that there is no blow up. The pressure tensors, and the velocity fields constitute an exact solution to the 3D Navier-Stokes equation for a compressible fluid (Muriel, Results in Physics, 2011). All calculated fields are smooth, producing no turbulence by any generous definition of turbulence. We raise the question: is the Navier-Stokes equation the correct problem definition for turbulence? (Muriel, The Quantum Nature of Turbulence, Nova Science Publishers, New York (2010). We will display the plots of the solution in a 3D toroid configuration. The solution found may be used to reformulate fluid dynamics using an initial value formulation. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L10.00007: Adaptive Control of the Forced Generalized Korteweg-de Vries-Burgers Equation Nejib Smaoui, Alaa El-Kadri, Mohamed Zribi The adaptive control problem of the forced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is $[0,1]$ is considered. Three different adaptive control laws are designed for the forced GKdVB equation. The $L^2$-global exponential stability of the solutions of these equations is shown for each of the proposed control laws by using the Lyapunov theory. Numerical simulations based on the Finite Element method (FEM) are presented to validate the analytical developments. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L10.00008: Phase space dynamical density functional theory for colloids with hydrodynamic interactions Benjamin Goddard, Andreas Nold, Petr Yatsyshin, Nikos Savva, Greg Pavliotis, Serafim Kalliadasis We study the dynamics of a colloidal fluid in the full position- momentum phase space. These dynamics are modelled by stochastic equations of motion for a large number of identical spherical particles. We include the full hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For large systems, the number of degrees of freedom prohibits a direct solution of the equations and a reduced model is necessary. Under certain assumptions, we derive a dynamical density functional theory (DDFT), i.e. a reduction to the dynamics of the reduced one-body distribution. Our formulation includes the case where the momentum distribution is not a local Maxwellian. Near equilibrium, it reduces to a Navier-Stokes-like equation with additional non-local terms. In the high friction limit, we show rigorously that it reduces to a previously-derived DDFT, describing only the position distribution, but with a novel definition of the diffusion tensor. [Preview Abstract] |
Monday, November 21, 2011 5:19PM - 5:32PM |
L10.00009: Attitudes Towards Fluids: the Impact of Flow Visualization Jean Hertzberg Since 2003, a course on flow visualization has been offered to mixed teams of engineering and fine arts photography students at the University of Colorado. A survey instrument has been developed that explores student perceptions of and attitude towards fluid physics. It has been administered to students in the flow visualization course, in a traditional junior level fluid mechanics course, and in a course on design. Survey results indicate that the students in the flow visualization course, after a semester of making images for art's sake, emerge believing that fluid mechanics is more important to themselves as engineers and to society than the students in the traditional course which is packed with real-life engineering examples . The use of photography in improving student perceptions is being extended to a course on perception of design; preliminary results from a survey on attitudes towards design will be presented. Examples of student images from both courses will be presented as well. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L10.00010: Applying the results of education research to help students learn more Rachel E. Pepper, Stephanie Chasteen, Michael Dubson, Katherine Perkins, Steven Pollock Over the past 5 years, the physics faculty at the University of Colorado have worked to transform three core courses in our upper-division undergraduate physics curriculum: Classical Mechanics/Math Methods, Electricity and Magnetism and Quantum Mechanics. We discuss our transformations as a potential model for transformation of other upper-division courses, such as fluid mechanics. The goal of our transformations was to improve student learning and to develop materials and approaches that other faculty could adopt or adapt. This work began with faculty in the department meeting regularly to define explicit course learning goals, which then served as a foundation for the subsequent course transformations. The development of the curriculum was also guided by the results of observations, interviews, and analysis of student work. We applied the principles of active engagement and learning theory to transform many elements of the course. Reforms included ``clicker'' questions, tutorials, modified homeworks, and more. In this talk, we will outline the process, the reforms, and present evidence of the effectiveness of these reforms relative to traditional courses. Some research-based fluid mechanics instructional materials will also be discussed. Our curriculum materials are available at http://www.colorado.edu/sei/departments/physics.htm. [Preview Abstract] |
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