Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session LR: General Fluid Mechanics: Theory |
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Chair: Grae Worster, University of Cambridge Room: 203A |
Monday, November 24, 2008 3:35PM - 3:48PM |
LR.00001: Velocity fluctuations and energy amplification in laminar fluid flows Jose M. Ortiz de Zarate, Jan V. Sengers We present a systematic procedure for evaluating the intrinsic velocity fluctuations and the resulting intrinsic energy amplification that are always present in laminar fluid flows. For this purpose we formulate a stochastic Orr-Sommerfeld equation and a stochastic Squire equation by applying a fluctuation-dissipation theorem for the random part of the dissipative stresses. From the solution of the stochastic Orr- Sommerfeld and Squire equations the intrinsic energy amplification can be deduced. As an illustration of the procedure we present an explicit solution for the case of planar Couette flow. We first solve the fluctuating hydrodynamics equations in the bulk, obtaining an exact representation of the spatial spectrum of the velocity fluctuations valid for large wave numbers. The resulting energy amplification is proportional to $Re^{3/2}$. Next, we show how to a good approximation confinement can be incorporated by a simple Galerkin projection technique. The effect of the boundary conditions is to reduce the energy amplification to a logarithmic dependence on $Re$. We shall also indicate how an exact solution for the case of confined geometries can be obtained by an expansion into a set of hydrodynamic modes, conveniently expressed in terms of Airy functions. [Preview Abstract] |
Monday, November 24, 2008 3:48PM - 4:01PM |
LR.00002: ABSTRACT WITHDRAWN |
Monday, November 24, 2008 4:01PM - 4:14PM |
LR.00003: Nonlinear Model of Turbulent Dynamo and Assimilation of Sunspot Data Irina Kitiashvili, Alexander Kosovichev, Nick West, Thomas Bewley, Joe Cessna, Christopher Colburn We investigate a non-linear dynamical model to describe the cyclic behavior of magnetic fields on the Sun. The model is derived by applying a low-mode approximation to the mean-field turbulent dynamo theory and taking into account variations of magnetic helicity. We show that the model reproduces the observed behavior of the Sun's global magnetic field: the periodic polarity reversals, migration towards the equator, and the relationship between the growth rate and the strength of the 11-year sunspot cycles. In addition, the model has chaotic regimes, which may be important for understanding the long-term behavior of the solar cycles. Since the properties of the solar dynamo, such as turbulent diffusion and helicity, are unknown, we apply data assimilation methods for obtaining the best estimate of the true state of the system and also for predicting the next cycle. In particular, we used the Ensemble Kalman Filter and recent modifications, to assimilate the sunspot data available for 1755-2008 into the model. We compare the assimilation results and discuss the predictions of the next sunspot cycle. [Preview Abstract] |
Monday, November 24, 2008 4:14PM - 4:27PM |
LR.00004: Entrainment Phenomena in Potential Flow: Brachistochrones and Finite-Time Corrections to Darwin's Drift Volume Matthew Moore, Rich McLaughlin, Roberto Camassa, Ashwin Vaidya For a body moving uniformly in an ideal fluid there exists a region in which particles are swept in the same direction as the motion of the body, called the drift region, as well as a region in which particles are forced in the opposite direction as that of the body, called the reflux region. In Darwin's Theorem, the drift volume is defined as the volume swept out by particles originating on a plane perpendicular to the motion of the body, as the body moves from an infinite distance upstream of the plane to an infinite distance downstream of the plane. Here, we present finite-time corrections to Darwin's calculation of the drift volume for a sphere, which extend the previously obtained semi-infinite correction of Eames, Belcher, and Hunt (1994). Additionally, we solve the problem of finding the particle who minimizes its time of flight for uniform flow past a sphere. The path of this particle who minimizes flight time is termed the brachistochrone path, and a connection is drawn to the geometry of the reflux region. [Preview Abstract] |
Monday, November 24, 2008 4:27PM - 4:40PM |
LR.00005: Float height and quasi-steady spin-down of a rotating disk Patrick Weidman Numerical integrations of the self-similar equations for steady fluid motion between parallel infinite disks are reported for the case where the upper impermeable disk rotates and the lower stationary disk has uniform transpiration. The numerics are facilitated by a high-Reynolds number asymptotic analysis. The results are applied to model the float height of the steadily spinning disk under gravity when the disk separation is small. We find that the disk will touch down when it has sufficiently high angular rotation. Boundaries separating regimes of radial outflow from counter-flow and disk touch down are determined over a range of blowing Reynolds numbers $R$ and swirl parameters $S$. In certain regimes of parameter space and disk geometry the results provide a quasi-steady estimate for the spin-down dymamics of a disk in free rotation over an air- bearing table. Experiments are under way to test the validity of this quasi-steady approximation. [Preview Abstract] |
Monday, November 24, 2008 4:40PM - 4:53PM |
LR.00006: Flow between concentric cylinders driven by an electromagnetic force Jose Nunez, Eduardo Ramos, Sergio Cuevas, Sergey Smolentsev We study a two-dimensional magnetohydrodynamic (MHD) laminar flow of a viscous electrically conducting fluid between concentric cylinders. The flow is produced by an electromagnetic force due to the interaction of a uniform axial magnetic field and a radial electrical current. We analyzed two situations, namely, when the electric current is produced by a steady potential difference between the walls of the cylinders and when the potential difference oscillates in time. The magnetic field induced by the fluid motion is assumed to be negligible compared to the applied magnetic field. In both cases, the flow is described in terms of closed analytical expressions. A parametric study covering a range of Hartmann numbers is conducted and it is found that for a given a electrical potential difference, the fluid velocity as a function of the Hartmann number has a local maximum. [Preview Abstract] |
Monday, November 24, 2008 4:53PM - 5:06PM |
LR.00007: The Hamiltonian description of incompressible fluid ellipsoids P.J. Morrison, N.R. Lebovitz, J.A. Biello We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler's equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie-Poisson form. [Preview Abstract] |
Monday, November 24, 2008 5:06PM - 5:19PM |
LR.00008: Taylor dispersion and the optimization of residential geothermal heating systems Jessica Townsend, Alexandra Ortan, Vincent Quenneville-Belair, B.S. Tilley Residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. These systems consist of tubing (2 cm radius, 1 km in length) buried below the ground surface through which a coolant flows. Tube length has a direct correlation to installation cost. The temperature of this fluid rises as it flows through the tubing, and the energy from this temperature difference is utilized to heat the residence. As a first model, we consider a single tube of fluid encased in an infinite medium of soil, with the goal to find the minimum length over which temperature variations occur. Through lubrication theory, we derive an evolution equation for the local soil temperature near the tubing. We find that Taylor dispersion of heat in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. Next, matched asymptotics is used to incorporate far-field temperature variations. Comparison of our model with experiment is presented. [Preview Abstract] |
Monday, November 24, 2008 5:19PM - 5:32PM |
LR.00009: Theoretical Analysis of the Two-Scale Direct-Interaction Approximation for the Turbulent Passive-Scalar Field Including Molecular Viscosity and Diffusion Effects Masayoshi Okamoto A fluctuating field of a passive scalar in turbulent flow is theoretically investigated by means of a two-scale direct-interaction approximation theory including the effects of a molecular viscosity and diffusion. Solving the fluctuating field in a perturbational manner, we get the energy and scalar intensity spectra and the eddy-viscosity representation for the Reynolds stress and scalar flux in the case that the Prandtl number is around 1. The derived spectrum of the passive scalar intensity is the Obukhov-Corrsin spectrum in the inertial subrange and is proportional to the -3 power law in the dissipation subrange. Applying the Pade approximation to the obtained spectrum expressions, the present spectra are consistent with the Pao's empirical ones. The new eddy-viscosity representations for the Reynolds stress and scalar flux include the molecular viscosity and diffusion effects through the turburent Reynolds number and Prandtl one. [Preview Abstract] |
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