Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R30: General Fluids IV |
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Chair: Roberto Camassa, University of North Carolina Room: 33A |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R30.00001: Are the wake angles of a duck and a ship really the same? Marc Rabaud, Frederic Moisy The wake of a disturbance moving at the water surface, like a ship or a duck, owes its shape to the dispersive property of surface gravity waves. According to Kelvin's theory, it is widely accepted, and sometimes observed, that the wake angle is independent of the disturbance velocity, and given by $\sin^{-1}(1/3) = 19.4$ degrees. However, field observations often show much smaller angles for fast ships, down to 5 - 10 degrees. The angle of these narrow wakes is actually found to decrease as the inverse of the disturbance velocity, similarly to the Mach cone of a supersonic disturbance in a non-dispersive medium. We propose here a simple model for this transition from a Kelvin regime (at low Froude number) to a Mach regime (at large Froude number) --- where the Froude number is based on the disturbance length. This model is confirmed by numerical simulations, reproducing the variety of wake patterns observed for disturbances of various size and velocity. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R30.00002: At the end of a moving string James Hanna, Christian Santangelo We address a basic problem in the dynamics of flexible bodies: the propagation of a shape along a string and its reflection at a free boundary. Although the string equations-- inertia balancing stress in an inextensible curve-- are quite old, the only exact solutions known for non-trivial geometries are traveling waves with spatially uniform stress. Suitable for closed ``lariats,'' these solutions are incompatible with a free end, where the stress must vanish. It is impossible to drag an open, flexible, curved string along its tangents. This is reflected in the unwrapping motion of a string or chain as it is pulled around an object, and has strong implications for slender structures in passive locomotion, whether industrial cables or the ribbons of rhythmic gymnastics. We consider planar dynamics restricted to time-independent, but spatially varying, stress. We find a new exact solution at a distance $\propto t^{\frac{4}{3}}$ from the free end; continuation to the end requires introduction of a secular error into the positions and velocities and a singularity in acceleration $\propto t^{-\frac{2}{3}}$ at the end, which appears to have a physical basis. This work is an early step towards understanding the dynamics of a wide class of industrial and natural thin-object systems. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R30.00003: Flow-induced oscillations of non-uniform pipes conveying fluid Gary Han Chang, Yahya Modarres-Sadeghi We study the influence of non-uniformity in the pipe cross-section and flow velocity on the oscillations of a pipe conveying fluid. A plain pipe conveying fluid~loses its stability by buckling or flutter, depending on the pipe's boundary condition and the system parameters. A uniform plain cantilevered pipe loses its stability by a Hopf bifurcation, leading to either planar or non-planar flutter for flow velocities beyond the critical flow velocity. By attaching a spring or an extra mass at the tip of the pipe, secondary instabilities are observed leading to quasiperiodic and chaotic oscillations. In this study, Hamilton's principle is used to derive nonlinear equations of motion for a pipe with non-uniform system properties along its length. The pipe cross-section and material properties as well as its flow velocity can vary along the length. The resulting equations are then solved using the Galerkin technique. The model can be used to study a tapered pipe or a pipe with a sudden change in geometry and also the effect of local stiffening, narrowing, and pressure drop. The effect of continuous external damping can also be considered. It is shown that these non-uniformities can have significant impact on the observed instabilities. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R30.00004: Unsteady flow near front and rear stagnation points Dmitry Kolomenskiy, Keith Moffatt, Marie Farge, Kai Schneider We consider unsteady flows near stagnation points on a cylindrical body immersed in a viscous incompressible fluid. This problem admits similarity solutions, assuming a hyperbolic time evolution of the free-stream velocity. These are exact solutions of the Navier--Stokes equations, having a boundary-layer character similar to that of classical steady forward stagnation-point flow. The velocity profiles are obtained by numerical integration of a non-linear ordinary differential equation. A wide range of possible behaviour is revealed, depending on whether the flow in the far field is accelerating or decelerating, and depending on the flow direction. For the forward-flow situation, the solution is unique for the accelerating case, but bifurcates for modest deceleration, while for sufficient rapid deceleration there exists a one-parameter family of solutions. For the rear-flow situation, a unique solution exists (remarkably!) for sufficiently strong acceleration, and a one-parameter family again exists for sufficient strong deceleration. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R30.00005: General Multi-Species Dynamical Density Functional Theory Benjamin Goddard, Andreas Nold, Nikos Savva, Grigorios A. Pavliotis, Serafim Kalliadasis We extend our recent study on the dynamics of single-species colloidal fluids in the full position-momentum phase space to the dynamics of multi-species colloidal fluids. We include both inertia and the full hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For many-particle systems, the number of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. Under minimal assumptions, we derive a dynamical density functional theory (DDFT), i.e. a reduction to the dynamics of the reduced one-body distribution. Via computations based on spectral methods extended to integral operators, we demonstrate the excellent agreement between this DDFT and the full Langevin equations for a range of multi-species systems. In suitable limits we recover existing DDFTs (which neglect inertia and/or hydrodynamic interactions) and we investigate the resulting corrections to these DDFTs. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R30.00006: Controlling the Dynamics of the 2-D Navier-Stokes Equations Nejib Smaoui, Mohamed Zribi The dynamics of the two-dimensional (2-d) Navier-Stokes (N-S) equations with spatially periodic and temporally steady forcing $f=(\frac{1}{Re} k^3 \sin ky, 0)$ is analyzed. First, a system of nine-dimensional nonlinear dynamical system is obtained by a truncation of the 2-d N-S equations for various values of $k$. We show that for $k=4$, the dynamics transforms from periodic solutions to chaotic attractors through a sequence of bifurcations including a period doubling scenarios. Then, a state feedback control is designed to drive the state of the system to any desired state. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R30.00007: A New Approach to Model Order Reduction of the Navier-Stokes Equations Maciej Balajewicz, Earl Dowell, Bernd Noack A new approach to model order reduction of the Navier-Stokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R30.00008: Single series skewness representation for passive scalar advection in laminar pipe and channel flow Roberto Camassa, Francesca Bernardi, Richard McLaughlin, Keith Mertens In this talk, we present an exact single series representation for scalar skewness time evolution. Prior studies have naturally derived multiple nested Fourier series solutions which suffer from slow convergence and cloud physical interpretation. Judicious change of variables and complex residue theory lead to single series representation formulae for the moments along streamwise slices from which quantities such as variance and skewness can be reconstructed. Small and long time asymptotics will be discussed for the first three moments in both channel and pipe geometries in steady Poiseuille flows. Comparisons of theory with Monte Carlo simulations and preliminary experiments exhibit differences between channel and pipe flows in the skewness evolution. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R30.00009: Friction drag reduction by air cavities Oleksandr Zverkhovskyi, Ren\'e Delfos, Tom van Terwisga, Jerry Westerweel Air lubrication is investigated, as it is potentially one of the most efficient frictional drag reduction technologies for ships. Unlike bubbles in the boundary layer, which are explained to be effective while reducing the density of the liquid, artificial air cavities underneath a ship may reduce the amount of wetted surface, which presumable reduces more drag than the extra drag created by the devices required to create the cavities. The efficiency of such cavities has been studied experimentally on laboratory scale in a medium-speed water tunnel containing an optically accessible test section, equipped with a PIV system and cameras to obtain boundary layer- and cavity characteristics, and a force balance to measure the drag. The results of this study confirm that the drag reduction is proportional to the amount of non-wetted area. Based on experimental observations, a design criterion is presented for obtaining stable cavities with a low rate of air consumption. Furthermore, the experiments give insight into the formation and stability of air cavities, including the interaction between a series of cavities along the streamwise direction. [Preview Abstract] |
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