Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session G9: General Fluid Dynamics: Theory |
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Chair: James Hanna, Virginia Polytechnic Institute and State University Room: B117 |
Monday, November 21, 2016 8:00AM - 8:13AM |
G9.00001: Bending and stretching of two-dimensional fluids and solids James Hanna Soap films, lipid membranes, and elastic sheets are often analyzed with similar (idealized) models that emphasize the geometric features of these surfaces. If deformations of these surfaces are area-preserving, simple and elegant expressions may be used to describe surface and bending energies and the corresponding equations of equilibrium. However, in general, one should make a distinction between geometric energies, as measured per unit area, and elastic energies, as measured per unit mass. I will discuss some of the differences between these types of energies, and the resulting potential difficulties and inelegancies in their mathematical descriptions. [Preview Abstract] |
Monday, November 21, 2016 8:13AM - 8:26AM |
G9.00002: Peeling, sliding, pulling and bending John Lister, Gunnar Peng The peeling of an elastic sheet away from thin layer of viscous fluid is a simply-stated and generic problem, that involves complex interactions between the flow and elastic deformation on a range of length scales. Consider an analogue of capillary spreading, where a blister of injected viscous fluid spreads due to tension in the overlying elastic sheet. Here the tension is coupled to the deformation of the sheet, and thus varies in time and space. A key question is whether or not viscous shear stresses ahead of the blister are sufficient to prevent the sheet sliding inwards and relieving the tension. Our asymptotic analysis reveals a dichotomy between fast and slow spreading, and between two-dimensional and axisymmetric spreading. In combination with bending stresses and gravity, which may dominate parts of the flow but not others, there is a plethora of dynamical regimes. [Preview Abstract] |
Monday, November 21, 2016 8:26AM - 8:39AM |
G9.00003: Fluid-driven fracturing of adhered elastica: evolution of the vapour tip Thomasina V. Ball, Jerome A. Neufeld The transient spreading of a viscous fluid beneath an elastic sheet is controlled by the dynamics at the tip. The large negative pressures needed to drive the viscous fluid into the narrowing gap necessitates a vapour tip separating the fluid front and the crack tip. Adhesion of the elastic sheet imposes a curvature at the tip giving rise to an elasto-capillary length scale and the possibility of a balance between elastic deformation and the strength of adhesion. Two dynamical regimes are therefore possible; viscosity dominant spreading controlled by the pressure in the vapour tip and adhesion dominant spreading controlled by interfacial adhesion. A series of constant flux experiments using clear PDMS elastic sheets allow for direct measurement of the vapour tip in the bending (thick sheet) limit. For small fluid fluxes, the experimental results can be explained by a constant interior pressure and a viscous boundary layer near the fluid front and result in an asymptotic model for the advance of adhesion and viscosity dominated fracture fronts resolving the vapour tip. Understanding the fluid-driven fracturing of adhered elastica provides insight into the spreading of shallow magmatic intrusions in the Earth's crust, and the fluid-driven fracturing of elastic media more generally. [Preview Abstract] |
Monday, November 21, 2016 8:39AM - 8:52AM |
G9.00004: Finite time singularities in the quasigeostrophic model richard scott A finite-time singularity in the evolution of a patch of surface temperature in the quasi-geostrophic equations via two distinct evolution routes is investigated with a grid-free, adaptive numerical scheme. In one case, the singularity proceeds through the formation of a corner, developing infinite curvature in the patch boundary in finite time. The corner is self-similar and the growth of curvature appears to be independent of initial patch shape. In the other case, the singularity proceeds through a self-similar cascade of filament instabilities with geometrically shrinking spatial and temporal scales, and the filament width approaches zero in a finite time. The spatially and temporally adaptive numerical scheme permits the accurate simulation of both corner and cascade singularities over a range of spatial scales spanning ten orders of magnitude. Some aspects of both singularity types exhibit universality, being independent of the initial patch shape and large-scale evolution; however, a simple extension of the initial temperature structure provides evidence that only the instability cascade persists in the case of a continuous initial temperature distribution. [Preview Abstract] |
Monday, November 21, 2016 8:52AM - 9:05AM |
G9.00005: The Lorentz gas in Kaluza's MHD: Transport equations Alfredo Sandoval-Villalbazo, Alma Rocio Sagaceta-Mejia, Jose Humberto Mondragon-Suarez Relativistic kinetic theory is applied to the study of the transport processes present in a Lorentz gas, using a geometric five-dimensional space-time. While the conventional transport equations are recovered in the Newtonian limit, it is shown that relativistic corrections to the conduction and diffusion fluxes arise within this formalism. A brief review of the conceptual advantages of the Kaluza-type approach to magnetohydrodynamics is also given. [Preview Abstract] |
Monday, November 21, 2016 9:05AM - 9:18AM |
G9.00006: Density Stoke's Law for Particles having the Density Lower than the Surrounding Medium Arjun Krishnappa It has been observed from our experiments that Stoke's Law can be used only when the particle density is greater than the surrounding medium. When a microbubble is horizontally steered in a liquid, then the Stoke's Law can't be used to calculate the velocity or drag force. The reason underlying is that the density of the microbubble is lower than the density of the liquid. To overcome the problem, a modified Stoke's Law called ``Density Stoke's Law (DSL)'' is proposed. DSL works not only for the particles having the density lower than the surrounding medium, but also for the particles having the density greater than the surrounding medium. Therefore DSL can be considered as a general Stoke's Law. [Preview Abstract] |
Monday, November 21, 2016 9:18AM - 9:31AM |
G9.00007: Investigation of Dalton and Amagat’s laws for gas mixtures with shock propagation Patrick Wayne, Ignacio Trueba Monje, Jason H. Yoo, C. Randall Truman, Peter Vorobieff Two common models describing gas mixtures are Dalton’s Law and Amagat’s Law (also known as the laws of partial pressures and partial volumes, respectively). Our work is focused on determining the suitability of these models to prediction of effects of shock propagation through gas mixtures. Experiments are conducted at the Shock Tube Facility at the University of New Mexico (UNM). To validate experimental data, possible sources of uncertainty associated with experimental setup are identified and analyzed. The gaseous mixture of interest consists of a prescribed combination of disparate gases -- helium and sulfur hexafluoride (SF$_6$). The equations of state (EOS) considered are the ideal gas EOS for helium, and a virial EOS for SF$_6$.The values for the properties provided by these EOS are then used used to model shock propagation through the mixture in accordance with Dalton's and Amagat's laws. Results of the modeling are compared with experiment to determine which law produces better agreement for the mixture. [Preview Abstract] |
Monday, November 21, 2016 9:31AM - 9:44AM |
G9.00008: Center of mass velocity during diffusion: Comparisons of fluid and kinetic models Erik Vold, Lin Yin, William Taitano, Kim Molvig, B. J. Albright We examine the diffusion process between two ideal gases mixing across an initial discontinuity by comparing fluid and kinetic model results and find several similarities between ideal gases and plasma transport. Binary diffusion requires a net zero species mass flux in the Lagrange frame to assure momentum conservation in collisions. Diffusion between ideal gases is often assumed to be isobaric and isothermal which requires constant molar density. We show this condition exists only in the lab frame at late times (many collision times) after a pressure transient relaxes. The sum of molar flux across an initial discontinuity is non-zero for species of differing atomic masses resulting in a pressure perturbation. The results show three phases of mixing: a pressure discontinuity forms across the initial interface (times of a few collisions), pressure perturbations propagate away from the mix region (time scales of an acoustic transit) and at late times characteristic of the diffusion process, the pressure relaxes leaving a non-zero center of mass flow velocity. The center of mass velocity associated with the outward propagating pressure waves is required to conserve momentum in the rest frame. Implications are considered in multi-species diffusion numerics and in applications. [Preview Abstract] |
Monday, November 21, 2016 9:44AM - 9:57AM |
G9.00009: Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots Laurence Keefe Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation $U(x,y,z+\Delta z)=e^{i k_0 (-1 + \sqrt{1+\tilde{Z}}\;\,)}\, U(x,y,z)$ for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator,$\tilde{Z}=\nabla_T^2+(n^2-1)$, involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques(on the assumption $\tilde{Z} \ll 1$) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts. [Preview Abstract] |
Monday, November 21, 2016 9:57AM - 10:10AM |
G9.00010: A Second Order Continuum Theory of Fluids -- Beyond the Navier-Stokes Equations Samuel Paolucci The Navier-Stokes equations have proved very valuable in modeling fluid flows over the last two centuries. However, there are some cases where it has been demonstrated that they do not provide accurate results. In such cases, very large variations in velocity and/or thermal fields occur in the flows. It is recalled that the Navier-Stokes equations result from linear approximations of constitutive quantities. Using continuum mechanics principles, we derive a second order constitutive theory that application of which should provide more accurate results is such cases. One important case is the structure of gas-dynamic shock waves. It has been demonstrated experimentally that the Navier-Stokes formulation yields incorrect shock profiles even at moderate Mach numbers. Current continuum theories, and indeed most statistical mechanics theories, that have been advanced to reconcile such discrepancies have not been fully successful. Thus, application of the second order theory based solely on a continuum formulation provides an excellent test problem. Results of the second-order equations applied to the shock structure are obtained for monatomic and diatomic gases over a large range of Mach numbers and are compared to experimental results. [Preview Abstract] |
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