Browsing by Subject "fluid"

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Analysis of the Cleburne, Texas, Earthquake Sequence from June 2009 to June 2010
(2013-12) Justinic, Ashley Howe; Stump, Brian; Hayward, Chris; Frohlich, Cliff; Frohlich, Cliff
On 9 June 2009, an M-bLg 2.8 earthquake shook Cleburne, Texas, a community not known to have previously experienced earthquakes. Over 50 small earthquakes followed by the end of December 2009. A temporary network of four and then five IRIS-Passcal broadband systems was deployed from June 2009 to June 2010, recording data that were used to locate 38 events with the most confident P- and S-arrival picks. Event locations were distributed along a 2 km long north-northeast trend. The location centroid was at 32.298 degrees N, 97.372 degrees W and at 3.6 km depth. This location is approximately 1.3 km from a saltwater disposal well that began injection in October 2007 and 3.2 km away from a second injection well that was active from September 2005 to late July 2009. Focal mechanisms estimated for the best-recorded events suggest a north-northeast-south-southwest-trending normal fault with a dip of similar to 50 degrees and a component of oblique motion (rake of similar to-80 degrees). This average solution is generally consistent with the north-northeast-trending extensional faults that are prevalent across parts of Texas, Oklahoma, Louisiana, and Arkansas. Stress drops calculated from P and S spectra for seven different events ranged from 3.9 to 90 bars, with most estimates between 40 and 50 bars, typical values for intraplate earthquakes. Because there were no known previous earthquakes, and the located events were close to the two injection wells and near the injection depth, the possibility exists that earthquakes may be related to fluid injection.
Dynamics of free surface perturbations along an annular viscous film
(2008-03) Smolka, Linda B.; North, Justin; Guerra, Bree K.; Guerra, Bree K.
It is known that the free surface of an axisymmetric viscous film flowing down the outside of a thin vertical fiber under the influence of gravity becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions, and viscosities to investigate the growth and dynamics of these interfacial perturbations and to test the assumptions made by previous authors. We find that the initial perturbation growth is exponential, followed by a slower phase as the amplitude and wavelength saturate in size. Measurements of the perturbation growth for experiments conducted at low and moderate Reynolds numbers are compared to theoretical predictions developed from linear stability theory. Excellent agreement is found between predictions from a long-wave Stokes flow model [Craster and Matar, J. Fluid Mech. 553, 85 (2006)] and data, while fair to excellent agreement (depending on fiber size ) is found between predictions from a moderate-Reynolds-number model [Sisoev et al., Chem. Eng. Sci. 61, 7279 (2006)] and data. Furthermore, we find that a known transition in the longer-time perturbation dynamics from unsteady to steady behavior at a critical flow rate Q(c) is correlated with a transition in the rate at which perturbations naturally form along the fiber. For Q < Q(c) (steady case), the rate of perturbation formation is constant. As a result, the position along the fiber where perturbations form is nearly fixed, and the spacing between consecutive perturbations remains constant as they travel 2 m down the fiber. For Q > Q(c) (unsteady case), the rate of perturbation formation is modulated. As a result, the position along the fiber where perturbations form oscillates irregularly, and the initial speed and spacing between perturbations varies, resulting in the coalescence of neighboring perturbations further down the fiber.
Harmonic moment dynamics in Laplacian growth
(2010-01) Leshchiner, Alexander; Thrasher, Matthew; Mineev-Weinstein, Mark B.; Swinney, Harry L.; Leshchiner, Alexander; Thrasher, Matthew; Swinney, Harry L.
Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem [S. Richardson, J. Fluid Mech. 56, 609 (1972)], so that all moments except the lowest one (the area of the bubble) are conserved in time. In our experiments, we directly determine the harmonic moments and show that for nonzero surface tension, all moments (except the lowest one) decay in time rather than exhibiting the divergences of other representations. Further, we derive an expression that relates the derivative of the k(th) harmonic moment M(k) to measurable quantities (surface tension, viscosity, the distance between the plates, and a line integral over the contour encompassing the growing bubble). The laboratory observations are in good accord with the expression we derive for dM(k)/dt, which is proportional to the surface tension; thus in the zero surface tension limit, the moments (above k=0) are all conserved, in accord with Richardson's theory. In addition, from the measurements of the time evolution of the harmonic moments we obtain a value for the surface tension that is within 20% of the accepted value. In conclusion, our analysis and laboratory observations demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust.
On Hamiltonian And Action Principle Formulations Of Plasma Dynamics
(2009-11) Morrison, P. J.; Morrison, P.J.
A general discussion of Hamiltonian and action principle formulations for fluid and plasma models is given. A procedure, based on Hamilton's principle of mechanics but adapted for continua, for the construction of action principles for fluid and kinetic models is given. The transformation from action principles in terms of the Lagrangian variable description to the Eulerian variable description in terms of noncanonical Poisson brackets is described. Two examples are developed: ideal MHD and Braginskii's fluid model with gyroviscosity.
Riemann Ellipsoids: Hamiltonian Formulation and Stability Analysis
(2015) Benavides, Santiago José; Morrison, Philip J.; Gamba, Irene M.
The equilibria and stability of self-gravitating liquid masses has been studied and debated for more than a century by great physicists and mathematicians such as Newton, Maclaurin, Jacobi, Poincaré, Dirichlet, Riemann, and Chandrasekhar, and is still drawing interest from researchers today. Here I present an original approach to formulating the problem in the context of Hamiltonian theory, namely by applying moments of the position and velocity to the constrained Poisson bracket for a fluid. I then study the stability of a certain family of equilibrium ellipsoids with internal flow that depends linearly on the spatial coordinates (Riemann ellipsoids) using this constrained Hamiltonian formulation of the problem. This formulation allows us to use robust stability analysis methods, as well as study the dynamics in a straightforward way. The spectral stability results agree qualitatively with that of Chandrasekhar's, but the parameter value is slightly off, and the nonlinear stability analysis results do not give a definite answer due to the nature of the bifurcation (steady-state). It is still possible to use the Rayleigh-Ritz method to determine whether our system is nonlinearly unstable, but due to time constraints this was not done.