Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series

Blending HF Radar and Model Velocities in Monterey Bay Through Normal Mode Analysis

Nowcasts of the surface velocity field in Monterey Bay are made for the period August 1-9, 1994, using HF radar observations blended with results from a primitive equation model. A spectral method called normal mode analysis was used. Objective spatial and temporal filtering were performed, and stream function, velocity potential, relative vorticity, and horizontal divergence were calculated over the domain. This type of nowcasting permits global spectral analysis of mode amplitudes, calculation of enstrophy, and additional analyses using tools like empirical orthogonal functions. The nowcasts reported here include open boundary flow information from the numerical model. Nowcasts using no open boundary flow information, however, still provide excellent results for locations within the observation footprint. This method, then, is useful for filtering high-resolution data like HF radar observations, even when open boundary flow information is unavailable. Also, since the nowcast velocity gradient fields were much less noisy than the observations, this may be an effective method for preconditioning high-resolution observation sets for assimilation into a numerical model. Copyright 2000 by the American Geophysical Union

Rubber friction on wet and dry road surfaces: the sealing effect

Rubber friction on wet rough substrates at low velocities is typically 20-30% smaller than for the corresponding dry surfaces. We show that this cannot be due to hydrodynamics and propose a novel explanation based on a sealing effect exerted by rubber on substrate "pools" filled with water. Water effectively smoothens the substrate, reducing the major friction contribution due to induced viscoelastic deformations of the rubber by surface asperities. The theory is illustrated with applications related to tire-road friction.Comment: Format Revtex 4; 8 pages, 11 figures (no color); Published on Phys. Rev. B (http://link.aps.org/abstract/PRB/v71/e035428); previous work on the same topic: cond-mat/041204

Rubber friction on (apparently) smooth lubricated surfaces

We study rubber sliding friction on hard lubricated surfaces. We show that even if the hard surface appears smooth to the naked eye, it may exhibit short wavelength roughness, which may give the dominant contribution to rubber friction. That is, the observed sliding friction is mainly due to the viscoelastic deformations of the rubber by the substrate surface asperities. The presented results are of great importance for rubber sealing and other rubber applications involving (apparently) smooth surfaces.Comment: 7 pages, 15 figure

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory

The vacuum effective potential of three-dimensional SU(2) lattice gauge theory in an applied color-magnetic field is computed over a wide range of field strengths. The background field is induced by an external current, as in continuum field theory. Scaling and finite volume effects are analyzed systematically. The first evidence from lattice simulations is obtained of the existence of a nontrivial minimum in the effective potential. This supports a ``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the basis of a one-loop calculation in (3+1)-dimensional QCD.Comment: 9pp (REVTEX manuscript). Postscript figures appende

Reconstructing Basin-Scale Eulerian Velocity Fields From Simulated Drifter Data

A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km x 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deployed in the 1000 km x 1400 km energetic western region. The base reconstruction error, achieved with full observation of the velocity field, ranges from 5% (with 191 basis functions) to 30% (with 65 basis functions). Specific analysis of the relation between spatial coverage and reconstruction error is presented using 180 drifters deployed in 100 different initial configurations that maximize coverage extremes. The simulated drifter data is projected on 107 basis functions for a 50-day period. The base reconstruction error of 15% is achieved when drifters occupy approximately 110 (out of 285) 70-km cells in the western region. Reconstructions from simulated mooring data located at the initial positions of representative good and poor coverage drifter deployments show the effect drifter dispersion has on data voids. The authors conclude that with appropriate coverage, drifter data could provide accurate basin-scale reconstruction of Eulerian velocity fields

Synoptic Lagrangian maps: Application to surface transport in Monterey Bay

Here we report on an effort to describe in detail the evolution of surface water particles in Monterey Bay from the time they first enter until the time they leave. The data used for this study are objective mappings from hourly surface currents obtained from high frequency (HF) radar measurements in Monterey Bay for the period 2 June through 4 August 1999. The basic concept is simple: compute the origin and fate of a large number of particles for every hour during the analysis period. However, analyzing and displaying the enormous amount of computed trajectory information required a new data compression technique: synoptic Lagrangian maps produced by representing each trajectory by its origin/fate and its residence time. The results show unexpected complexity and variability not apparent in the Eulerian current archive. For example, the fraction of particles that escaped to the open ocean during this period varied from about 17 to more than 92 percent. Mean particle residence times ranged from 4.5 to 11 days. The distribution of particle residence times and transport pathways varied over time scales from hours to weeks, and space scales from 2 to 40 km. The wide range of variability in particle properties reported here shows that surface transport studies in Monterey Bay require detailed wind and tidal current information over the entire bay, as well as information about the flow along the open ocean boundary