151,346 research outputs found
Intermittency and regularity issues in 3D Navier-Stokes turbulence
No full textTwo related open problems in the theory of 3 D Navier-Stokes turbulence are discussed in this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation-range intermittency was first discovered experimentally by Batchelor and Townsend over fifty years ago. It is characterized by spatio-temporal binary behaviour in which long, quiescent periods in the velocity signal are interrupted by short, active ‘events’ during which there are violent fluctuations away from the average. The second and related problem is whether solutions of the 3 D Navier-Stokes equations develop finite time singularities during these events. This paper shows that Leray’s weak solutions of the three-dimensional incompressible Navier-Stokes equations can have a binary character in time. The time-axis is split into ‘good’ and ‘bad’ intervals: on the ‘good’ intervals solutions are bounded and regular, whereas singularities are still possible within the ‘bad’ intervals. An estimate for the width of the latter is very small and decreases with increasing Reynolds number. It also decreases relative to the lengths of the good intervals as the Reynolds number increases. Within these ‘bad’ intervals, lower bounds on the local energy dissipation rate and other quantities, such as || u (·, t )|| ∞ and ||∇ u (·, t )|| ∞ , are very large, resulting in strong dynamics at sub-Kolmogorov scales. Intersections of bad intervals for n ≧1 are related to the potentially singular set in time. It is also proved that the Navier-Stokes equations are conditionally regular provided, in a given ‘bad’ interval, the energy has a lower bound that is decaying exponentially in time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46170/1/205_2005_Article_382.pd
NAVIER–STOKES EQUATIONS ON THE β-PLANE
No full textMathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy
Stokes diagnostics of simulated solar magneto-convection
No full textWe present results of synthetic spectro-polarimetric diagnostics of radiative MHD simulations of solar surface convection with magnetic fields. Stokes profiles of Zeeman-sensitive lines of neutral iron in the visible and infrared spectral ranges emerging from the simulated atmosphere have been calculated in order to study their relation to the relevant physical quantities and compare with observational results. We have analyzed the dependence of the Stokes-I line strength and width as well as of the Stokes-V signal and asymmetries on the magnetic field strength. Furthermore, we have evaluated the correspondence between the actual velocities in the simulation with values determined from the Stokes-I (Doppler shift of the centre of gravity) and Stokes-V profiles (zero-crossing shift). We confirm that the line weakening in strong magnetic fields results from a higher temperature (at equal optical depth) in the magnetic flux concentrations. We also confirm that considerable Stokes-V asymmetries originate in the peripheral parts of strong magnetic flux concentrations, where the line of sight cuts through the magnetopause of the expanding flux concentration into the surrounding convective donwflow
Publication in BMC Research Notes: Shifts in soil and plant functional diversity along an altitudinal gradient in the French Alps
No full textAuthors: Stokes A., Angeles G., Barois I., Bounous M, Cruz-Maldonaldo N, Decaëns T, Freschet G., Gabriac Q, Hernandez D., Jimenez L., Ma J, Mao Z, Marin-Castro B, Merino-Martin L, Mohamed A, Reverchon F, Selli L., Sieron K., Weemstra M., Roumet
Large-time behavior of the weak solution to 3D Navier-Stokes equations
No full textThe weak solution to the Navier–Stokes equations in a bounded domain D ⊂ R[superscript 3] with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t ≥ 0. In a bounded domain D the solution decays exponentially
fast as t → ∞if the force term decays at a suitable rat
Integral representation of a solution to the Stokes-Darcy problem
No full textWith methods of potential theory we develop a representation of a solution of the coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H-1/2
Staci J. Stokes' Graduate Recital
No full textOriginal Format: CassetteComposers in the first graduate recital: Keiko Abe; John Beck; Bill Molenhoff; Russel PeckComposers in the second graduate recital: Julie Spencer; David Kovins; Victor Feldman; Scott Seils; Minoru MikiFirst Recital: PercussionSecond Recital: Percussio
A sequential regularization method for time-dependent incompressible Navier--Stokes equations
No full textThe objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is , where is the number of the SRM iterations and is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit-difference scheme is analyzed and its stability is proved under the usual step-size condition of explicit schemes. It appears that the SRM formulation is new in the Navier--Stokes context. Unlike other regularizations or pseudocompressibility methods in the Navier--Stokes context, the regularization parameter in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any . Hence the stability condition is independent of even for explicit time discretization. Numerical experiments are given to verify our theoretical results
The C. Ray Stokes Collection
No full textFinding aid for The C. Ray Stokes CollectionC. Ray Stokes was the first employee of the Texas College of Osteopathic Medicine in 1969. He served as founding director of development, business manager, purchasing agent, public relations director and as registrar. Stokes opened TCOM's first office and hired his wife Edna as secretary and bookkeeper. He hired the school's first Dean, Henry Hardt, Ph.D. Stokes was instrumental in raising funds for the purchase of some of the properties acquired near Med Ed I, later named the Carl E. Everett Education and Administration Building. He also coordinated the effort to raise money from osteopathic physicians around the state to support of the school. Stokes received TCOM's Founders' Medal in 1986.The C. Ray Stokes Collection consists of documents related to C. Ray Stokes while he served as an employee of the Texas College of Osteopathic Medicine. The materials include a scrapbook, agreements, reports, newsletters, meetings minutes, and papers
Refined saddle-point preconditioners for discretized Stokes problems
No full textThis paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies are available online
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