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## Navier-Stokes Equations (Navier-Stoke + equation)
Kinds of Navier-Stokes Equations
## Selected Abstracts## Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2008Thomas Y. HouIn this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the three-dimensionaFinal Navier-Stokes equations. The nonlinear structure of the one-dimensional model has some very interesting properties. On one hand, it can lead to tremendous dynamic growth of the solution within a short time. On the other hand, it has a surprising dynamic depletion mechanism that prevents the solution from blowing up in finite time. By exploiting this special nonlinear structure, we prove the global regularity of the three-dimensional Navier-Stokes equations for a family of initial data, whose solutions can lead to large dynamic growth, but yet have global smooth solutions. © 2007 Wiley Periodicals, Inc. [source] ## Synthesis of charged ultrafiltration poly(styrene- co -divinyl benzene) composite membrane JOURNAL OF APPLIED POLYMER SCIENCE, Issue 1 2008Sonny SachdevaAbstract A ceramic supported crosslinked polystyrene composite membrane has been prepared from its monomers using a dual initiator system. The nonionic hydrophobic membrane so prepared has been chemically modified by a low temperature (50°C), single step reaction with chloroacetic acid. The carboxylated membrane has acid functional groups on its surface making it negatively charged and highly hydrophilic in nature. The membranes (unmodified and carboxylated) have been used for the separation of hazardous chromium (VI) salt solution where observed and intrinsic rejection has been studied as a function of pressure and concentration of the feed solution. The intrinsic rejection has been determined by calculating the concentration at the membrane surface (Cm) using Speigler-Kedam model and osmotic pressure model. The observed rejection for the chemically modified membrane decreases with increasing pressure but the intrinsic rejection is found to be more than 80% for all concentrations in the range of study. The experimental results have been fitted using Space-Charge model to obtain the membrane wall potential and the membrane surface concentration which are difficult to measure directly. The transport through the membrane capillaries has been described by the two dimensional model using Nernst-Planck equation for ion transport, Navier-Stokes equation and Poisson-Boltzmann equation for the radial distribution of potential. We have then presented a semianalytical series solution to the highly nonlinear Poisson-Boltzmann equation to reduce the computational time required to solve the set of coupled differential equations. The effective wall potential of the carboxylated membrane was found to be ,28.07 mV. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] ## Viscocapillary model of slide coating: Effect of operating parameters and range of validity, AICHE JOURNAL, Issue 10 2009K. TjiptowidjojoAbstract Slide coating is one of the premetered high-precision coating methods. The layer thickness is set by the flow rate and web speed. The uniformity of the layer, however, can be affected by other operating conditions. Modeling the flow in the coating bead is necessary in developing the range of operability conditions where the layer is adequately uniform. Lubrication and viscocapillary models have been used to describe the flow and some of the operability limits of different coating processes. However, the available models of slide coating were developed with adhoc hypotheses that compromise their accuracy. We present a critical review of the available viscocapillary models and proposed changes to improve its range of applicability. The accuracy of the model is tested by comparing its predictions to the solution of the full two-dimensional Navier-Stokes equation. The model is valid at low capillary and Reynolds number regime and at low gap-to-wet thickness ratio. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] ## On the Navier-Stokes equation with boundary conditions based on vorticity MATHEMATISCHE NACHRICHTEN, Issue 1 2004Hamid BelloutAbstract We treat the Stokes and the Navier-Stokes equation with the conditions curlku · n = 0 (k = 0, 1, 2) on the boundary of the flow field. The approach is based on a spectral analysis and properties of operator curl. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Design Considerations for Plate and Frame Ultrafiltration Modules by Computational Fluid Dynamics Analysis, THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2006Mauro M. Dal-CinAbstract Pressure and flow maldistributions were studied in a full-scale industrial plate and frame ultrafiltration module, operating in a Z flow pattern, for the recovery of used motor oils. Solutions were obtained using (1) a three-dimensional solution of the Navier-Stokes equation using computational fluid dynamics and (2) Bernoulli's equation and a momentum balance in one dimension. Fluid decelerations and accelerations generated pressure increases and decreases in the distributor and collector, respectively, biasing the flow distribution to the last channel. Several modifications to the original design were evaluated; the most effective was larger distributor and collector diameters, which greatly improved the uniformity of the flow distribution and transmembrane pressure, and reduced the overall pressure drop in a bank. A variable diameter distributor and collector module was designed using the 1-D model. Flow distribution was significantly improved but also yielded an undesirable overall higher pressure drop and a pressure maldistribution in the bank. The maldistribution of the main inlet manifold to the distributors in the first bank was strongly dependent on the module design. The flow distribution across the width of a channel became uniform within a short distance, essentially eliminating the need to consider this design aspect any further. Flows at the bank outlets, and hence inlets of the following bank, showed uniform lateral distribution in all cases, suggesting that future modelling work can be limited to a fraction of the module width, based on symmetry, in order to gain computational efficiency. On a étudié les mauvaises distributions de pression et d'écoulement dans un module d'ultrafiltration à plateaux et à cadres à l'échelle industrielle, fonctionnant dans un schéma d'écoulement en Z, pour la récupération des huiles de moteurs usées. Des solutions ont été obtenues avec (1) une solution tridimensionnelle de l'équation de Navier-Stokes utilisant la mécanique des fluides par ordinateur, et (2) l'équation de Bernoulli et un bilan de quantité de mouvement unidimensionnel. Les décélérations et accélérations de fluide entraînent des augmentations et diminutions de pression dans le distributeur et le collecteur, respectivement, ce qui fausse la distribution d'écoulement dans le dernier canal. On a évalué plusieurs modifications du concept original; la plus efficace sont des diamètres de distributeur et de collecteur plus larges, qui permettent d'améliorer grandement l'uniformité de la distribution d'écoulement et la pression transmembranaire, et qui réduisent la perte de charge globale dans une batterie. Un module de distributeur et de collecteur de diamètres variables a été conçu au moyen du modèle 1D. La distribution d'écoulement est significativement améliorée mais cause une perte de charge globale plus grande indésirable et une mauvaise distribution de pression dans la batterie. La mauvaise distribution du manifold d'entrée principal vers les distributeurs dans la première batterie est fortement dépendante de la conception du module. La distribution d'écoulement dans toute la largeur d'un canal devient uniforme sur une courte distance, éliminant essentiellement le besoin d'approfondir cet aspect de la conception. L'écoulement en sortie de batteries et donc à l'entrée des batteries suivantes montre une distribution latérale uniforme dans tous les cas, ce qui suggère que le travail de modélisation futur peut se limiter à une fraction de la largeur du module, pour des raisons de symétrie, pour gagner de l'efficacité numérique. [source] ## Malliavin calculus for the stochastic 2D Navier,Stokes equation COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2006Jonathan C. MattinglyWe consider the incompressible, two-dimensional Navier-Stokes equation with periodic boundary conditions under the effect of an additive, white-in-time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finite-dimensional projection of the solution possesses a smooth, strictly positive density with respect to Lebesgue measure. In particular, our conditions are viscosity independent. We are mainly interested in forcing that excites a very small number of modes. All of the results rely on proving the nondegeneracy of the infinite-dimensional Malliavin matrix. © 2006 Wiley Periodicals Inc. [source] ## Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finite-dimensional approximation COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2001Weinan EWe study Galerkin truncations of the two-dimensional Navier-Stokes equation under degenerate, large-scale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. Our results rely heavily on the structure of the nonlinearity. © 2001 John Wiley & Sons, Inc. [source] ## Local block refinement with a multigrid flow solver INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2002C. F. LangeAbstract A local block refinement procedure for the efficient computation of transient incompressible flows with heat transfer is presented. The procedure uses patched structured grids for the blockwise refinement and a parallel multigrid finite volume method with colocated primitive variables to solve the Navier-Stokes equations. No restriction is imposed on the value of the refinement rate and non-integer rates may also be used. The procedure is analysed with respect to its sensitivity to the refinement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous significant savings in computing time and memory requirements. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Counter-current gas-liquid wavy film flow between the vertical plates analyzed using the Navier-Stokes equations AICHE JOURNAL, Issue 8 2010Yu. Ya.Abstract The article is devoted to a theoretical analysis of counter-current gas-liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier-Stokes system and (2) the simplified Benjamin-Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u- velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative u- velocities take place in the neighbourhood of the film thickness minimum. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] ## Millisecond catalytic wall reactors: I. Radiant burner AICHE JOURNAL, Issue 5 2001J. M. RedeniusShort-contact-time reactors have potential for high throughput in reactors much smaller than their traditional counterparts. While they operate adiabatically, heat can be exchanged at short contact time by integrating heat exchange into the reactor. Hot effluent of exothermic reaction systems can be redirected over feed gases to recuperate a portion of the sensible heat. Placing catalyst directly on reactor walls eliminates the resistance to heat transfer in the thermal boundary layer so that heat released by combustion can be effectively coupled to an emitter, such as in a radiant burner. A radiant heater was constructed, operated, and simulated incorporating short contact time, energy recuperation, and a catalytic wall. This burner operated stably for many hours at a firing rate from ,50 to > 160 kW/m2 at a radiant temperature of 950 to 1,150 K at a radiant efficiency of ,60% with a residence time in the reacting zone of ,10 ms. This reactor was modeled using 2-D Navier-Stokes equations including detailed models for chemistry and heat transport. Temperature and compositions predicted agreed well with experimental measurements. [source] ## Fast measurement of intracardiac pressure differences with 2D breath-hold phase-contrast MRI, MAGNETIC RESONANCE IN MEDICINE, Issue 6 2003Richard B. ThompsonAbstract Intracardiovascular blood pressure differences can be derived from velocity images acquired with phase-contrast (PC) MRI by evaluating the Navier-Stokes equations. Pressure differences within a slice of interest can be calculated using only the in-plane velocity components from that slice. This rapid exam is proposed as an alternative to the lengthy 3D velocity imaging exams. Despite their good spatial coverage, the 3D exams are prone to artifacts and errors from respiratory motion and insufficient temporal resolution, and are unattractive in the clinical setting due to their excessive scan times (>10 min of free breathing). The proposed single-slice approach requires only one or two breath-holds of acquisition time, and the velocity data can be processed for the calculation of pressure differences online with immediate feedback. The impact of reducing the pressure difference calculation to two dimensions is quantified by comparison with 3D data sets for the case of blood flow within the cardiac chambers. The calculated pressure differences are validated using high-fidelity pressure transducers both in a pulsatile flow phantom and in vivo in a dog model. There was excellent agreement between the transducer and PC-MRI results in all of the studies. Magn Reson Med 49:1056,1066, 2003. Published 2003 Wiley-Liss, Inc. [source] ## A finite element modified method of characteristics for convective heat transport NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2008Mofdi El-AmraniAbstract We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier-Stokes equations including density variation through the Boussinesq approximation. The solution procedure consists of combining an essentially non-oscillatory modified method of characteristics for time discretization with finite element method for space discretization. These numerical techniques associate the geometrical flexibility of the finite elements with the ability offered by modified method of characteristics to solve convection-dominated flows using time steps larger than its Eulerian counterparts. Numerical results are shown for natural convection in a squared cavity and heat transport in the strait of Gibraltar. Performance and accuracy of the method are compared to other published data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] ## A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equations NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006C. CalgaroAbstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] ## Second-order Galerkin-Lagrange method for the Navier-Stokes equations (retracted article), NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2005Mohamed BensaadaAbstract It has come to the attention of the editors and publisher that an article published in Numerical Methods and Partial Differential Equations, "Second-order Galerkin-Lagrange method for the Navier-Stokes equations," by Mohamed Bensaada, Driss Esselaoui, and Pierre Saramito, Numer Methods Partial Differential Eq 21(6) (2005), 1099,1121 included large portions that were copied from the following paper without proper citation: "Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations," Endre Suli, Numerische Mathematik, Vol. 53, No. 4, pp. 459,486 (July, 1988). We have retracted the paper and apologize to Dr. Suli Numer Methods Partial Differential Eq (2007)23(1)211. [source] ## Uniform stability of spectral nonlinear Galerkin methods NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004Yinnian HeAbstract This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier-Stokes equations with some appropriate assumption of the data (,, u0, f). If the backward Euler scheme with the semi-implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint ,t , (2/,,1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints ,t = O(,) and ,t = O(,), respectively, where , , ,, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source] ## Block factorized preconditioners for high-order accurate in time approximation of the Navier-Stokes equations NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2003Alessandro VenezianiComputationally efficient solution methods for the unsteady Navier-Stokes incompressible equations are mandatory in real applications of fluid dynamics. A typical strategy to reduce the computational cost is to split the original problem into subproblems involving the separate computation of velocity and pressure. The splitting can be carried out either at a differential level, like in the Chorin-Temam scheme, or in an algebraic fashion, like in the algebraic reinterpretation of the Chorin-Temam method, or in the Yosida scheme (see 1 and 19). These fractional step schemes indeed provide effective methods of solution when dealing with first order accurate time discretizations. Their extension to high order time discretization schemes is not trivial. To this end, in the present work we focus our attention on the adoption of inexact algebraic factorizations as preconditioners of the original problem. We investigate their properties and show that some particular choices of the approximate factorization lead to very effective schemes. In particular, we prove that performing a small number of preconditioned iterations is enough to obtain a time accurate solution, irrespective of the dimension of the system at hand. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 487,510, 2003 [source] ## Error estimate and regularity for the compressible Navier-Stokes equations by Newton's method NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2003Sang Dong KimAbstract The finite element discretization error estimate and H1 regularity are shown for the solution generated by Newton's method to the stationary compressible Navier-Stokes equations by interpreting Newton's method as an equivalent iterative method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 511,524, 2003 [source] ## An optimal memory-reduced procedure for calculating adjoints of the instationary Navier-Stokes equations OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2006Michael HinzeAbstract This paper discusses approximation schemes for adjoints in control of the instationary Navier,Stokes system. It tackles the storage problem arising in the numerical calculation of the appearing adjoint equations by proposing a low-storage approach which utilizes optimal checkpointing. For this purpose, a new proof of optimality is given. This new approach gives so far unknown properties of the optimal checkpointing strategies and thus provides new insights. The optimal checkpointing allows a remarkable memory reduction by accepting a slight increase in run-time caused by repeated forward integrations as illustrated by means of the Navier,Stokes equations. In particular, a memory reduction of two orders of magnitude causes only a slow down factor of 2,3 in run-time. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Coupling 3D and 1D fluid-structure interaction models for blood flow simulations PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006L. FormaggiaThree-dimensional (3D) simulations of blood flow in medium to large vessels are now a common practice. These models consist of the 3D Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall structure. However, it is still computationally unaffordable to simulate very large sections, let alone the whole, of the human circulatory system with fully 3D fluid-structure interaction models. Thus truncated 3D regions have to be considered. Reduced models, one-dimensional (1D) or zero-dimensional (0D), can be used to approximate the remaining parts of the cardiovascular system at a low computational cost. These models have a lower level of accuracy, since they describe the evolution of averaged quantities, nevertheless they provide useful information which can be fed to the more complex model. More precisely, the 1D models describe the wave propagation nature of blood flow and coupled with the 3D models can act also as absorbing boundary conditions. We consider in this work the coupling of a 3D fluid-structure interaction model with a 1D hyperbolic model. We study the stability of the coupling and present some numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Towards High Order Numerical Simulation of Aeolian Tones PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Bernhard MüllerStrictly stable high order finite difference operators have been applied to the compressible Navier-Stokes equations in perturbation form for low Mach number computational aeroacoustics. Aeolian tones generated by vortex shedding from a circular cylinder have been simulated. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Modeling and Simulation of Fires in Vehicle Tunnels PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003I. Teleaga M.Sc.Starting with compressible Navier-Stokes equations we derive a new fluid model by applying a low-Mach number asymptotic. The model is used to simulate fire events in vehicular tunnels. [source] ## The Noise Prediction Model SATIN PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003J. Ostertag Dipl.-Ing.This paper presents the noise prediction model SATIN (Statistical Approach to Turbulence Induced Noise) which is based on Lighthill's acoustic analogy. It allows to predict both, the far-field noise radiation as well as near-field wall-pressure fluctuations. Far-field noise radiation may result from the scattering of wall-pressure fluctuations at geometrical discontinuities and is therefore important for many practical problems. Within this paper, we focus on the calculation of far-field noise radiation. The required input values of SATIN are local properties of turbulence, namely the turbulent kinetic energy and the integral length scale which can be obtained by steady solutions of the Reynolds-averaged Navier-Stokes equations with a two equation turbulence model. It is assumed that the turbulence is axisymmetric and homogenous, which is taken into account by introducing two anisotropy parameters. The validation of SATIN is done for trailing-edge noise originating from a thin flat plate using measurements of a phased array. As expected, the anisotropic formulation of SATIN improves the prediction quality considerably compared to isotropic turbulence. [source] ## The Effects of Surface Waviness and Length on Electrokinetic Transport in Wavy Capillary THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2006Noor QuddusAbstract An electrokinetic model for a wavy capillary has been developed. Poisson-Nernst-Planck and Navier-Stokes equations constitute the model that governs fluid and ionic fluxes and electric potential distribution inside the capillary. In the present paper, a finite wavy cylindrical capillary with a large reservoir at both capillary ends is analyzed using finite element method. The model is used primarily to examine the influence of capillary surface waviness on the electrokinetic transport behaviours. Different frequencies and amplitudes of the wavy surface are considered to investigate the influence of surface waviness on electrokinetic transport. Fluctuations in potential and ionic concentration distribution increase with the increase in either amplitude or frequency of the capillary surface waviness. However, for higher frequencies the fluctuation diminishes for all surface waviness amplitudes. It is observed that for any irregularity in the capillary surface results in higher salt rejection. Salt rejection is found to be dependent on capillary axial length as well as flow velocity. A critical Peclet number, beyond which salt rejection attains a constant steady value, dictates maximum salt rejection. On a mis au point un modèle électrocinétique pour un capillaire onduleux. Les équations de Poisson-Nernst-Planck et de Navier-Stokes constituent le modèle qui gouverne le fluide et les flux ioniques ainsi que la distribution de potentiel électrique dans le capillaire. Dans le présent article, on analyse par la méthode des éléments finis un capillaire cylindrique onduleux fini possédant un grand réservoir aux deux extrémités du capillaire. Le modèle sert principalement à examiner l'influence de l'ondulation de la surface capillaire sur les comportements de transport électrocinétiques. On prend en compte différentes fréquences et amplitudes de la surface onduleuse pour étudier l'influence de l'ondulation de surface sur le transport électrocinétique. Les fluctuations dans la distribution de concentration potentielle et ionique augmentent l'amplitude ou la fréquence d'ondulation de surface capillaire. Toutefois, pour des fréquences plus élevées, la fluctuation diminue pour toutes les amplitudes d'ondulation de surface. On a observé que toute irrégularité dans la surface capillaire entraîne un plus grand rejet de sel. On a trouvé que le rejet de sel était dépendant de la longueur axiale de capillaire ainsi que de la vitesse d'écoulement. Un nombre de Peclet critique, au-delà duquel le rejet de sel atteint une valeur stable constante, dicte le rejet de sel maximum. [source] ## Suction vortices and spiral breakdown in numerical simulations of tornado-like vortices ATMOSPHERIC SCIENCE LETTERS, Issue 2 2009Brian FiedlerAbstract Three-dimensional simulations of tornado-like vortices are presented. The simulations are from a numerical model of the incompressible Navier-Stokes equations, with a Reynolds number, based on scales of the entire recirculating updraft, of up to 4.0 × 104. In a companion axisymmetric model, the theory for the corner flow swirl ratio provides an excellent prediction of the results. For the three-dimensional nonaxisymmetric model, the corner flow swirl ratio is not easily applied a priori, but nonetheless provides a framework for identifying a consistent departure of the three-dimensional simulations from the axisymmetric simulations. Copyright © 2009 Royal Meteorological Society [source] ## Vanishing viscosity limit of the Navier-Stokes equations to the euler equations for compressible fluid flow COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2010Gui-Qiang G. ChenWe establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup-norm of solutions with respect to the physical viscosity coefficient may not be directly controllable. Furthermore, convex entropy-entropy flux pairs may not produce signed entropy dissipation measures. To overcome these difficulties, we first develop uniform energy-type estimates with respect to the viscosity coefficient for solutions of the Navier-Stokes equations and establish the existence of measure-valued solutions of the isentropic Euler equations generated by the Navier-Stokes equations. Based on the uniform energy-type estimates and the features of the isentropic Euler equations, we establish that the entropy dissipation measures of the solutions of the Navier-Stokes equations for weak entropy-entropy flux pairs, generated by compactly supported C2 test functions, are confined in a compact set in H,1, which leads to the existence of measure-valued solutions that are confined by the Tartar-Murat commutator relation. A careful characterization of the unbounded support of the measure-valued solution confined by the commutator relation yields the reduction of the measurevalued solution to a Dirac mass, which leads to the convergence of solutions of the Navier-Stokes equations to a finite-energy entropy solution of the isentropic Euler equations with finite-energy initial data, relative to the different end-states at infinity. © 2010 Wiley Periodicals, Inc. [source] ## Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial velocity COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2010Qionglei ChenIn this paper, we prove global well-posedness for compressible Navier-Stokes equations in the critical functional framework with the initial data close to a stable equilibrium. This result allows us to construct global solutions for the highly oscillating initial velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms. © 2010 Wiley Periodicals, Inc. [source] ## Dynamic stability of the three-dimensional axisymmetric Navier-Stokes equations with swirl COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2008Thomas Y. HouIn this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the three-dimensionaFinal Navier-Stokes equations. The nonlinear structure of the one-dimensional model has some very interesting properties. On one hand, it can lead to tremendous dynamic growth of the solution within a short time. On the other hand, it has a surprising dynamic depletion mechanism that prevents the solution from blowing up in finite time. By exploiting this special nonlinear structure, we prove the global regularity of the three-dimensional Navier-Stokes equations for a family of initial data, whose solutions can lead to large dynamic growth, but yet have global smooth solutions. © 2007 Wiley Periodicals, Inc. [source] ## On the finite-time singularities of the 3D incompressible Euler equations COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2007Dongho ChaeWe prove the finite-time vorticity blowup, in the pointwise sense, for solutions of the 3D incompressible Euler equations assuming some conditions on the initial data and its corresponding solutions near initial time. These conditions are represented by the relation between the deformation tensor and the Hessian of pressure, both coupled with the vorticity directions associated with the initial data and solutions near initial time. We also study the possibility of the enstrophy blowup for the 3D Euler and the 3D Navier-Stokes equations, and prove the finite-time enstrophy blowup for initial data satisfying suitable conditions. Finally, we obtain a new blowup criterion that controls the blowup by a quantity containing the Hessian of the pressure. © 2006 Wiley Periodicals, Inc. [source] ## Bellman equations associated to the optimal feedback control of stochastic Navier-Stokes equations COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2005Fausto GozziIn this paper we study infinite-dimensional, second-order Hamilton-Jacobi-Bell-man equations associated to the feedback synthesis of stochastic Navier-Stokes equations forced by space-time white noise. Uniqueness and existence of viscosity solutions are proven for these infinite-dimensional partial differential equations. © 2005 Wiley Periodicals, Inc. [source] ## On the regularity of flows with Ladyzhenskaya Shear-dependent viscosity and slip or non-slip boundary conditions, COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2005H. Beirão da VeigaNavier-Stokes equations with shear dependent viscosity under the classical non-slip boundary condition have been introduced and studied, in the sixties, by O. A. Ladyzhenskaya and, in the case of gradient dependent viscosity, by J.-L. Lions. A particular case is the well known Smagorinsky turbulence model. This is nowadays a central subject of investigation. On the other hand, boundary conditions of slip type seems to be more realistic in some situations, in particular in numerical applications. They are a main research subject. The existence of weak solutions u to the above problems, with slip (or non-slip) type boundary conditions, is well known in many cases. However, regularity up to the boundary still presents many open questions. In what follows we present some regularity results, in the stationary case, for weak solutions to this kind of problems; see Theorems 3.1 and 3.2. The evolution problem is studied in the forthcoming paper [6]; see the remark at the end of the introduction. © 2004 Wiley Periodicals, Inc. [source] |