By Charles R. Doering

ISBN-10: 0521445574

ISBN-13: 9780521445573

ISBN-10: 052144568X

ISBN-13: 9780521445689

The Navier-Stokes equations are a suite of nonlinear partial differential equations that describe the basic dynamics of fluid movement. they're utilized many times to difficulties in engineering, geophysics, astrophysics, and atmospheric technological know-how. This e-book is an introductory actual and mathematical presentation of the Navier-Stokes equations, targeting unresolved questions of the regularity of strategies in 3 spatial dimensions, and the relation of those concerns to the actual phenomenon of turbulent fluid movement. The target of the e-book is to give a mathematically rigorous research of the Navier-Stokes equations that's available to a broader viewers than simply the subfields of arithmetic to which it has routinely been constrained. for that reason, effects and methods from nonlinear sensible research are brought as wanted with an eye fixed towards speaking the basic rules in the back of the rigorous analyses. This booklet is suitable for graduate scholars in lots of parts of arithmetic, physics, and engineering.

Show description

Read or Download Applied Analysis of the Navier-Stokes Equations PDF

Similar fluid dynamics books

Micro- and Nanoscale Fluid Mechanics: Transport in - download pdf or read online

This article specializes in the physics of fluid shipping in micro- and nanofabricated liquid-phase structures, with attention of fuel bubbles, sturdy debris, and macromolecules. this article used to be designed with the target of bringing jointly numerous parts which are usually taught individually - particularly, fluid mechanics, electrodynamics, and interfacial chemistry and electrochemistry - with a concentrated target of getting ready the trendy microfluidics researcher to investigate and version continuum fluid mechanical structures encountered while operating with micro- and nanofabricated units.

Mechanik der Gase - download pdf or read online

Kenntnisse über die Bewegung von Gasteilchen, deren Geschwindigkeit und Energie sind eine wichtige Voraussetzung zum Verständnis moderner Technologien, z. B. der Vakuumtechnik, und eng damit verknüpft der Vakuumphysik oder der Handhabung von Gasen. Mit dem vorliegenden Buch wird eine intestine verständliche Darstellung der Mechanik der Gase gegeben.

New PDF release: Mechanics and Mathematics of Fluids of the Differential Type

This article is the 1st of its type to assemble either the thermomechanics and mathematical research of Reiner-Rivlin fluids and fluids of grades 2 and three in one e-book. every one a part of the publication might be regarded as being self-contained. the 1st a part of the publication is dedicated to an outline of the mechanics, thermodynamics, and balance of flows of fluids of grade 2 and grade three.

Additional info for Applied Analysis of the Navier-Stokes Equations

Example text

Discuss the nature of the bifurcation at the critical Rayleigh number. 1) is an exact stationary solution of the Navier-Stokes equations corresponding to a fluid sheared between a stationary plate at z = 0 and one moving with speed U in the x-direction at z = h. 5 Imposing periodic conditions on [0, L1] and [0,L21 in the x- and y-directions respectively, reduce the linear stability analysis to ordinary differential equations for the eigenvalue problem. Can you solve them? Set up the nonlinear stability analysis for Couette flow as described in the previous exercise.

Corrections. 4. Although this example has been developed for illustrative purposes with a minimum of fitting parameters (one), it does reproduce some essential features of the conventional wisdom concerning the structure of both the mean and Reynolds stress profiles. Together with logarithmic corrections, the R2 scaling of the turbulent drag is supported by experiments in wall bounded shear flows. 26), however, constitute uncontrolled approximations which do not follow rigorously (or even "formally" or systematically) from the Navier-Stokes equations.

Integrated over a thin shell around Ikl = k in wavenumber space, this density gives the contribution to the kinetic energy in the flow field from motion on the length scale 2ir/k. For the moment let us focus on the 3d case. )I2) d3k = =: I 2L3 f (27r)3 JE(k)dk. 7) Isotropic turbulence means that on average, there is no preferred direction in the flow. Spectra, Kolmogorov's scaling theory, and turbulent length scales 51 The density E(k) is the contribution to the total average kinetic energy per unit mass from each length scale 27c/k and the total is - (IIu112) = f>_2a/L E(k)dk.

Download PDF sample

Applied Analysis of the Navier-Stokes Equations by Charles R. Doering


by Daniel
4.1

Rated 4.87 of 5 – based on 39 votes