3 edition of Singularities of the Euler equation and hydrodynamic stability found in the catalog.
Singularities of the Euler equation and hydrodynamic stability
by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va
Written in English
|Series||NASA contractor report -- 189720., ICASE report -- no. 92-54., NASA contractor report -- NASA CR-189720., ICASE report -- no. 92-54.|
|Contributions||Langley Research Center.|
|The Physical Object|
Twelfth Brooke Benjamin Lecture - 5pm Monday 21 January Alexander A. Kiselev, Duke University Small Scale and Singularity Formation in Fluid Mechanics. The Euler equation describing motion of ideal fluids goes back to The analysis of the equation is challenging since it is nonlinear and nonlocal. On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics. “Singularities of the Euler equation and hydrodynamic stability, On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics. Math No – (). https://doi Cited by: 5.
The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book. A commonly used  model, especially in computational fluid dynamics, is to use two flow models: the Euler equations away from the body, and boundary layer equations in a region close to the body. The two solutions can then be matched with each other, using the method of matched asymptotic expansions.
Vorticity, Turbulence, and Acoustics in Fluid Flow. Related Databases. On the finite-time singularities of the 3D incompressible Euler equations. Communications on Pure and Applied Mathematics , Singularities of the Euler equation and hydrodynamic stability. Physics of Fluids A: Fluid Dynamics , Cited by: equation is the equation of motion of a ﬂuid element, ρ(dvi/dt) = −∂ip, where pis pressure, and (−∂ip) is the force per unit volume. In terms of the velocity ﬁeld v(t,x) this gives the Euler equation, ρ(∂tvi+vk∂kvi) = −∂ip. Using the continuity equation (), one can rewrite the Euler equation in the form of momentum File Size: KB.
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Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical : S.
Tanveer, Charles G. Speziale. Get this from a library. Singularities of the Euler equation and hydrodynamic stability. [S Tanveer; Langley Research Center.]. Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived.
Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular. Book description. Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a by: Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived.
Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular Author: Charles G. Speziale and S. Tanveer. The ideal equation of state links the temperature, pressureand number density N of the gas particles: P = NkT ↔ P = ρkT µ () where k =× 10−16 erg/K is the Boltzmann constant.
Another aspect of the ideal gas is the equation of state relating the pressure to the internal speciﬁc energy e P =(γ − 1)ρe ().
for future analytical studies on the unstable manifolds for the 2D Euler equation. In Ref. 6, we have begun numerical studies on the unstable manifolds for the 2D Euler equation. The current study is also important in the linear hydrodynamic stability theory.
By utilizing. Solutions of Euler equations might seem more unstable than they really are, or to be more precise, the notion of stability appropriate for them is a more generous one, that of orbital stability. An example of this nuance is the case of Kirchhoﬀ ellipses, which are special solutions of two dimensional Euler equations.
These are ellipses that., Michael Zingale document git version: 4de1fef51af the source for these notes are available online (via git). In fluid dynamics, the Euler equations are a set of quasilinear hyperbolic equations governing adiabatic and inviscid are named after Leonhard equations represent Cauchy equations of conservation of mass (continuity), and balance of momentum and energy, and can be seen as particular Navier–Stokes equations with zero viscosity and zero thermal.
The solution of the Euler equations at times t > sufficiently small can then be ex- tended analytically into the complex domain . There is strong numerical evidence in 2D and also in 3D that such flow does not stay entire and develops singularities at certain complex locations for any t > [4, 10, 12, 14].
ICASE Report No. S ICASE DEC 4 LCD C SINGULARITIES OF THE EULER EQUATION AND HYDRODYNAMIC STABILITY S. Tanveer Charles G. Speziale PDlroved tw z fteeme Contract Nos. NAS and NASI October Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hampton, Virginia.
Singularities of Euler Flow. Not Out of the Blue. Singularities of the Euler equation and hydrodynamic stability, Phys. Fluids A (). Numerical study of singularity formation in a class of Euler and Navier-Stokes Cited by: It splits the Euler equations into two sets of equations: one for u+ = u+ (r,z,t) containing all non-negative wavenumbers (in z) and the second for.
The equations for u+ are exactly the Euler Author: Saleh Tanveer. This book provides an introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism. It is assumed that the reader has had some (but not necessarily an exhaustive) exposure to introductory fluid dynamics, hydrodynamic stability theory, finite dimensional.
6 An Introduction to Hydrodynamic Stability Fig. Oscillations in a continuously and stably stratiﬁed ﬂuid where gis the acceleration due to gravity and ı is the density difference between the parcel and the ambient ﬂuid at z 0C ı is inﬁnitesimal, it can be ex-pressed as ı D ızd=d z.
We may rewrite ()as d2ız dt2File Size: KB. Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time. This blowup problem is still open.
After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are. Hydrodynamic Stability. Cambridge University Press,  Conservation laws and formation of singularities in relativistic theories of extended objects.
In Nonlinear Waves, Development of singular solutions to the axisymmtric Euler equations. () Singularities of the Euler equation and hydrodynamic stability.
Physics of Fluids A: Fluid Dynamics() On the ‘δ-equations’ for vortex sheet by: ICASE Report No. ICASE SINGULARITIES OF THE EULER EQUATION AND HYDRODYNAMIC STABILITY S. Tanveer Charles G. Speziale Contract Nos. NAS and NAS October Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hampton, Virginia Operated by the Universities Space.
Trigonometric polynomials are instances of entire functions, that is, functions which are analytic in the whole complex domain.
The only singularities of such functions are at complex infinity. The solution of the Euler equations at times t>0 sufficiently small can then be extended analytically into the complex domain , , .Cited by: Euler's Equations of Motion (Bdb) Euler's Equations of Motion in Other Coordinates (Bdc) Vorticity (Bdd) Circulation (Bde) Kelvin's Theorem (Bdj) Velocity Potential (Bdf) Bernoulli's Equation (Bdg) Energy Implications of Bernoulli's Equation (Bdh) Momentum Theorem (Be) Linear Momentum Theorem (Bea) Example: Arbitrary Duct (Beb).In Section 2 we introduce a rescaled form of the two-dimensional Euler equation, in particular its limit, describe Taylor expansions of its solutions, their relation to complex singularities and to the short-time behaviour of solutions.
In Section 3 we give a detailed account of the short-time asymptotic régime, Cited by: 5.