A correction term for the swirling jet

When the constants in the second-order model of turbulence are set so as to correctly predict the spreading rate of the axisymmetric jet, the model does not correctly predict the spreading rate of the swirling axisymmetric jet. In order to correct this problem an additional term to the dissipation source term is suggested. Initial results indicate this greatly improves the model's performance for the swirling axisymmetric jet.     

Nonlinear breakup of a self-gravitating column

Using the method of strained coordinates, a weakly nonlinear theory of the breakup of a gravitating column is presented. It is shown that the self-gravitating column breaks into the main celestial bodies and their satellites whose dimensions are sensitive to the wavenumbers.     

Nonlinear instability of a viscous liquid jet

We investigate the weakly nonlinear temporal instability of an axisymmetric Newtonian liquid jet. Early nonlinear studies on the capillary instability of inviscid liquid jets were carried up to the third order contributions to the jet deformation and showed the nonlinear interaction between different modes. A recent study on the weakly nonlinear instability of planar Newtonian liquid sheets revealed the role of the liquid viscosity in the sheet stability behavior and showed a complicated influence [1]. Here, the instability of a liquid jet is examined as the axisymmetric counterpart of the sheet, in search for corresponding insight into the role of the liquid viscosity in the jet instability mechanism. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The swirling,radial free jet in the presence of a transverse magnetic field

Zusammenfassung Diese Arbeit ist eine Erweiterung früherer Arbeiten vonRiley [1] undMoreau [2, 3]. Der wirbelnde achsensymmetrisch-radiale Strahl einer leitenden Flüssigkeit in Gegenwart eines axialen magnetischen Feldes wird untersucht.     

Nonlinear perturbation of linear evolution equations in a banach space

Summary Let X be a Banach space and {A(t)|t ε [0, T]} a family of closed linear, densely defined m-accretive operators in X. This paper is concerned with the additive perturbation of {A(t)|t ε [0, T]} by a continuous family of nonlinear accretive operators {B(t)|t ε [0, T]}. Namely solutions are provided for the integral equation u(t, τ, x) = W(t, τ)x − W(t, s)B(s) · · u(s, τ, x)ds, u(τ, τ, x) = x where W(t, s) is the linear evolution operator associated with the linear differential equation v'(t, s, x) + A(t)v(t, s, x) = 0, v(s, s, x) = x. Entrata in Redazione il 30 luglio 1975.     

Nonlinear evolution equation for describing waves in a viscoelastic tube

Propagation of the nonlinear waves in a viscoelastic tube filled with a liquid is studied. The bending of the tube wall is taken into account. By using the reductive perturbation method the fifth order nonlinear evolution equation is derived. Exact solutions for this equation is obtained by means of the simplest equation method. Properties of nonlinear waves in a viscoelastic tube filled with a liquid are discussed.     

Nonlinear self-adjointness of a 2D generalized second order evolution equation

We study the nonlinear self-adjointness of a general class of quasilinear 2D second order evolution equations which do not possess variational structure. For this purpose, we use the method of Ibragimov, devised and developed recently. This approach enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjoint sub-class in the general case. Then, we establish the conservation laws for important particular cases: the Ricci Flow equation, the modified Ricci Flow equation and the nonlinear heat equation.     

Nonlinear evolution systems and green's function

In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on.     

Nonlinear evolution equations in Banach spaces

The evolution problem 0∈du/dt+A(t)u(t),u(s)=x, where theA(t) are nonlinear operators acting in a Banach space, is studied. Evolution operators are constructed from theA(t) under various assumptions. Basic properties of these evolution operators are established and their relationship to the evolution equation is determined. The results obtained extend several known existence theorems and provide generalized solutions of the evolution equation in more general cases. Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462. and in part by the Office of Naval Research under Contract N000-14-69-A-0200-4022. Reproduction in whole or in part is permitted for any purpose of the United States Government. This research was partially supported by the NSF Grant #GP-18127.     

Generative mechanism of air column oscillations in a Hartmann-Sprenger tube excited by an air jet issuing from a convergent nozzle

Summary In this paper, a theory of the origin of the air column oscillations in the Hartmann-Sprenger (HS) tube excited by an air jet issuing from a convergent nozzle is presented.For the analysis, the following basic configuration is assumed. The air jet issuing from a nozzle forms a steady stagnation flow between the nozzle and the open end of the tube, and the air column in the tube remains at rest. A massless hypothetical membrane is assumed at the open end of the tube. When a sinusoidal vibration of the membrane with very small amplitude is assumed, its radiation impedance is obtained by calculating the reactive forces of the flow field acting on the membrane on each side. If the real part of the radiation impedance is negative, the field is unstable, and the air column in the HS tube will be excited to oscillation.The analytical results can explain well the experimental observations.

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Zusammenfassung Im vorliegenden Bericht wird der Schwingungsmechanismus der Luftsäule im Hartmann-Sprenger Rohr betrachtet für den Fall, dass diese durch einen Gasstrahl von einer konvergenten Düse angeregt wird. Für die Analysis wird die folgende Fundamentalkonfiguration angenommen: Der Gasstrahl der Düse bildet die stationäre Stauströmung zwischen der Düse und der Mündung des HS Rohres, und die Luftsäule im HS Rohr ist in Ruhe. An der Rohrmündung wird eine hypothetische Membrane angenommen. Wenn diese Membrane mit einer kleinen Amplitude sinusförmig schwingt, dann ist die Strahlungsimpedanz dieser Membrane durch die Gegenkräfte auf die Membrane gegeben. Wenn der Realteil der Strahlungsimpedanz negativ ist, ist das System selbsterregend und die Luftsäuleschwingung im HS Rohr wird erzeugt.Das analytische Resultat stimmt mit dem experimentellen gut überein.

     

Nonlinear evolution equations and the Euler flow

A new theorem on abstract nonlinear equations of evolution is proved. As an application, the existence, uniqueness, regularity, and continuous dependence on the data are proved for the solution of the Euler equation for incompressible fluids in a bounded domain in R^m.