Inviscid stability analysis

Boundary Conditions Required for the CFD Simulation 349 ILL-POSEDNESS BOUNDARY—INVISCID STABILITY ANALYSIS... 

Much of the procedure for the analysis of jet stability has already been set down in connection with the discussion of undamped surface waves on deep water. A fundamental difference in the jet problem from plane deep water waves is that it is axisymmetric with an imposed characteristic length scale equal to the jet radius a. Since the undisturbed jet is considered to be inviscid and in uniform flow, it can be reduced to a state of rest simply by a Galilean transformation. With gravity neglected and only surface tension forces acting, the pressure at any point within the jet is -I- ala. This then describes the basic flow needed for the first step of the stability analysis. 

The general structure of stability Equation 18 remains unchanged when different quasi-steady models are applied for the various shear stresses terms. Moreover, even when the viscous effects are completely ignored, resorting to an inviscid K-H stability type of analysis, the structure of the resulting stability condition. Equation 18, is still maintained while Equation 19 for attains different expression. For instance, the long wave K-H stability analysis on two inviscid layers (rectangular channel) yields ... 

Indeed, various early studies employed inviscid K-H stability analysis for predicting the stratified/nonstratified transition boundary in gas-liquid two-phase flow (Kordyban and Ranov [33], Kordyban [34], Wallis and Dobson [35], Taitel and Dukler [19]). However, claiming that for pyp, = Pq Pl Equation 21 has been reduced to (ignoring the contribution of U H / [U (l - H)] in Equa-... 

In this Section we present the theory for inviscid compound jets. The motivation comes from printing technologies as described in [32] other applications include production of compound particles and coating flows. Sanz and Meseguer [65] have carried out a linear stability analysis of a reduced one-dimensional system of equations which retains the full... 

There have been significant contributions initially made by Helmholtz, Kelvin and Rayleigh (1880, 1887) using inviscid analysis. In their quest to justify their inviscid analysis, an assumption was made that viscous action due to its dissipative nature can be only stabilizing. Such was the impact of this observation that when Heisenberg (1924) submitted his dissertation solving perturbation equations including viscous terms for boundary layer... 

A key idea from the preceding analysis, as well as the analysis of capillary instability in section A, is that viscous effects often cannot change the conditions for instability of a rest state, but only moderate the rate of growth or decay of disturbances. In such cases, analysis of the stability (or instability) of the inviscid limit can be extremely useftd in identifying the conditions for instability. In view of the fact that the inviscid analysis is very much simpler, this is an important observation. 

The criteria (12-138) for stability of an inviscid fluid had actually been obtained by Rayleigh using qualitative arguments long before any detailed analysis had been done. Rayleigh stated the condition for stability as... 

The conclusion from this discussion is that the linear stability of flows is a complicated topic, even if we restrict ourselves to a simple class of problems such as steady, 2D, unidirectional flows, and it is not possible to provide a comprehensive summary in the space available. Instead, we consider only an introduction to the stability for this limited class of problems, with the intention of giving a qualitative sense of the analysis and some very basic results. In particular, we summarize the theory for an inviscid fluid, which has been... 

We suppose that we have a fluid of density p contained within a spherical interface of radius R. This spherical body of fluid is surrounded by an unbounded body of fluid of density p2. The interfacial tension is denoted as y. To facilitate the analysis, we consider the fluids to be incompressible and also inviscid. You may assume that the change in radius R(t) is specified (and thus too R and R). We wish to analyze the linear stability of the spherical interface to perturbations of shape of the form (4-298),... 

Ramos JI, Asymptotic analysis and stability of inviscid liquid sheets, J. Math. Anal. Appl. 250, 512, 2000. 

We begin with an analysis of the stability of the interface between two inviscid, incompressible fluids which initially have uniform velocities and Vg. respectively, in the x direction (see Figure 5.9). Kelvin s interest in this problem... 

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