摘要:

The linear stability of miscible displacement processes in porous media is examined in the absence of diffusion and dispersion. Bounds for the rate of growth of the disturbance are derived. The asymptotic behavior of the rate of growth as a function of the wavenumber of the disturbance and the mobility profile characteristics is obtained for both small and large wavenumbers. A closed‐form solution is also presented for a particular mobility profile. It is shown that such displacement processes are linearly unstable in the case when the mobility profile contains any segments of decreasing mobility, and marginally stable in the opposite case. The effect of gravity on linear stability, in the case of compressible flows, is also briefly discusse

ISSN:0022-2526    

DOI:10.1002/sapm198674293

年代:1986

数据来源: WILEY

摘要:

We present a systematic asymptotic theory for resonantly interacting weakly nonlinear hyperbolic waves for a single space variable in a homogeneous, time independent medium. This theory extends the results previously presented by A. Majda and R. Rosales, under similar hypotheses, to the case where waves break and shocks form. Similarly the theory of nonresonant interacting waves for general hyperbolic systems developed recently by J. Hunter and J. B. Keller, when specialized to a single space variable, is included as a special case. However, we are also able to treat the general situation when resonances occur in the hyperbolic system. Such resonances are the typical case when the hyperbolic system has at least three equations and when, for example, small‐amplitude periodic initial data are prescribed. In the important physical example of the 3 ✕ 3 system describing compressible fluid flow in a single space variable, the resonant asymptotic theory developed by the authors yields, as limit equations, a pair of inviscid Burgers equations coupled through a linear integral operator with known kernel defined through the initial data for the entropy wave. These are the same equations derived by Majda and Rosales previously. However, the waves are displaced relative to the positions prescribed by t

ISSN:0022-2526    

DOI:10.1002/sapm1986742117

年代:1986

数据来源: WILEY

摘要:

The shapes of a steadily translating pair of equal and opposite vortices with vortex sheets on their boundaries is determined. A continuum of solutions is found to exist between the two extremes: a hollow vortex pair and a vortex pair with no vortex sheets.

ISSN:0022-2526    

DOI:10.1002/sapm1986742139

年代:1986

数据来源: WILEY

摘要:

The thermohaline and other related problems in which competitiOn between stabilizing and destabilizing physical mechanisms can create oscillatory, steady, or multiple instabilities has been much studied in the literature. Various techniques have been used to find the finite‐amplitude description near the multiple bifurcation point, but there appear to be differences in the coefficients of the nonlinear evolution equation. We address this problem by presenting a comparative study of its derivation using the classical method of multiple scales and the lesser‐known (but more powerful) methods of center manifold with normal forms. The two approaches are shown to yieldidenticalequations and provide insights into the source of the differen

ISSN:0022-2526    

DOI:10.1002/sapm1986742155

年代:1986

数据来源: WILEY

摘要:

In contrast to the usual (and successful) direct methods for Toeplitz systemsAx = b, we propose an algorithm based on the conjugate gradient method. The preconditioner is a circulant, so that all matrices have constant diagonals and all matrix‐vector multiplications use the Fast Fourier Transform. We also suggest a technique for the eigenvalue problem, where current methods are less satisfactory. If the first indications are supported by further experiment, this new approach may have useful applications—including nearly Toeplitz systems, and parallel computati

ISSN:0022-2526    

DOI:10.1002/sapm1986742171

年代:1986

数据来源: WILEY