7,959 research outputs found
Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet
The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified
The MHD Kelvin-Helmholtz Instability III: The Role of Sheared Magnetic Field in Planar Flows
We have carried out simulations of the nonlinear evolution of the
magnetohydrodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible
fluids in -dimensions, extending our previous work by Frank et al
(1996) and Jones \etal (1997). In the present work we have simulated flows in
the x-y plane in which a ``sheared'' magnetic field of uniform strength
``smoothly'' rotates across a thin velocity shear layer from the z direction to
the x direction, aligned with the flow field. We focus on dynamical evolution
of fluid features, kinetic energy dissipation, and mixing of the fluid between
the two layers, considering their dependence on magnetic field strength for
this geometry. The introduction of magnetic shear can allow a Cat's Eye-like
vortex to form, even when the field is stronger than the nominal linear
instability limit given above. For strong fields that vortex is asymmetric with
respect to the preliminary shear layer, however, so the subsequent dissipation
is enhanced over the uniform field cases of comparable field strength. In fact,
so long as the magnetic field achieves some level of dynamical importance
during an eddy turnover time, the asymmetries introduced through the magnetic
shear will increase flow complexity, and, with that, dissipation and mixing.
The degree of the fluid mixing between the two layers is strongly influenced by
the magnetic field strength. Mixing of the fluid is most effective when the
vortex is disrupted by magnetic tension during transient reconnection, through
local chaotic behavior that follows.Comment: 14 pages including 9 figures (4 figures in degraded jpg format), full
paper with original quality figures available via anonymous ftp at
ftp://canopus.chungnam.ac.kr/ryu/mhdkh2d.uu, to appear in The Astrophysical
Journa
Slowly modulated oscillations in nonlinear diffusion processes
It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion
Pulse-coupled resonate-and-fire models
We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation
reveals that an anti-phase state is an attractor of this model. We can
analytically explain the stability of anti-phase states by means of a return
map of firing times, which we propose in this paper. The resultant stability
condition turns out to be quite simple. The phase diagram based on our theory
shows that there are two types of anti-phase states. One of these cannot be
seen in coupled integrate-and-fire models and is peculiar to resonate-and-fire
models. The results of our theory coincide with those of numerical simulations.Comment: 15 pages, 8 figure
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