Broad Range Of Wavenumbers Research Articles

Oscillatory instabilities in rapid directional solidification: bifurcation theory

Merchant and Davis performed a linear stability analysis on a model for the rapid directional solidification a dilute binary alloy. The model has a velocity-dependent distribution coefficient and liquidus slope, and a linear form for attachment kinetics. The analysis revealed that in addition to the Mullins and Sekerka cellular mode there is a new oscillatory instability; the zero wavenumber pulsatile mode is most dangerous in the linear theory. In the present paper, a weakly nonlinear analysis is performed to describe the nonlinear behavior of this oscillatory mode. The analysis leads to a complex Ginzburg-Landau equation governing the evolution of the solid-liquid interface shape. Parametric regions of supercritical (subcritical) bifurcation giving smooth (jump) transitions to the pulsatile mode are demarked. Further analysis is made to determine how non-zero wavenumber disturbances compete with the zero wavenumber pulsation. In the low speed limit, these disturbances have a relatively broad range of wavenumbers in which they are stable. In the high speed limit, only very long waves are selected. The very long waves correspond approximately to solute bands, in which the solute distribution in the solid is layered in the direction of growth with no lateral segregation. In the three-dimensional case, spiral waves are solutions to the Ginzburg-Landau equation and these may be related to the spiral waves that have been observed by Thoma et al. in melt spinning.

The Stability of a Warped Accretion Disc

AbstractAn accretion disc becomes warped when subjected to a torque which is misaligned with the disc plane. Such torques may be caused by Lense-Thirring precession near a spinning compact object, or the quadrupole field of a binary star. Here the flow in an adiabatic warped disc is modelled as a two-dimensional shear layer with linear velocity profile and free surface boundary conditions, and is investigated by means of a linear stability analysis.The flow is found to be unstable whenever it contains a critical layer, i.e., a level at which the shear velocity is equal to the phase velocity. The instability occurs over a broad wavenumber range and has a typical dimensionless growth rate ≈ 0.1 for both the compressible and incompressible cases. These waves grow with a time-scale of about one orbital period, and are likely to have a major effect on the disc viscosity.

Spatial correlation functions of surface-layer atmospheric turbulence in neutral stratification

The longitudinal (i.e., in the direction of the mean wind) spectra and cospectra of wind components and temperature fluctuations in the atmospheric surface layer during neutral conditions were carefully investigated by Kader (1984, 1987) for a broad range of wave numbers which included wavelengths far beyond the large-scale limit of the inertial subrange. At the same time, some direct measurements of spatial correlation functions of the longitudinal wind component and temperature were performed by Zubkovskii and Fedorov (1986) and Zubkovskii and Sushko (1987). Section 2 of the present paper gives a review of the available results on longitudinal spectra and cospectra of wind velocity and temperature fluctuations in neutral stratification and examines the consequences of these results related to the longitudinal autocorrelation and symmetrized cross-correlation functions of surface-layer turbulence. In Section 3 it is shown that the correlation equations of Section 2 agree satisfactorily with some recent measurements of the longitudinal correlation functions in the range of distances from 3 m to 100 m. Some measurements of the lateral correlation functions of atmospheric turbulence are also presented in Section 3. It is shown that these measurements lead to some predictions concerning the never-measured lateral space spectra of surface-layer turbulence.

Simulations of electron beam excited modes in the high‐altitude magnetosphere

Excitation of waves by electron distributions consisting of hot, beam, and cold populations is investigated theoretically and with the help of particle simulations. The main modes excited include the upper hybrid oscillation for nearly perpendicular propagation; the whistler mode at oblique angles, which becomes the plasma two‐stream oscillation for parallel propagation; and the electron acoustic mode for nearly parallel propagation. The whistler mode, excited by thermal fluctuation enhancement, has a broad range of wave numbers and quasi‐linearly decreases the beam slope, while the electron acoustic mode, which is linearly unstable, has a narrow spread in phase velocities and traps the beam and the warm electrons forming a double humped distribution. Both modes contribute to forming a tail in the cold electron distribution. The resulting wave spectrum is discussed in the context of DE 1 observations.