Transient growth and minimal defects: Two possible initial paths of transition to turbulence in plane shear flows
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Two possible initial paths of transition to turbulence in simple wall-bounded shear flows are examined by looking at the development in space of infinitesimal disturbances. The first is the—by-now-classical—transient growth scenario which may have an important role in the bypass transition of flows for which traditional eigenmode analysis predicts asymptotic stability. It is studied by means of a simplified parabolic model justified by the underlying physics of the problem; results for optimal disturbances and maximum transient growth are found in excellent agreement with computations based on the full Orr–Sommerfeld/Squire equations. The second path starts with the exponential amplification, in nominally subcritical conditions, of modal disturbances superposed to base flows mildly distorted compared to their idealized counterparts. Such mean flow distortions might arise from the presence of unwanted external forcing related, for example, to the experimental environment. A technique is described that is capable of providing the worst case distortion of fixed norm for any ideal base flow, i.e., that base flow modification capable of maximizing the amplification rate of a given instability mode. Both initial paths considered here provide feasible initial conditions for the transition process, and it is likely that in most practical situations algebraic and exponential growth mechanisms are concurrently at play in destabilizing plane shear flows.Abstract We present the first theoretical γ Doradus instability strip. We find that our model instability strip agrees very well with the previously established, observationally based, instability strip of Handler & Shobbrook (2002). We stress, as in Guzik et al. (2000), that the convection zone depth plays the major role in the determination of our instability strip. Once this depth becomes too deep or too shallow, the convection zone no longer allows for pulsational instability.
Instability strip
Convective instability
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Envelope (radar)
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It has been demonstrated using numerical simulation of two-dimensional ion temperature gradient (ITG) equations that a periodic array consisting of large scale convective cells is subject to shear flow instability. A dynamically global and self-consistent evolution of linearly unstable modes, close to marginal instability, leads to the formation of poloidal shear flow through the process of peeling-instability. The saturated state thus comprises radially localized and polloidally extended length scales, namely, zonal flows. The zonal flows are predominantly led by the perturbed shear flow, whose growth rate is larger than the linear ITG instability.
Marginal stability
Zonal flow (plasma)
Convective instability
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It has been shown in an earlier paper [Phys. Fluids B 5, 344 (1993)] that the ion flow speed of a plasma can be much smaller than the E×B speed in a strongly double-sheared electric field. In this paper, the stability of the plasma is investigated. It is found that a new instability, driven by the difference between the ion and electron flow speed, occurs and may dominate the Kelvin–Helmholtz (KH) instability in a nonuniform plasma. This new instability has a driving mechanism similar to that of the Simon–Hoh instability and is thus called the collisionless Simon–Hoh (CSH) instability. When the CSH instability dominates, the plasma does not become more unstable as the electric field is increased, in contrast to scenarios where the KH instability is dominant.
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The mirror instability is prevalent in planetary and cometary magnetosheaths and other high beta environments. We review the physics of the linear instability. Although the instability was originally derived from magnetohydrodynamic fluid theory, later work showed that there were significant differences between the fluid theory and a more rigorous kinetic approach. Here we point out that the instability mechanism hinges on the special behavior of particles with small velocity along the field. We call such particles resonant particles by analogy with other uses of the term, but there are significant differences between the behavior of the resonant particles in this instability and in other instabilities driven by resonant particles. We comment on the implications of these results for our understanding of the observations of mirror instability‐generated signals in space.
Richtmyer–Meshkov instability
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We report that a secondary, Rayleigh‐Taylor type instability can exist in cosmic‐ray dominated media which are perturbed by the 1D acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the 1D acoustic instability itself in the cases we have considered. We show that flows in the precursor and postshock regions can become highly turbulent due to the secondary instability. As in the 1D acoustic instability, however, the cosmic‐ray pressure is not significantly affected by the presence of the secondary instability, because the cosmic ray diffusion timescale from the perturbations is much smaller than the growth timescale of the instability.
WKB approximation
Streaming instability
Rayleigh–Taylor instability
Richtmyer–Meshkov instability
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The equation of motion whose general restoring terms are modified from these derived in the previous paper is analyzed to show the physical explanation of the instability phenomena of the previous system. This analysis shows that the instability characteristics are decided by the symmetry of the non-diagonal elements of the restoring term. Based on this result, the instability analysis of the previous system is performed more exactly than in the previous paper. As a result of the analysis, the following new points are found : the difference of the instability tendency between models M-4 and S-4 is caused by the instability type i.e. statical or dynamical instability ; Statical instability as well as dynamical instability can occur in model M-4 ; Statical instability can occur also in model S-2.
Constant (computer programming)
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Abstract Freezing colloidal suspensions widely exists in nature and industry. Interface instability has attracted much attention for the understandings of the pattern formation in freezing colloidal suspensions. However, the interface instability modes, the origin of the ice banding or ice lamellae, are still unclear. In-situ experimental observation of the onset of interface instability remains absent up to now. Here, by directly imaging the initial transient stage of planar interface instability in directional freezing colloidal suspensions, we proposed three interface instability modes, Mullins-Sekerka instability, global split instability and local split instability. The intrinsic mechanism of the instability modes comes from the competition of the solute boundary layer and the particle boundary layer, which only can be revealed from the initial transient stage of planar instability in directional freezing.
Richtmyer–Meshkov instability
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