Unstable Interval Research Articles

Instability of Baroclinic Currents That Are Locally Nonzonal

The zonally localized instability of a zonal flow that has an added meridional component in the zonal interval |x| < a is examined. The flow occurs on the infinite β plane and is analyzed in a two-layer model. The basic flow in the lower layer is zero. The zonal flow velocity is small enough so that it is subcritical with regard to baroclinic instability. The flow is rendered unstable only by its horizontal change of direction, which introduces the meridional flow. The stability problem is solved by matching simple plane wave solutions in the regions upstream, downstream, and within the region of meridional flow. Localized instability is found for all values of the unstable interval a. The growth rate diminishes as a shrinks, but no critical value of a ≠ 0 needs to be exceeded for instability. For small values of a, the disturbance extends well beyond a as a wake of slowly damped downstream radiating waves. However, the heat fluxes driving the instability are sharply confined to |x| < a. Although the instability is possible only because the meridional component of the flow is different from zero, the baroclinic energy conversion of the available potential energy associated with the zonal flow is at least as large as, and usually larger than, that associated with the meridional flow. The authors suggest that the process described in this simple model may be present whenever zonally accelerated flows are locally unstable since the region of zonal acceleration of the flow must be accompanied by meridional flow.

Cardiac instability amplified by use-dependent Na channel blockade.

Drugs that exhibit use-dependent Na channel blockade, including antiarrhythmic agents, tricyclic antidepressants, opiate-like analgesics, and cocaine, are linked with an increased susceptibility to cardiac arrhythmias and sudden death. Computer simulations indicate that Na channel blockade retards recovery of excitability, thereby increasing the spatial dispersion of refractoriness, a precursor of many cardiac arrhythmias. In isolated rabbit left atria, stimuli timed to occur at increasing intervals following conditioning stimuli reveal an unstable interval (vulnerable period) during which single stimuli initiate trains of responses. The vulnerable period is extended by use-dependent Na channel blockade and provides a model for assaying proarrhythmic potential and probing cardiac instability.

Some stability-instability problems in phase transitions modelled by piecewise linear elastic or viscoelastic constitutive equations

This paper compares an elastic model of van der Waals type for phase transitions with a Maxwell type viscoelastic model which has in equilibrium the same pressure-volume relation. A typical perturbed quasistatic “piston problem” which will move the body from one phase to another is discussed. The problem is treated for both models as a dynamical one since the loss of stability seems to be better described in a dynamic frame. The elastic problem is ill-posed in the sense that it may fail to have a solution in the phase transition interval (also called the unstable interval). The viscoelastic problem has always solutions and any perturbation is damped out outside the phase transition interval and it may be exponentially amplified in the phase transition interval. This behaviour of the viscoelastic model agrees qualitatively well with the experimental observations of phase transitions in both fluids and solids.

Local baroclinic instability of flow over variable topography

Local baroclinic instability is studied in a two-layer quasi-geostrophic model. Variable meridional bottom slope controls the local supercriticality of a uniform zonal flow. Solutions are found by matching pressure, velocity, and upper-layer vorticity across longitudes where the bottom slope changes abruptly so as to destabilize the flow in a central interval of limited zonal extent. In contrast to previous results from heuristic models, an infinite number of modes exist for arbitrarily short intervals. For long intervals, modal growth rates and frequencies approach the numerical and WKB results for the most unstable mode. For intervals of length comparable to and smaller than the wavelengths of unstable waves in the homogeneous problem, the WKB results lose accuracy. The modes retain large growth rates (about half maximum) for intervals as short as the internal deformation radius. Evidently, the deformation radius and not the homogeneous instability determines the fundamental scale for local instability. Maximum amplitudes occur near the downstream edge of the unstable interval. Lower-layer amplitudes decay downstream more rapidly than upper-layer amplitudes. For short intervals, the instability couples motions with widely disparate horizontal scales in the upper and lower layers. Heat flux is more strictly confined than amplitude. Growth rates increase linearly with weak supercriticality.

Simple Models for Local Instabilities in Zonally Inhomogeneous Flows

Two very simple model equations, suggested by the form of the standard baroclinic instability dispersion relation. are studied to investigate the nature of the instability of zonally inhomogeneous flows. In particular, the simplifications of the model problems allow the consideration of examples in which the interval of instability is of the same order or even smaller than the characteristic wavelength of the free plane wave modes of the zonally homogeneous problem, a limit inaccessible to standard WKB procedures. In both model problems it is shown that the zonally gravest mode always remain no matter how small the locally unstable interval may be. Further, this gravest mode is eddy-like rather than wave-like, i.e., it has no internal nodes. When the free wave solutions are allowed to propagate, the structures of the bound modes are altered. They are squeezed against the exit edges of the unstable domain but again one mode, the bound eddy mode, is always possible. This study is complementary to the more elaborate WKB analyses recently published and, in agreement with these studies, it is shown that only local maxima in supercriticality are required to yield trapped modes. The bound eddy mode is, however,. a feature allowable only when WKB analysis fails. It is suggested that such bound eddies, anchored to local maxima in supercriticality may be regarded as the preliminary stage for the production of isolated, coherent structures.

Development of the Criterion Task Set Performance Data Base

The initial phase of a large-scale experimental study was conducted involving the training and testing of fifty human subjects on the Criterion Task Set (Version 1.0). Testing was performed under baseline conditions and the stressors of noise and sleep loss. The resulting data base includes CTS performance data and subjective ratings obtained using the Subjective Workload Assessment Technique (SWAT) for each task, along with information on subject individual differences. This paper presents the methodology used for the data collection and analysis efforts and provides a summary of the performance and subjective assessment information. In general, no performance differences were found under the noise stress condition. Following sleep loss, response times for the central processing tasks deteriorated as did performance on the Unstable Tracking and Interval Production tasks.

High-Frequency Flutelike Instabilities in Multicomponent Plasmas

Plasma in a magnetic field B is subject to unstable electrostatic gyroharmonic waves propagating across B, if the distribution of f0 of particle velocities v⊥(⊥ to B) has a region where ∂f0/∂v⊥ &amp;gt; 0. Stability limits are found for f0 representative of mirror-confined plasmas having a “warm” Maxwellian species, an otherwise identical “hot” species with a region of positive ∂f0/∂v⊥, and a neutralizing background. The waves are stable if the ratio of mean energies of the warm to hot species exceeds 0.1, or if the ratio of densities does not fall in an unstable interval roughly characterized by 0.01 ≲ NW/NH ≲ 1, with more precise criteria given by Eqs. (5) and (6). It is important for fusion experiments that the conditions necessary for stability are less restrictive than the sufficient condition: ∂f0/∂v⊥ &amp;lt; 0 for all the species.