Unstable Side Research Articles

Plasma instabilities observed in the E region over Arecibo and a proposed nonlocal theory

We describe simultaneous radar observations made with the Cornell University Portable Radar Interferometer (CUPRI) at 50 MHz and the Arecibo incoherent scatter radar (ISR) at 430 MHz during the El Coquí campaign of 1992 in Puerto Rico. The goal was to study the plasma instabilities that cause coherent radar backscatter from the E region at mid-latitudes. The common volume data reveal that the coherent CUPRI echoes come from sporadic-E layers that exhibit no obvious gravity wave modulation but possess high densities and sharp gradients. The echoes with positive (negative) Doppler shifts, i.e. eastward (westward) plasma wave phase velocities, come from the top (bottom) of the layer, in agreement with simple local equatorial gradient-drift instability theory, even though this theory is not valid at mid-latitudes, where nonlocal shorting effects along magnetic field lines play a crucial role. We have developed a nonlocal theory that takes these effects into account. Our theory, which is discussed in detail in a companion paper, does not invoke any unusual layer geometry, in contrast to the ideas proposed in several papers in recent years. The unstable eigenmodes are a sum of plane waves with k -vectors having a small component parallel to the geomagnetic field, such that the modes are confined primarily to either the top or bottom of the layer, depending on the driving electric field. The direction of these k -vectors deviates from normal to the magnetic field by at most a few tenths of a degree. The k -vectors are also approximately aligned with the E × B drift. While both the density and potential fluctuations peak in amplitude on the unstable side of the layer, the density peak is closer to the maximum of the layer than is the potential peak. We do not in this paper deal with the “quasi-periodic” or QP nature of the radar echoes that is sometimes, but certainly not always, seen.

Numerical study of the effects of rotation on heat transfer in channels with and without ribs

Large eddy simulation of rotating channel and ribbed channel flows with and without heat transfer is reported. The rotation axis is parallel to the spanwise direction of the parallel plate channel. An implicit finite-volume scheme was used to solve the preconditioned time-dependent filtered Navier–Stokes equations using a dynamic subgrid-scale model to account for the subgrid-scale effects. The distribution of mean velocity and mean temperature were influenced by system rotation, transforming from a symmetric profile into a non-symmetric profile. The shift of peak values was toward the stable side of the channel. Near the stable (leading) side, the turbulent intensities and heat transfer were suppressed, but turbulence was enhanced with increasing shear stress and turbulent kinetic energy near the unstable (trailing) side.

A nonlocal theory of the gradient-drift instability in the ionospheric E-region plasma at mid-latitudes

The instability which arises in thin ionization layers in the ionospheric E region is inherently nonlocal at mid-latitudes because of the high conductivity along the inclined magnetic field lines. We attack the gradient-drift stability problem using a numerical matrix method, with a finite Fourier basis for the density and potential perturbations, and find complex eigenfunctions and eigenvalues. A thin density layer with steep edges, superimposed on a constant background, is unstable at modes that are centered on the locally unstable side but extend into the locally stable region. The finite background density is essential, but of course there always is such a background in the ionosphere. An interesting aspect of the solutions is that the electric field perturbations peak at distances farther away from the layer than do the density perturbations. The growth rate of the nonlocal modes is significantly smaller than that predicted by local theory (which omits the damping effect of coupling along the magnetic field lines), as expected, and so the waves must be strongly driven. But for ambient electric field strengths of a few mV/m, or an equivalent wind velocity, the growth rates are sufficient to explain sounding rocket and radar observations of plasma waves associated with sporadic- E layers. We also find that the unstable plasma waves propagate in directions that differ from normal to the magnetic field by less than a degree, probably less than half a degree, in agreement with radar observations.

Infant Sleeping Position and the Risk of Sudden Infant Death Syndrome in California, 1997–2000

Li, De-Kun; Petitti, Diana B.; Willinger, Marian; McMahon, Robin; Odouli, Roxana; Vu, Hong; Hoffman, Howard J.

The effect of instability and subsequent anterior shoulder repair on proprioceptive ability

Proprioceptive ability was prospectively evaluated in patients with recurrent traumatic anterior instability who subsequently underwent anterior shoulder repair. Thirty consecutive patients were evaluated for passive position sense and detection of motion with the shoulder in flexion, abduction, and external rotation 1 week before surgery. They were then retested at 6 and 12 months postoperatively. A significant deficit in proprioception was found when the unstable side was compared with the uninvolved side before surgery. Six months after surgical repair, position sense showed an improvement of approximately 50% but was still found to be significantly different on the involved side; detection of motion was no longer significantly different from the uninvolved shoulder. One year after open anterior shoulder repair, both position sense and detection of motion were equivalent to those of the uninvolved shoulder. (J Shoulder Elbow Surg 2003;12:105-9)

Infant sleeping position and the risk of sudden infant death syndrome in California, 1997-2000.

To assess the association between infant sleeping position and risk of sudden infant death syndrome (SIDS) in an ethnically diverse US population, the authors conducted a population-based case-control study in 11 counties in California from May 1997 through April 2000. The authors conducted in-person interviews with the mothers of 185 SIDS cases and 312 randomly selected race/ethnicity- and age-matched controls to collect information on sleeping positions. Infants who had last been put down to sleep in the prone or side position were at greater risk of SIDS than were infants who had last been put down on their backs (adjusted odds ratio (AOR) = 2.6 (95% confidence interval (CI): 1.5, 4.5) and AOR = 2.0 (95% CI: 1.2, 3.4) for the prone and side positions, respectively). The risk of SIDS was especially high for an unstable side position in which an infant was placed on its side and found prone (AOR = 8.7, 95% CI: 3.3, 22.7). Infants who were usually placed on their backs to sleep but had last been put down in the prone or side position (an unaccustomed position) had a significantly high risk of SIDS (AOR = 8.2 (95% CI: 2.6, 26.0) and AOR = 6.9 (95% CI: 2.3, 20.6) for the prone and side positions, respectively). Infants placed in an unaccustomed prone or side sleeping position had a higher risk of SIDS than infants who were always placed prone or on the side.

Thermozymes and Their Applications: A Review of Recent Literature and Patents

Enzymes from thermophilic microorganisms, thermozymes, have unique characteristics such as temperature, chemical, and pH stability. They can be used in several industrial processes, in which they replace mesophilic enzymes or chemicals. Thermozymes are often used when the enzymatic process is compatible with existing (high-temperature) process conditions. The main advantages of performing processes at higher temperatures are reduced risk of microbial contamination, lower viscosity, improved transfer rates, and improved solubility of substrates. However, cofactors, substrates, or products might be unstable or other side reactions may occur. Recent developments show that thermophiles are a good source of novel catalysts that are of great industrial interest. Thermostable polymer-degrading enzymes such as amylases, pullulanases, xylanases, proteases, and cellulases are expected to play an important role in food, chemical, pharmaceutical, paper, pulp, and waste-treatment industries. Considerable research efforts have been made to better understand the stability of thermozymes. There are no major conformational differences with mesophilic enzymes, and a small number of extra salt bridges, hydrophobic interactions, or hydrogen bounds seem to confer the extra degree of stabilization. Currently, overexpression of thermozymes in standard Escherichia coli allows the production of much larger quantities of enzymes, which are easy to purify by heat treatment. With wider availability and lower cost, thermophilic enzymes will see more application in industry.

Increased inversion angle replication error in functional ankle instability.

The inversion-angle replication error of the ankle joint was measured in subjects with a functionally stable or unstable ankle. Testing was performed as a passive set-active replication design. The absolute replication error on the unstable side of 23 unilaterally, functionally, and mechanically unstable subjects was found to be significantly greater (2.5 degrees) than the error on the healthy contralateral side (2.0 degrees ; P < 0.05) and the error in a group of 40 ankle healthy controls (1.7 degrees; P < 0.01). In 10 ankle-healthy high-level cross-country runners the replication error was reduced by 38% after warming up (P = 0.04).

Magnetohydrodynamic spectrum of gravitating plane plasmas with flow

The ideal magnetohydrodynamic spectrum of gravitating plane plasmas with equilibrium flow is investigated. Flow makes the spectral problem non-self-adjoint, so that the spectrum can become overstable. The criteria for cluster spectra to appear are derived analytically and both stable and unstable sides of the spectrum are examined numerically. Above certain critical values of the shear flow at the resonant surface, the gravitating interchange modes disappear. However, the local extrema of the continua can then take over the cluster spectrum.

On the convection in an enclosed container with unstable side wall temperature distributions

A numerical study of natural convection in a two-dimensional container of unity aspect ratio with unstable temperature distributions on the side walls and adiabatic top and bottom walls is discussed for a Boussinesq fluid with unity Prandtl number. For sufficiently low Rayleigh numbers and symmetric boundary conditions a unique 2 × 2 steady cellular flow with horizontal and vertical symmetry exists. At a critical Rayleigh number a pitchfork bifurcation occurs creating a pair of asymmetric steady solutions. Further increasing the Rayleigh number causes the asymmetric pair of steady solutions to undergo a subcritical Hopf bifurcation resulting in a large amplitude limit cycle. Hysteresis behavior is observed between the stable steady flows and the stable limit cycle for a range of Rayleigh numbers. The limit cycle disappears at a minimum Rayleigh number in what appears to be a double homoclinic orbit. Applying asymmetric temperature boundary conditions causes an unfolding of the pitchfork bifurcation. The character of the Hopf bifurcations and resulting limit cycle behavior is deeply affected by the introduction of asymmetry. As the Rayleigh number is increased a progression of limit cycles containing from two to 206 small amplitude oscillations and one large amplitude ‘relaxation’ oscillation per period are separated by what may be a series of homoclinic orbits. The steady and limit cycle solution structure has a large influence on the heat transfer rate through the container.

Nonlinear dynamics of a nuclear-coupled boiling channel with forced flows

The nonlinear dynamics of a nuclear-coupled boiling channel with forced flows was explored on the basis of the Galerkin nodal approximation method for the channel fluid flow and point kinetics for the neutron field dynamics. The marginal stability boundary (MSB) for a Freon boiling channel predicted by the model agreed well with experimental data from previous available literature, thereby verifying the model accuracy. A strip of limit cycle oscillation on the unstable side of the boundary was found to be system dependent. The marginal stability boundaries for boiling water channels with/without nuclear-coupled effects were also obtained. Moreover, the characteristics of limit cycle oscillations on the boundary were investigated. Routes from limit cycle oscillation to chaotic oscillation were identified under high inlet subcooling conditions. The strange attractor found in this study was characterized by a correlation dimension of 1.69±0.01.

Chaotic itinerancy with preferred transition routes appearing in an atmospheric model

By using an atmospheric model with realistic topography, we obtain a chaotic itinerancy phenomenon in which system trajectories stay within attractor ruins for a long time, moving promptly among them. There are preferred routes in transitions among attractor ruins. These characteristics coincide well with those of weather regimes in the real atmosphere. The dynamical basis of preferred transition routes is as follows: Three or more attractors coexist at stable sides of parameter values. When parameters are changed to unstable sides, these attractors lose their stability one by one at different parameter values. This is to the lack of spatial symmetry in the attractors of the present system. Trajectories starting from one attractor ruin converge into another attractor. With further changes in parameters, an explosive bifurcation takes place, after which trajectories itinerate among attractor ruins. The existence of preferred routes is understood as a natural consequence of the spatial asymmetry among the original attractors. The result is robust: In wide ranges of parameters, attractor ruins are recognizable and system trajectories have preferred routes in transitions.

Near-wall Reynolds-stress modelling in noninertial frames of reference

Second-moment closure predictions of fully developed turbulent Poiseuille and Couette flow subjected to spanwise rotation are verified against direct numerical and large eddy simulations in addition to recent experimental results. Near-wall effects are modelled by elliptic relaxation which is used in conjunction with a nonlinear, variable-coefficient pressure strain model consistent with the principle of material frame indifference (MFI) in the limit of two-dimensional turbulence. The dissipation rate model equation is modified in the near-wall region to become explicitly dependent on the imposed system rotation, however, without violating the MFI principle. The model predictions exhibit many of the features due to the Coriolis force on the turbulence and mean flow field, respectively. These include an almost irrotational region in the channel core, augmentation of the turbulence on the unstable side and a corresponding reduction on the stable side, relaminarisation caused not only by stabilising rotation but also by sufficiently high destabilising rotation in Couette flow and, finally, localised regions in the core of the Poiseuille flow where mean flow energy is extracted from the turbulence. The effects of rotational-induced secondary motions on the flow field are also addressed.

Numerical Analysis of Rotating Channel Flow with an Anisotropic $k-\varepsilon$ Turbulence Model

An anisotropic k-.epsilon. turbulence model for predicting the rotating flows is proposed with the simple inclusion of a new parameter dealing with the extra straining effects in the .epsilon.-equation. This model is employed to compute the effects of Coriolis forces on fully-developed flow in a rotating channel. The predicted results indicate that the present model captures fairly well the striking rotational-induced effects on the Reynolds stresses and the mean flow distributions, including the argumentation of turbulent transport on the unstable side (pressure surface) of the channel and its damping on the stable side (suction surface).

Experimental study of heat and momentum transfer in rotating channel flow

The enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolis instability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non-linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non-linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation.

A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water

The modified nonlinear Schrödinger equation of Dysthe [ Proc. Roy. Soc. Lond. Ser. A, 369, 105–114 (1979)] is extended by relaxing the narrow bandwidth constraint to make it more suitable for application to a realistic ocean wave spectrum. The new equation limits the bandwidth of unstable wave number perturbations of a Stokes wave in good agreement with the exact results of McLean et al. [ Phys. Rev. Lett. 46, 817–820 (1981)]. Results are presented for the parametric bifurcation boundary between collinear and oblique most unstable side band perturbations of a Stokes wave.

The boundaries of large-scale collapse on the flanks of Mount Etna, Sicily

Abstract Proposals for flank collapse on Etna find agreement from recent authors but models differ considerably in the scale and nature of the instability. Our work, including a new compilation of subsurface data, identifies the Ragalna system of linked faults and cinder cones as defining the southern margin of a very wide sector of flank instability comprising over 50% of the volcanic edifice. The Mascalucia and Trecastagni faults, previously identified as the southern boundary, occur within this sector and are now regarded as two examples of a number of relatively superficial faults accommodating differential movement. By comparison, faulting on the Ragalna system has produced very fresh-appearing scarps up to 20 m in height associated with dominantly dip-slip displacement. This pattern is expected on a boundary fault, the unstable side of which is moving downslope. The problem of the enigmatic triangular horst which abruptly terminates the surface expression of the Ragalna system at its upslope end may now be viewed in the light of new scale-model experiments which predict that such features are the likely result of spreading within a volcanic edifice. This helps explain the lack of a clear surface connection between the obviously active Ragalna faulting and the summit rifting. If this explanation is correct the Ragalna system assumes similar continuity and dimensions as the Pernicana — a system of linked structures generally accepted as defining the northern boundary of instability. The scale of the collapse is well within that predicted by the model experiments. Topographic buttressing on the northwestern arc of the volcano is mirrored by the absence of such support on the unstable southeastern arc where the flanks are bordered either by the sea or by a sedimentary trough (Gela-Catania Foredeep) occupied by recent plastic clays close to sea level. In addition, the rapidly growing volcanic edifice, approaching 3.5 km in some 300 ka, straddles the thrusted nappes of the Appennine-Maghrebian Chain to the northwest and the weak sediments of the Gela-Catania Foredeep to the southeast, with their contact beneath the volcano probably contributing to the location of the unstable sector. Minimum long-term slip rates determined from outcrop information on the Ragalna, and determined independently from subsurface data on the basal detachment underlying the collapsing sector are similar, arguing for a mechanical connection as would be expected if the Ragalna system formed the boundary to the basal detachment. A deep detachment model is consistent with focal depths on the Ragalna and with recent data on the timing of regional deformation in the Chain compared to the later timing of local (collapse-induced) deformation within the Etnean realm. The amplitude and wavelength of the local deformation, particularly on the southern margin of the volcano, is inconsistent in magnitude with that expected mechanically if the detachment was relatively superficial. A deep detachment is also indicated by the space requirements of a plutonic sequence postulated on geological and geophysical grounds below the summit region of the volcano.

Three-dimensional structure of straight and curved plane wakes

The formation and evolution of the three-dimensional structure of straight and mildly curved ($b/\bar{R} &lt; 2\%$) flat plate wakes at relatively high Reynolds numbers (Reb = 28 000) have been studied through detailed measurements of the mean and fluctuating velocities. In both cases, the role of initial conditions was examined by generating wakes from untripped (laminar) and tripped (turbulent) initial boundary layers. The curved wake was affected by the angular momentum instability such that the inside half of the wake was unstable, whereas the outside half was stable. In both the straight and curved untripped wakes, large spanwise variations, in the form of ‘pinches’ and ‘crests’, were observed in the contours of mean velocity and Reynolds stresses. Well-organized, ‘spatially stationary’ streamwise vorticity was generated in the near-field region in the form of quadrupoles, to which the spanwise variations in the velocity contours were attributed. The presence of mean streamwise vorticity had a significant effect on the wake growth and defect decay rates, mainly by providing additional entrainment. In the straight wake, the mean streamwise vorticity decayed on both sides of the wake such that it had decayed completely by the far-field region. However, in the curved case, the mean streamwise vorticity on the unstable side decayed at a rate significantly lower than that on the stable side. Despite the decay of mean streamwise vorticity, the spanwise variations persisted into the far wake in both cases. The effects of curvature were also apparent in the Reynolds stress results which showed that the levels on the unstable side were increased significantly compared to those on the stable side, with the effect much stronger in the initially laminar wake. With the initial boundary layers tripped, spatially stationary streamwise vortex structures were not observed in either the straight or curved wakes and the velocity contours appeared nominally two-dimensional. This result further confirms the strong dependency of the three-dimensional structure of plane wakes on initial conditions.

Solitons, solitary waves, and voidage disturbances in gas-fluidized beds

In this paper, we consider the evolution of an initially small voidage disturbance in a gas-fluidized bed. Using a one-dimensional model proposed by Needham &amp; Merkin (1983), Crighton (1991) has shown that weakly nonlinear waves of voidage propagate according to the Korteweg–de Vries equation with perturbation terms which can be either amplifying or dissipative, depending on the sign of a coefficient. Here, we investigate the unstable side of the threshold and examine the growth of a single KdV voidage soliton, following its development through several different regimes. As the size of the soliton increases, KdV remains the leading-order equation for some time, but the perturbation terms change, thereby altering the dependence of the amplitude on time. Eventually the disturbance attains a finite amplitude and corresponds to a fully nonlinear solitary wave solution. This matches back directly onto the KdV soliton and tends exponentially to a limiting size. We interpret the series of large-amplitude localized pulses of voidage formed in this way from initial disturbances as corresponding to the ‘voidage slugs’ observed in gas fluidization in narrow tubes.

Laminar burning velocities and Markstein numbers of [formula omitted] flames

Effects of positive flame stretch on the laminar burning velocities of hydrocarbon air mixtures were studied experimentally using outwardly propagating spherical flames. The test conditions included propane, methane, ethane, and ethyleneair flames at various fuel-equivalence ratios and normal temperature and pressure. Karlovitz numbers generally were less than 0.3 so that the flames were remote from quenching conditions. Within this range, the ratio of the unstretched (plane flames) to stretched laminar burning velocities varied linearly with Karlovitz numbers, yielding Markstein numbers that were independent of Karlovitz numbers for a particular reactant mixture. In addition, Markstein numbers varied in a roughly linear manner with fuel-equivalence ratios over the range of the measurements, which were somewhat removed from flammability limits where behavior might differ. Effects of stretch were substantial: Markstein numbers varied from −2.5 to 7.2 yielding corresponding laminar burning velocity variations of 0.4–2.7 times the value for an unstretched (plane) flame over the test range. The ranges of fuel-equivalence ratios for unstable preferential-diffusion conditions (negative Markstein numbers) were as follows: propane, greater than 1.44; methane, less than 0.74; ethane, greater than 1.68; and ethylene, greater than 1.95. Fuel-equivalence ratios for maximum flame temperatures and laminar burning velocities are near unity for the present flames; therefore, neutral preferential-diffusion conditions are shifted toward fuel-equivalence ratios on the unstable side of unity, in qualitative agreement with recent approximate theories treating the effects of stretch on laminar premixed flames.