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At least 19 records

Nonlinear equilibration of localized instabilities on a baroclinic jet

Dynamical mechanisms underlying the equilibration of absolute instability are examined in a nonlinear, quasigeostrophic, two-layer model. The key to understanding the nonlinear equilibration is in recognizing that linear absolute instabilities can be stabilized both by a reduction of the vertical shear and by enhancement of the mean barotropic velocity. In a localized domain, the equilibration process proceeds with the creation of locally convectively unstable regions downstream, which encroach onto the locally absolutely unstable region until the local instability is suppressed. That local instabilities exist only if absolutely unstable regions span a minimum size is verified by eigenvalue calculations of three-dimensional flows. Numerical examples suggest that this critical size is at least 9000 km for a wide range of parameter values chosen to investigate the midlatitude storm tracks. Fluctuations arising from local absolute instability obtain maximum amplitude in the downstream convectively unstable regions rather than in the absolutely unstable regions themselves. Together, these results suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 900 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability.

Delsole, Timothy M.↗

Explorer 18 study of the stability of the magnetopause using a Kelvin-Helmholtz instability criterion

Explorer 18 magnetometer and plasma probe data are used to calculate the magnitude of the Kelvin-Helmholtz instability criterion for 42 crossings of the magnetopause. The 30 crossings through the dipole field region show that for low levels of geomagnetic disturbance ( Kp less than or equal to 2) large regions of the magnetopause near the nose are stable, whereas for higher levels of geomagnetic disturbance (Kp greater than 2) only a small region near the nose is stable. The unstable regions are found further downstream. Similarly, the 12 crossings through the tail show that the unstable regions are downstream of the stable regions. The Kelvin-Helmholtz mechanism might be the 'viscous interaction' discussed by Axford and Hines (1961) and the relevant parameter for worldwide geomagnetic disturbance, just as the southward interplanetary field has been firmly established as the major relevant parameter in the case of substorm activity.

Boller, B. R.↗

Anomalous heating of the polar E region by unstable plasma waves. II - Theory

It is found that anomalous electron temperatures in the disturbed high-latitude E region can be quantitatively explained in terms of heating by unstable plasma waves. The electron temperatures at 110 km have been measured to be as high as 1500 K instead of the expected value of about 300 K. It is shown that by using quasi-linear theory there is an ample source of heat in the unstable waves and that the measured electron temperature profiles have a shape very similar to what is expected from plasma wave heating by the modified two-stream instability. It is found that there is even more heating going to the ion gas, but that the resulting effect on the ion temperature may be difficult to measure. The best estimate of the wave heating rates leads to the conclusion that wave heating can be as much as 50% of the Joule heating for dc electric field strengths of the order of 45 mV/m or greater.

St.-Maurice, J. P.↗

Absolute and convective instability of a cylinder wake

The stability behavior of a circular cross-section cylinder's wake at Reynolds number values of up to 45 is presently investigated by means of local linear stability theory. The steady-wake profiles computed are Navier-Stokes solutions of a uniform, incompressible viscous flow around a cylinder obtained by a spectral method. An absolutely unstable region is found to begin to form at a Reynolds number of about 20, and grows with incresing Reynolds number. The onset of global instability response must be characterized by a critical length of an absolutely unstable region; a critical Reynolds number criterion and preferred frequency are proposed based on linear stability analysis.

Yang, X.↗

Ion-cyclotron waves at Jupiter - Possibility of detection by Ulysses

Recent thermal plasma data and a computer code by Horne (1989) are employed to evaluate the linear-path-integrated gain of waves propagating through the Io to predict the Jovian plasma-wave environment. Estimates of the nonlinear saturation amplitudes are utilized with the thermal plasma data from two frequency bands to study the convective growth of the ion-cyclotron (IC) waves. Strong cyclotron resonant damping is theorized to prevent wave propagation to the lower latitudes, and the thermal plasma and cyclotron resonant energetic ions are expected to further confine the IC waves. L-mode waves below the O(+) gyrofrequency in the equatorial region of the torus are shown to inhabit an unstable region. The IC waves probably achieve nonlinear amplitudes regardless of plasma properties due to the rapid amplification in this region. It is suggested that the Ulysses data complicate the identification of the waves because the magnetometer is not adequately sensitive and because of the low frequency of the plasma-wave detector.

Mei, YI↗

Carbon Dioxide Convection in the Martian Polar Night and Its Implications for Polar Processes

Each Martian year nearly 30% of the atmosphere is exchanged with the polar ice caps. This exchange occurs through a combination of direct surface condensation and atmospheric precipitation of carbon dioxide. It has long been thought the amount of condensation within the polar night is maintained by a balance between diabatic processes such as radiative cooling and latent heating from condensing CO2. This assumption manifests itself in Mars General Circulation Models (GCM) in such a way as to never allow the atmospheric temperature to dip below the saturation temperature of CO2. However, observations from Mars Global Surveyor (MGS) Radio Science (RS) and the Thermal Emission Spectrometer (TES) have demonstrated this assumption to be, at best, approximate. Both RS and TES observations within the polar nights of both poles indicate substantial supersaturated regions with respect to CO2. The observed temperature profiles suggest conditionally unstable regions containing planetary significant amounts of potential convective energy. Presented here are estimates of the total planetary inventory of convective available potential energy (CAPE) and the potential convective energy flux (PCEF). The values for CAPE and PCEF are derived from RS temperature profiles and compared to Mars GCM results using a new convective CO2 cloud model that allows for the formation of CAPE.

Colaprete, A.↗

Titan's Stratospheric Condensibles at High Northern Latitudes During Northern Winter

The Infrared Interferometer Spectrometer (IRIS) instrument on board Voyager 1 caught the first glimpse of an unidentified particulate feature in Titan's stratosphere that spectrally peaks at 221 per centimeter. Until recently, this feature that we have termed 'the haystack,' has been seen persistently at high northern latitudes with the Composite Infrared Spectrometer (CIRS) instrument onboard Cassini, The strength of the haystack emission feature diminishes rapidly with season, becoming drastically reduced at high northern latitudes, as Titan transitions from northern winter into spring, In contrast to IRIS whose shortest wavenumber was 200 per centimeter, CIRS extends down to 10 per centimeter, thus revealing an entirely unexplored spectral region in which nitrile ices have numerous broad lattice vibration features, Unlike the haystack, which is only found at high northern latitudes during northern winter/early northern spring, this geometrically thin nitrile cloud pervades Titan's lower stratosphere, spectrally peaking at 160 per centimeter, and is almost global in extent spanning latitudes 85 N to 600 S, The inference of nitrile ices are consistent with the highly restricted altitude ranges over which these features are observed, and appear to be dominated by a mixture of HCN and HC3N, The narrow range in altitude over which the nitrile ices extend is unlike the haystack, whose vertical distribution is significantly broader, spanning roughly 70 kilometers in altitude in Titan's lower stratosphere, The nitrile clouds that CIRS observes are located in a dynamically stable region of Titan's atmosphere, whereas CH4 clouds, which ordinarily form in the troposphere, form in a more dynamically unstable region, where convective cloud systems tend to occur. In the unusual situation where Titan's tropopause cools significantly from the HASI 70.5K temperature minimum, CH4 should condense in Titan's lower stratosphere, just like the aforementioned nitrile clouds, although in significantly larger abundances. We will present the spectral and vertical distribution of Titan's stratospheric particulates during northern winter on Titan. The drastically changing abundance of the haystack over a small latitude range will be highlighted, specifically comparing the IRIS and CIRS epochs, Finally, we will discuss the situation in which CH4 condenses in Titan's lower stratosphere, forming an unexpected quasi steady-state stratospheric Ice cloud.

Anderson, Carrie↗

The Stability of the Steady State and Bistable Response of a Flexible Rotor Supported on Squeeze Film Dampers

The stability of the steady state response, the bistable response, and the jumping characteristics are analyzed for the case when a system accelerates or decelerates through the bistable region of a flexible rotor-centralized squeeze film damper system. It was found that the system steady state responses have two unstable regions. The larger the unbalance parameter and the smaller the bearing parameter and the external damping ratio, the easier it is for the system to lose stability. The larger the mass ratio and the smaller the stiffness ratio, the lower the threshold rotating speed of instability. The instability of the system steady-state response determined here is due to the system nonsynchronous response in many cases.

Meng, Guang↗

Review of linear compressible stability theory

Aspects of the linear compressible stability theory are considered, with special attention given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For the case of highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region is found to include supersonic outgoing waves. A previously unknown neutral incoming wave has also been identified. An example of viscous multiple solutions is provided, and calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode are presented. It is noted that compressible stability theory is missing a firm connection with boundary-layer transition.

Mack, Leslie M.↗

On radiating baroclinic instability of zonally varying flow

A quasi-geostrophic, two-layer, beta-plane model is used to study the baroclinic instability characteristics of a zonally inhomogeneous flow. It is assumed that the disturbance varied slowly in the cross-stream direction, and the stability problem was formulated as a 1D initial value problem. Emphasis is placed on determining how the vertically averaged wind, local maximum in vertical wind shear, and length of the locally supercritical region combine to yield local instabilities. Analysis of the local disturbance energetics reveals that, for slowly varying basic states, the baroclinic energy conversion predominates within the locally unstable region. Using calculations of the basic state tendencies, it is shown that the net effect of the local instabilities is to redistribute energy from the baroclinic to the barotropic component of the basic state flow.

Finley, Catherine A.↗

Intraseasonal and Interannual Variability of the Quasi-Two Day Wave in the Northern Hemisphere Summer Mesosphere

This study uses global synoptic meteorological fields from a high-altitude data assimilation system to investigate the spatial and temporal characteristics of the quasi-2 day wave (Q2DW) and migrating diurnal tide during the Northern Hemisphere summers of 2007, 2008, and 2009. By applying a 2-dimensional fast Fourier transform to meridional wind and temperature fields, we are able to identify Q2DW source regions and to diagnose propagation of Q2DW activity into the upper mesosphere and lower thermosphere. We find that Q2DW is comprised primarily of westward propagating zonal wavenumber 3 and wavenumber 4 components that originate from within baroclinically unstable regions along the equatorward flank of the summer midlatitude easterly jet. Amplitude variations of wavenumbers 3 and 4 tend to be anti-correlated throughout the summer, with wavenumber 3 maximizing in July and wavenumber 4 maximizing in late June and early August. Monthly mean Q2DW amplitudes between 30 50N latitude are largest when diurnal tidal amplitudes are smallest and vice versa. However, there is no evidence of any rapid amplification of the Q2DW via nonlinear interaction with the diurnal tide. Instead, variations of Q2DW amplitudes during July are closely linked to variations in the strength and location of the easterly jet core from one summer to the next, with a stronger jet producing larger Q2DW amplitudes. Linear instability model calculations based on the assimilated wind fields find fast growing zonal wavenumber 3 and 4 modes with periods near 2 days in the vicinity of the easterly jet.

Two day wave↗

Thickening of axisymmetric accretion disks and flows

A study is made to determine whether or not hot plasma flowing from the inner edge of an accretion disk around a black hole can thicken out of the disk plane with the onset of a Pringle-Rees thermal instability. The instability is caused by the density thinning caused by the sharp increase in radial infall velocity near the radius of the marginally stable circular orbit, or by abrupt variations in viscosity or Lightman-Eardly secular instabilities. An estimate of the thickening timescale is given. Various physically realistic situations involving radial steady-state flow and where significant disk thickening can occur in the region of the radius of the marginally stable circular orbit are identified. It is noted that its evolution into a large spherical cloud would require large velocities of the viscosity parameter and the amount of energy dissipated in the unstable region.

Stoeger, W. R.↗

Convective instabilities in SN 1987A

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

Benz, Willy↗

Backscattering cascade of beam modes off ambient density fluctuations

The effects of a given nonthermal low-frequency density-fluctuation spectrum on the amplification of Langmuir waves by a 'bump-on-tail' beam of electrons are studied. The density-fluctuation spectrum is assumed to contain a uniform distribution of wavelengths ranging from much shorter than the beam mode wavelength to of the same order. This permits multiple large-angle (back) scattering to occur. One-dimensional numerical solutions of the kinetic equations are found which yield criteria for linear saturation of the beam instability of a cascade of backscattering to high wavenumber. The relevant time scales and spectral shapes are also determined in both the stable and unstable regions. Linear damping and Cerenkov emission by a possible nonthermal tail of electrons is taken into account. An application is made to the beam modes observed simultaneously with density fluctuations off the Jovian bow shock. It is shown that the observed level of density fluctuations is sufficient to saturate the unstable Langmuir waves, although nonthermal Landau damping may prevent a cascade to very high wavenumbers.

Russell, D. A.↗

Flight Investigation using Variable-Stability Airplanes of Minimum Stability Requirements for High-Speed, High-Altitude Vehicles

The pilot opinion of the flying qualities of vehicles covering a wide range of longitudinal dynamic characteristics has been determined by the use of a variable-stability airplane. Particular emphasis has been placed on determining the minimum level of stability and control characteristics that the pilot can cope with. There was considerable pilot learning associated with operation in the regions of poor stability characteristics. In the statically stable region the maximum acceptable value of time to damp to half amplitude of the longitudinal mode for normal operation was about 1 second. For emergency conditions the damping could be reduced to zero over most of the frequency range. The extreme lim it of controllability corresponded to a time to double amplitude of the oscillation of about 1 - 1/2 seconds. In the statically unstable region somewhat shorter times to double amplitude were acceptable to the pilots. The boundary for emergency operation corresponded roughly to time to double amplitude of about 2/3 second and the limit of controllability of about l/3 second.

McFadden, Norman M.↗

Low-frequency quasi-periodic oscillations in low-mass X-ray binaries and galactic black hole candidates

We consider the inner regions of accretion disks surrounding black holes and neutron stars and investigate the nonlinear time-dependent evolution of thermal-viscous instabilities. The viscous stress is assumed to be proportional to the gas pressure with the viscosity parameter formulated as alpha = min alpha (sub zero) (h/r) (exp n), alpha(sub max), where h is the local scale height, r is the distance from the central compact object, and n, alpha(sub zero) and alpha(sub max) are constants. It is found that the disk is unstable for alpha sufficiently sensitive to h (n greater than or equal to 1.2). The instabilities are globally coherent in the entire unstable region of the disk, and, depeding on the viscosity parameters, the time variability of the mass accretion rates are manifested as periodic or quasi-periodic oscillations. We show that, the low-frequency (approximately 0.04 Hz) quasi-periodic oscillations (QPOs) discovered recently in some of the black hole candidates (Cyg X-1 and GRO J0422+32) and a low-mass X-ray binary (Rapid Burster MXB 1730-335) may be explicable by the thermal-viscous instabilities in accretion disks. The observations of QPOs place constraints on the viscosity parameters and suggest that (n, alpha(sub zero) approximately (1.6, 30) for the Rapid Burster with a 1.4 solar mass neutron star. In the case of black hole candidates, the dependence of alpha on h/r is less steep corresponding to n approximately 1.2-1.3 for black holes less than 10 solar mass.

Chen, Xingming↗

Nonlinear axisymmetric flexural vibration of spherical shells

Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.

Kunieda, H.↗