Doubly symmetric finite-core heton equilibria

2012 ◽  
Vol 708 ◽  
pp. 397-417 ◽  
Author(s):  
V. G. Makarov ◽  
M. A. Sokolovskiy ◽  
Z. Kizner
Keyword(s):  
Potential Vorticity ◽  
Critical Size ◽  
Frame Of Reference ◽  
Rotating Fluid ◽  
Initial State ◽  
Transverse Axis ◽  
Dimensional Parameters ◽  
The Stability ◽  
Front Point ◽  
Half Length

AbstractA finite-core heton is a baroclinic $f$-plane modon of a special type: it is composed of two patches of uniform quasi-geostrophic potential vorticity (PV) residing in different layers of a two-layer rotating fluid. This paper focuses on numerical construction of steadily translating, doubly symmetric, finite-core hetons and testing their stability. Such a heton, which possesses symmetry about the translation axis and the transverse axis, is a stationary solution to the equations of PV conservation in each of the layers when considered in a comoving frame of reference. When constructing the heton solutions and examining their bifurcations, we identify a heton by a pair of independent non-dimensional parameters, the half-length (in the translation direction) of a PV patch and the distance of the front point of the upper patch from the translation axis. The advantage of this method over other tried approaches is that it allows one to obtain solutions of new, previously unknown types. The results of testing the heton stability are presented on the plane made by a mean radius of a PV patch and the (horizontal) separation between the centroids of the patches. Two kinds of stability are tested separately, the stability to arbitrary perturbations that do not preserve the symmetry of the initial state and the stability to so-called symmetric perturbations that do not violate the initial symmetry. The hetons comparable in size with the Rossby radius, and smaller, are always stable in both senses. However, when some critical size is exceeded, the heton stability becomes dependent on the separation, and the larger the heton, the higher the separation required for stability. The separation guaranteeing the stability to symmetric perturbations is smaller than that required for the stability to arbitrary perturbations. Interrelations between instabilities and bifurcations are briefly discussed.

scholarly journals On the stability of ocean overflows

2008 ◽  
Vol 602 ◽  
pp. 241-266 ◽  
Author(s):  
LARRY J. PRATT ◽  
KARL R. HELFRICH ◽  
DAVID LEEN
Keyword(s):  
Potential Vorticity ◽  
Growth Rates ◽  
Deep Ocean ◽  
Basic Flow ◽  
Necessary Condition ◽  
Zero Energy ◽  
Coriolis Parameter ◽  
Hydraulic Behaviour ◽  
Zero Potential ◽  
The Stability

The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ>0, with the reverse occurring for κ<0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.

Output Feedback of Uncertain Multi-Input Systems

2020 ◽  
pp. 169-198
Author(s):  
Yang Zhu ◽  
Miroslav Krstic
Keyword(s):  
Output Feedback ◽  
Stability Result ◽  
Initial State ◽  
Linear Controller ◽  
Single Input ◽  
The Stability ◽  
Input Delays ◽  
Local Result ◽  
Practical Sense ◽  
Initial Delay

This chapter evaluates output feedback of uncertain multi-input systems. Similar to the case of single-input delay, the result of multi-input delays obtained in the chapter is not global, as it does not believe the problem where the actuator state is not measurable and the delay value is unknown at the same time is solvable globally, since the problem is not linearly parameterized. In a practical sense, the stability result proven in the chapter is not a highly satisfactory result since it is local both in the initial state and in the initial parameter error. This means that the initial delay estimate needs to be sufficiently close to the true delay. Under such an assumption, one might as well use a linear controller and rely on robustness of the feedback law to small errors in the assumed delay value. Nevertheless, the chapter presents the local result here as it highlights quite clearly why a global result is not obtainable when both the delay value and the delay state are unavailable.

Zur Formalisierung gruppendynamischer Konzepte / Inquiries in formalizing group-dynamic concepts

1975 ◽  
Vol 4 (2) ◽  
Author(s):  
Bruno Meile
Keyword(s):  
Set Theory ◽  
Group Structure ◽  
Frame Of Reference ◽  
Group Dynamic ◽  
Descriptive Model ◽  
Group Research ◽  
Basic Frame ◽  
The Stability

AbstractThe author tries to establish a formal-descriptive model for group-dynamic concepts in related logical terms and set theory. Cybernetics form the basic frame of reference. Herewith some fundamental principles such as ‘group’, ‘group structure’ and ‘change of group structure’ are defined exactly. - The consequences for empirical group research are shown by some examples: (1) a possible way out of the ‘methodological dilemma’ in sociometry,(2) a design for empirical description of the changes in group structure, (3) the formalization of a group-dynamic theorem, whereby groups of friends form according to the principle of individuals who share the same attributes. (4) The reshaping of the theorem allows the deduction of exact terminological hypotheses. New hypotheses, concerning the stability of group structure, can be gained through consideration of the cybernetic implications.

Introduction to Inertial Navigation

1956 ◽  
Vol 9 (3) ◽  
pp. 249-259 ◽  
Author(s):  
D. E. Adams
Keyword(s):  
Inertial Navigation ◽  
Frame Of Reference ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Initial State ◽  
Velocity Change

Inertia is that property of matter which opposes change of motion. Inertial navigation systems utilize this property for the detection and measurement of linear accelerations and rotations in order to arrive at velocity change and displacement relative to some known initial state in a particular frame of reference.

Co-rotating stationary states and vertical alignment of geostrophic vortices with thin cores

1998 ◽  
Vol 357 ◽  
pp. 321-349 ◽  
Author(s):  
GEORGI G. SUTYRIN ◽  
JAMES C. McWILLIAMS ◽  
R. SARAVANAN
Keyword(s):  
Potential Vorticity ◽  
Numerical Solutions ◽  
Pair Interaction ◽  
Evolutionary Stage ◽  
Stationary States ◽  
Rotating Fluid ◽  
Dynamics Model ◽  
Vertical Alignment ◽  
Vortex Interactions ◽  
Strong Vortex

We investigate the evolution of nearby like-sign vortices whose centres are at different vertical levels in a stably stratified rotating fluid. We employ two differently singularized representations of the potential vorticity distribution in the quasi-geostrophic equations (QG), in order to elucidate the pair-interaction behaviour previously seen in non-singular QG numerical solutions. The first is an analytically tractable conservative (Hamiltonian) elliptical-moment model (EM) for thin-core vortices, which exhibits a regime of very strong horizontal elongation of a vortex in response to the strain induced by its partner. We interpret this as an early evolutionary stage towards the irreversible dissipative merger and alignment interactions. This interpretation is strengthened by weakly dissipative numerical solutions of a thin-core contour-dynamics model (CD), which exhibit even further progress towards the completion of these vortex interactions in the same regime.In the EM model we classify the co-rotating stationary states which exist always for vertically offset thin-core vortices. However, the mutual strain field among the vortices cannot be balanced by co-rotation in a weakly elongated stationary state for a certain class of neighbouring, but substantially non-aligned, vortex configurations, and our interpretive assumption is that such configurations will rapidly evolve in non-singular QG solutions towards a more aligned configuration through significantly non-conservative reorganizations of the potential vorticity field. Both the EM and CD models show qualitatively similar regime boundaries between evolutions with weakly and strongly deformed vortices. In particular, there is a fairly close correspondence between the occurrence of strong vortex elongation in the EM solutions and significant filamentation and splitting in the CD solutions.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

2019 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega ◽  
Michele Greco
Keyword(s):  
Natural Frequency ◽  
Fundamental Mode ◽  
Second Step ◽  
Pressure Side ◽  
Dimensional Model ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Flutter Analysis ◽  
Dimensional Parameters ◽  
The Stability

Abstract A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot’s criterion stating that seals supported in the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the non-dimensional work-per-cycle is derived and new non-dimensional parameters controlling the seal stability identified. It is finally concluded the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.

The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models

1991 ◽  
Vol 231 ◽  
pp. 575-598 ◽  
Author(s):  
D. W. Waugh ◽  
D. G. Dritschel
Keyword(s):  
Green Function ◽  
Shear Flow ◽  
Stream Function ◽  
Potential Vorticity ◽  
Two Dimensional ◽  
Interaction Range ◽  
Inversion Operator ◽  
The Green Function ◽  
The Stability ◽  
Background Shear

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.

scholarly journals YOUNG PEOPLE FEEL WISE, OLD PEOPLE FEEL ENERGETIC: COMPARING AGE STEREOTYPES AND SELF-EVALUATIONS ACROSS ADULTHOOD

2019 ◽  
Vol 3 (Supplement_1) ◽  
pp. S787-S787
Author(s):  
Anna E Kornadt ◽  
Catherine E Bowen ◽  
Svenja M Spuling ◽  
Maja Wiest
Keyword(s):  
Older Adults ◽  
Young People ◽  
Age Groups ◽  
Frame Of Reference ◽  
Questionnaire Data ◽  
Old People ◽  
Younger Adults ◽  
Age Stereotypes ◽  
The Stability

Abstract Using questionnaire data from the MIDUS study (N=6.325) we examined the extent to which people in their late 20s, 40s, and 60s think that positive stereotypic “old” and “young” characteristics describe themselves, their age peers, and other age groups. A constellation of “old” characteristics (e.g., wise, caring, calm) was seen as more descriptive of older adults, while a constellation of “young” characteristics (e.g., healthy, energetic) was seen as more descriptive of younger adults. Self-evaluations were highly positive and largely consistent across age groups. Compared to their age peers, younger adults saw themselves as having as many positive “young” characteristics but more positive “old” characteristics whereas older adults saw themselves as having more positive “young” characteristics but fewer positive “old” characteristics. The results support the stability of the aging self despite the existence of age stereotypes and the role of negative age stereotypes as a frame of reference for making self-evaluations.

Moving sliding mode controller for overhead cranes suffering from matched and unmatched disturbances

2020 ◽  
pp. 014233122092210
Author(s):  
Xiutao Gu ◽  
Weimin Xu
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Time Varying ◽  
Initial State ◽  
Overhead Cranes ◽  
State Variable ◽  
Chattering Free ◽  
The Stability ◽  
Variable Errors

In this paper, a novel time-varying gain extended state observer (ESO)-based moving sliding mode control method is proposed for anti-sway and positioning control of two-dimensional underactuated overhead cranes. The designed moving sliding mode surface can adjust its slope in real time according to the state variable errors; in addition, a dynamic exponential term is added into the moving sliding mode surface so as to drive any initial state variable errors into the sliding surface rapidly, and thereby the robustness of crane systems is improved. Then, a chattering-free reaching law is designed to realize fast convergence of the system state errors, and the input is modelled as a saturated one due to the fact the motor torque is bounded and the control law and adaptive updating law of switching gain are derived in the sense of Lyapunov function, so the stability can be guaranteed even under the input saturation. Moreover, to suppress the matched and unmatched disturbance occurring in crane dynamic systems, a time-varying gain ESO is constructed to estimate the lumped disturbance, then the estimated value is used for feedforward compensation to establish the controller. Finally, the simulation results confirm the effectiveness of the proposed controller.

scholarly journals About the Reliability of Manual Model PV Corrections to Improve Forecasts

2012 ◽  
Vol 27 (6) ◽  
pp. 1554-1567 ◽  
Author(s):  
Philippe Arbogast ◽  
Karine Maynard ◽  
Catherine Piriou
Keyword(s):  
Potential Vorticity ◽  
Initial Conditions ◽  
Primary Source ◽  
Weather Forecast ◽  
Initial State ◽  
Sea Level Pressure ◽  
Potential Vorticity Inversion ◽  
Human Modification ◽  
Balanced Distribution ◽  
Source Of Information

Abstract The National Weather Forecast Centre of Météo-France has developed a tool that corrects the state of the atmosphere within the Action de Recherche Petite Echelle Grande Echelle (ARPEGE) operational global model by adjusting the potential vorticity when the initial conditions and available observations disagree. Among observational datasets, geostationary satellite data are the primary source of information. Here, the representation of the coherent structures of the tropopause in the model is assessed with Meteosat ozone and water vapor images. Modifications to the initial conditions of the potential vorticity (PV) in areas where the model fails can be applied using a potential vorticity inversion, thus providing a new balanced distribution of the wind and temperature that will then be used as a new initial state. The purpose of the paper is to investigate the degrees of weakness of the present qualitative approach. To this end, PV modifications to the initial conditions are applied by different experts on the eve of the windstorm Klaus (24 January 2009) that hit southwestern France. The different initial PV fields and the subsequent forecasts show significant differences in terms of wind and mean sea level pressure, while sharing some common features. The human modification process is therefore partially reproducible and skillful since the forecast is improved most of the time.

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