scholarly journals Vortex Layer on the β-Plane in the Miles – Ribner Formulation. Pole on the Real Axis

2021 ◽  
Vol 28 (5) ◽  
Author(s):  
V. G. Gnevyshev ◽  
T. V. Belonenko ◽  
◽  
Keyword(s):  
Rossby Waves ◽  
Zonal Flow ◽  
Stationary Wave ◽  
Linear Wave ◽  
Background Flow ◽  
Pure Radiation ◽  
New Class ◽  
Vortex Layer ◽  
Wave Disturbances ◽  
Definition Of

Purpose. The problem of a non-zonal vortex layer on the β-plane in the Miles – Ribner formulation is considered. It is known that in the absence of the β-effect, the vortex layer has no neutral eigenmodes, and the available two ones (varicose and sinusoidal) are unstable. Initially, generalization of the problem to the β-plane concerned only the zonal case. The problem for a non-zonal vortex layer is examined for the first time in the paper. It is known that in the WKB approximation for the linear wave disturbances (regardless of whether a zonal or non-zonal background flow is considered), there is an adiabatic invariant in the form of the law of the enstrophy (vorticity) conservation. For the zonal vortex layer, the enstrophy conservation law also holds, and no vorticity exchange occurs between the waves and the flow in the zonal case. The non-zonal vortex layer has qualitatively different features; particularly, it does not retain enstrophy. Thus, as a result, there appears a new class of solutions which can be interpreted as pure radiation of the Rossby waves by a non-zonal flow. Generalizing the vortex layer problem on the β-plane to the non-zonal case constitutes the basic aim of the present study. Methods and Results. A new class of linear stationary wave solutions, namely the Rossby waves, is found. It is shown a non-zonal flow can be directed in one way, whereas the stationary wave disturbances can move in the opposite (contrary) direction. The coexistence of such solutions for the shear non-zonal flow and stationary wave disturbances takes place due to the influence of the external force and mathematically comes from a non-self-adjoining character of the linear operator for a non-zonal background flow. Conclusions. There exists a new class of solutions that can be interpreted as pure radiation of the Rossby waves by a non-zonal flow. There is no such solution for a zonal flow. It is just non-zoning that gives the effect of pure radiation and corresponds to the classical definition of radiation. This approach makes it possible to eliminate inconsistency in terminology, when instabilities are mistakenly called radiation, and radiation – pure radiation.

Time Scale and Feedback of Zonal-Mean-Flow Variability

2008 ◽  
Vol 65 (3) ◽  
pp. 935-952 ◽  
Author(s):  
Seok-Woo Son ◽  
Sukyoung Lee ◽  
Steven B. Feldstein ◽  
John E. Ten Hoeve
Keyword(s):  
Time Scale ◽  
Lower Boundary ◽  
Zonal Flow ◽  
Stationary Wave ◽  
Mean Flow ◽  
Background Flow ◽  
Dominant Form ◽  
Flow Variability ◽  
Zonal Index ◽  
Single Jet

Abstract The physical processes that determine the time scale of zonal-mean-flow variability are examined with an idealized numerical model that has a zonally symmetric lower boundary. In the part of the parameter space where the time-mean zonal flow is characterized by a single (double) jet, the dominant form of zonal-mean-flow variability is the zonal index (poleward propagation), and the time-mean potential vorticity gradient is found to be strong and sharp (weak and broad). The e-folding time scale of the zonal index is found to be close to 55 days, much longer than the observed 10-day time scale. The e-folding time scale of the poleward propagation is about 40 days. The long e-folding time scales for the zonal index are found to be consistent with an unrealistically strong and persistent eddy–zonal-mean-flow feedback. A calculation of the refractive index indicates that the background flow supports eddies that are trapped within midlatitudes, undergoing relatively little meridional propagation. Additional model runs are performed with an idealized mountain to investigate whether zonal asymmetry can disrupt the eddy feedback. For single-jet states, the time scale is reduced to about 30 days if the mountain height is 4 km or less. The reduction in the time scale occurs because the stationary eddies excited by the mountain alter the background flow in a manner that leads to the replacement of zonal-index events by shorter-time-scale poleward propagation. With a 5-km mountain, the time scale reverts and increases to 105 days. This threshold behavior is again attributed to a sharpening of the background zonal jet, which arises from an extremely strong stationary wave momentum flux convergence. In contrast, for double-jet states, the time scale changes only slightly and the poleward propagation is maintained in all mountain runs.

scholarly journals Observation and simulation of wave breaking in the southern hemispheric stratosphere during VORCORE

2013 ◽  
Vol 31 (4) ◽  
pp. 675-687
Author(s):  
M. Moustaoui ◽  
H. Teitelbaum ◽  
A. Mahalov
Keyword(s):  
Wave Breaking ◽  
Rossby Waves ◽  
Surf Zone ◽  
Three Dimensional ◽  
Polar Vortex ◽  
Stationary Wave ◽  
Linear Wave ◽  
Rossby Wave Breaking ◽  
Wind Speeds ◽  
Antarctic Polar Vortex

Abstract. An interesting occurrence of a Rossby wave breaking event observed during the VORCORE experiment is presented and explained. Twenty-seven balloons were launched inside the Antarctic polar vortex. Almost all of these balloons evolved in the stratosphere around 500K within the vortex, except the one launched on 28 October 2005. In this case, the balloon was caught within a tongue of high potential vorticity (PV), and was ejected from the polar vortex. The evolution of this event is studied for the period between 19 and 25 November 2005. It is found that at the beginning of this period, the polar vortex experienced distortions due to the presence of Rossby waves. Then, these waves break and a tongue of high PV develops. On 25 November, the tongue became separated from the vortex and the balloon was ejected into the surf zone. Lagrangian simulations demonstrate that the air masses surrounding the balloon after its ejection were originating from the vortex edge. The wave breaking and the development of the tongue are confined within a region where a planetary Quasi-Stationary Wave 1 (QSW1) induces wind speeds with weaker values. The QSW1 causes asymmetry in the wind speed and the horizontal PV gradient along the edge of the polar vortex, resulting in a localized jet. Rossby waves with smaller scales propagating on top of this jet amplify as they enter the jet exit region and then break. The role of the QSW1 on the formation of the weak flow conditions that caused the non-linear wave breaking observed near the vortex edge is confirmed by three-dimensional numerical simulations using forcing with and without the contribution of the QSW1.

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

2008 ◽  
Vol 602 ◽  
pp. 303-326 ◽  
Author(s):  
E. PLAUT ◽  
Y. LEBRANCHU ◽  
R. SIMITEV ◽  
F. H. BUSSE
Keyword(s):  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Quantitative Agreement ◽  
Model Systems ◽  
Geometrical Factor ◽  
Wave Flow ◽  
Nonlinear Frequency ◽  
Two Dimensional ◽  
Reynolds Stresses

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

scholarly journals Some Inequalities for LR-$$\left({h}_{1}, {h}_{2}\right)$$-Convex Interval-Valued Functions by Means of Pseudo Order Relation

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Kottakkaran Sooppy Nisar ◽  
Khadiga Ahmed Ismail ◽  
...  
Keyword(s):  
Applied Mathematics ◽  
Critical Role ◽  
Order Relation ◽  
Strong Relationship ◽  
New Class ◽  
Starting Point ◽  
Interval Valued Function ◽  
Fejér Inequality ◽  
Definition Of ◽  
Interval Valued

AbstractIn both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued function (LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-$$\left({h}_{1}, {h}_{2}\right)$$ h 1 , h 2 -convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.

scholarly journals Towards a Theory for Unintended Consequences in Engineering Design

2019 ◽  
Vol 1 (1) ◽  
pp. 3411-3420
Author(s):  
Hannah Walsh ◽  
Andy Dong ◽  
Irem Tumer
Keyword(s):  
Failure Analysis ◽  
Engineering Design ◽  
Bifurcation Analysis ◽  
Real World ◽  
Unintended Consequences ◽  
Novel Technologies ◽  
New Class ◽  
Failure State ◽  
Engineered Systems ◽  
Definition Of

AbstractConventional failure analysis ignores a growing challenge in the responsible implementation of novel technologies into engineered systems - unintended consequences, which impact the engineered system itself and other systems including social and environmental systems. In this paper, a theory for unintended consequences is developed. The paper proposes a new definition of unintended consequences as behaviors that are not intentionally designed-into an engineered system yet occur even when a system is operating nominally, that is, not in a failure state as conventionally understood. It is argued that the primary cause for this difference is the bounded rationality of human designers. The formation of unintended consequences is modeled with system dynamics, using a specific real-world example, and bifurcation analysis. The paper develops propositions to guide research in the development of new design methods that could mitigate or control the occurrence and impact of unintended consequences. The end goal of the research is to create a new class of failure analysis tools to manage unintended consequences responsibly to facilitate engineering design for a more sustainable future.

scholarly journals The role of the observed tropical convection in the generation of frost events in the southern cone of South America

2008 ◽  
Vol 26 (6) ◽  
pp. 1379-1390 ◽  
Author(s):  
G. V. Müller ◽  
T. Ambrizzi ◽  
S. E. Ferraz
Keyword(s):  
South America ◽  
Large Scale ◽  
Rossby Waves ◽  
Tropical Convection ◽  
The Other ◽  
Linear Wave ◽  
Frequency Of Occurrence ◽  
The South ◽  
Cold Events ◽  
Extreme Cold

Abstract. Based on previous results obtained from observations and linear wave theory analysis, the hypothesis that large-scale patterns can generate extreme cold events in southeast South America through the propagation of remotely excited Rossby waves was already suggested. This work will confirm these findings and extend their analysis through a series of numerical experiments using a primitive equation model where waves are excited by a thermal forcing situated in positions chosen according to observed convection anomalies over the equatorial region. The basic state used for these experiments is a composite of austral winters with maximum and minimum frequency of occurrence of generalized frosts that can affect a large area known as the Wet Pampas located in the central and eastern part of Argentina. The results suggest that stationary Rossby waves may be one important mechanism linking anomalous tropical convection with the extreme cold events in the Wet Pampas. The combination of tropical convection and a specific basic state can generate the right environment to guide the Rossby waves trigged by the tropical forcing towards South America. Depending on the phase of the waves entering the South American continent, they can favour the advection of anomalous wind at low levels from the south carrying cold and dry air over the whole southern extreme of the continent, producing a generalized frost in the Wet Pampa region. On the other hand, when a basic state based on the composites of minimum frosts is used, an anomalous anticyclone over the southern part of the continent generates a circulation with a south-southeast wind which brings maritime air and therefore humidity over the Wet Pampas region, creating negative temperature anomalies only over the northeastern part of the region. Under these conditions even if frosts occur they would not be generalized, as observed for the other basic state with maximum frequency of occurrence of generalized frosts.

Centroidal frames in dynamical systems I. Point vortices

1992 ◽  
Vol 439 (1907) ◽  
pp. 441-463 ◽  
Keyword(s):  
Point Vortices ◽  
Centre Of Mass ◽  
Permutation Symmetry ◽  
Chaotic Motions ◽  
Small Perturbations ◽  
New Class ◽  
Angular Velocities ◽  
Mass Frame ◽  
Definition Of ◽  
Asymptotic Symmetries

The dynamics of point vortices is studied in Part I of the paper. It is well known that the (translational) centre-of-mass frame decomposes the motion of a mechanical system into simpler components. It is less known, however, that special rotational frames have also been suggested for the same purpose. In contrast to the centre-of-mass frame, the angular velocities of these rotational frames are not given explicitly that limits their application to small perturbations of rigid body rotations. A new class of centroidal frames (CF) related to different groups such as translation, rotation, dilation, etc., is introduced in this paper. The CFS decompose the motion of point vortices into a group and a relative components without restriction to small perturbations of pure group motions. The definition of the CFS is based on an averaging of motion or on minimization of energy of the relative motion, where an appropriate energy function is expressed through generators of the group action. As a result, the linear and angular velocities as well as other characteristics of the CFS can be obtained explicitly. Part I of the paper presents application of the CFS to a hamiltonian system of point vortices. Examples of integrable and chaotic motions in the CFS visualize dynamical patterns that are completely hidden in the conventional fixed frame (ff). Motions which look like chaotic in the FF reveal a variety of stable and unstable structures in the CFS. Quasi-periodic and chaotic motions coexist for all energies and the CFS permit to clearly distinguish between them. A new phenomenon of asymptotic symmetries (in rotational CFS) of some chaotic motions is discovered. This is related to a permutation symmetry of the hamiltonian.

scholarly journals Inhomogeneous spatial point processes by location-dependent scaling

2003 ◽  
Vol 35 (02) ◽  
pp. 319-336 ◽  
Author(s):  
Ute Hahn ◽  
Eva B. Vedel Jensen ◽  
Marie-Colette van Lieshout ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Spatial Point Processes ◽  
New Approach ◽  
Local Scaling ◽  
New Class ◽  
Spatial Point ◽  
New Process ◽  
Markov Point Processes ◽  
Global Scaling ◽  
Definition Of

A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensities differ only by a scale factor. This is achieved by replacing volume measures used in the density with locally scaled analogues defined by a location-dependent scaling function. The new approach is particularly appealing for modelling inhomogeneous Markov point processes. Distance-interaction and shot noise weighted Markov point processes are discussed in detail. It is shown that the locally scaled versions are again Markov and that locally the Papangelou conditional intensity of the new process behaves like that of a global scaling of the homogeneous process. Approximations are suggested that simplify calculation of the density, for example, in simulation. For sequential point processes, an alternative and simpler definition of local scaling is proposed.

scholarly journals The Role of the Divergent Circulation for Large-Scale Eddy Momentum Transport in the Tropics. Part I: Observations

2019 ◽  
Vol 76 (4) ◽  
pp. 1125-1144 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Momentum Flux ◽  
Large Scale ◽  
Zonal Flow ◽  
Stationary Wave ◽  
Hadley Cell ◽  
Momentum Transport ◽  
Mean Flow ◽  
Meridional Transport ◽  
The Tropics

Abstract This work investigates the role played by the divergent circulation for meridional eddy momentum transport in the tropical atmosphere. It is shown that the eddy momentum flux in the deep tropics arises primarily from correlations between the divergent eddy meridional velocity and the rotational eddy zonal velocity. Consistent with previous studies, this transport is dominated by the stationary wave component, associated with correlations between the zonal structure of the Hadley cell (zonal anomalies in the meridional overturning) and the climatological-mean Rossby gyres. This eddy momentum flux decomposition implies a different mechanism of eddy momentum convergence from the extratropics, associated with upper-level mass convergence (divergence) over sectors with anomalous westerlies (easterlies). By itself, this meridional transport would only increase (decrease) isentropic thickness over regions with anomalous westerly (easterly) zonal flow. The actual momentum mixing is due to vertical (cross isentropic) advection, pointing to the key role of diabatic processes for eddy–mean flow interaction in the tropics.

Sign in / Sign up

Export Citation Format

Share Document