Non-Normal Effects on Salt Finger Growth

2005 ◽  
Vol 35 (5) ◽  
pp. 616-627 ◽  
Author(s):  
Ian Eisenman
Keyword(s):  
Normal Mode ◽  
Stability Theory ◽  
Normal Modes ◽  
Growth Dynamics ◽  
Normal Growth ◽  
Initial Growth ◽  
Transient Effects ◽  
Salt Fingers ◽  
Long Time ◽  
The Difference

Abstract Salt fingers, which occur because of the difference in diffusivities of salt and heat in water, may play an important role in ocean mixing and circulation. Previous studies have suggested the long-time dominance of initially fastest growing finger perturbations. Finger growth has been theoretically derived in terms of the normal modes of the idealized system, which include a growing mode and a pair of decaying internal wave modes. Because these normal modes are not orthogonal, however, transient effects can occur related to the interaction between the modes, as explained by the generalized stability theory of non-normal growth. Initial growth of a perturbation that is not along a normal mode can be faster than the leading normal mode. In this study, the effects of non-normal growth on salt finger formation are investigated. It is shown that some salt finger perturbations that are a superposition of the growing mode and the decaying modes initially grow faster than pure growing normal mode perturbations. These non-normal effects are found to be significant for up to 10 or more e-folding times of the growing normal mode. The generalization of the standard idealized salt finger growth dynamics to include non-normal effects is found to lead to fastest-growing fingers that agree less well with observed fully developed salt fingers than the fastest-growing normal mode previously investigated.

On the Sensitivity of Non-Generic Bifurcation of Non-Linear Normal Modes

2007 ◽  
Author(s):  
C. H. Pak ◽  
Y. S. Choi
Keyword(s):  
Normal Mode ◽  
Natural Frequencies ◽  
Normal Modes ◽  
New Normal ◽  
Perturbed System ◽  
Saddle Node ◽  
Non Linear ◽  
The Difference ◽  
Generic Bifurcation ◽  
The Stability

It is shown that a non-generic bifurcation of non-linear normal modes may occur if the ratio of linear natural frequencies is near r-to-one, r = 1, 3, 5 ·······. Non-generic bifurcations are explicitly obtained in the systems having certain symmetry, as observed frequently in literatures. It is found that there are two kinds of non-generic bifurcations, super-critical and sub-critical. The normal mode generated by the former kind is extended to large amplitude, but that by the latter kind is limited to small amplitude which depends on the difference between two linear natural frequencies and disappears when two frequencies are equal. Since a non-generic bifurcation is not generic, it is expected generically that if a system having a non-generic bifurcation is perturbed then the non-generic bifurcation disappears and generic bifurcation appear in the perturbed system. Examples are given to verify the change in bifurcations and to obtain the stability behavior of normal modes. It is found that if a system having a super-critical non-generic bifurcation is perturbed, then two new normal modes are generated, one is stable, but the other unstable, implying a saddle-node bifurcation. If the system having a sub-critical non-generic bifurcation is perturbed, then no new normal mode is generated, but there is an interval of instability on a normal mode, implying two saddle-node bifurcations on the mode. Application of this study is discussed.

scholarly journals Measuring α-FPUT Cores and Tails

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 879-887
Author(s):  
Sergej Flach
Keyword(s):  
Normal Mode ◽  
Normal Modes ◽  
Numerical Data ◽  
One Dimensional ◽  
The Core ◽  
Long Time ◽  
Good Agreement

Almost 70 years ago, the Fermi–Pasta–Ulam–Tsingou (FPUT) paradox was formulated in, observed in, and reported using normal modes of a nonlinear, one-dimensional, non-integrable string. Let us recap the paradox. One normal mode is excited, which drives three or four more normal modes in the core. Then, that is it for quite a long time. So why are many normal modes staying weakly excited in the tail? Furthermore, how many? A quantitative, analytical answer to the latter question is given here using resonances and secular avalanches A comparison with the previous numerical data is made and extremely good agreement is found.

Inter-country inequality as a dynamic process and the problem of post-industrial development

2018 ◽  
pp. 5-29 ◽  
Author(s):  
L. M. Grigoryev ◽  
V. A. Pavlyushina
Keyword(s):  
Economic Growth ◽  
Political Institutions ◽  
Industrial Development ◽  
Modern World ◽  
New Approach ◽  
Development Level ◽  
The World ◽  
Long Time ◽  
The Difference ◽  
Post Industrial

The phenomenon of economic growth is studied by economists and statisticians in various aspects for a long time. Economic theory is devoted to assessing factors of growth in the tradition of R. Solow, R. Barrow, W. Easterly and others. During the last quarter of the century, however, the institutionalists, namely D. North, D. Wallis, B. Weingast as well as D. Acemoglu and J. Robinson, have shown the complexity of the problem of development on the part of socioeconomic and political institutions. As a result, solving the problem of how economic growth affects inequality between countries has proved extremely difficult. The modern world is very diverse in terms of development level, and the article offers a new approach to the formation of the idea of stylized facts using cluster analysis. The existing statistics allows to estimate on a unified basis the level of GDP production by 174 countries of the world for 1992—2016. The article presents a structured picture of the world: the distribution of countries in seven clusters, different in levels of development. During the period under review, there was a strong per capita GDP growth in PPP in the middle of the distribution, poverty in various countries declined markedly. At the same time, in 1992—2016, the difference increased not only between rich and poor groups of countries, but also between clusters.

Psychology: Volume 5

2019 ◽  
Keyword(s):  
World View ◽  
Science Volume ◽  
Western World ◽  
Mental Life ◽  
Long Time ◽  
The Difference ◽  
New Perspective ◽  
Indian Setting ◽  
The Mind ◽  
The Relationship

This survey of research on psychology in five volumes is a part of a series undertaken by the ICSSR since 1969, which covers various disciplines under social science. Volume Five of this survey, Explorations into Psyche and Psychology: Some Emerging Perspectives, examines the future of psychology in India. For a very long time, intellectual investments in understanding mental life have led to varied formulations about mind and its functions across the word. However, a critical reflection of the state of the disciplinary affairs indicates the dominance of Euro-American theories and methods, which offer an understanding coloured by a Western world view, which fails to do justice with many non-Western cultural settings. The chapters in this volume expand the scope of psychology to encompass indigenous knowledge available in the Indian tradition and invite engaging with emancipatory concerns as well as broadening the disciplinary base. The contributors situate the difference between the Eastern and Western conceptions of the mind in the practice of psychology. They look at this discipline as shaped by and shaping between systems like yoga. They also analyse animal behaviour through the lens of psychology and bring out insights about evolution of individual and social behaviour. This volume offers critique the contemporary psychological practices in India and offers a new perspective called ‘public psychology’ to construe and analyse the relationship between psychologists and their objects of study. Finally, some paradigmatic, pedagogical, and substantive issues are highlighted to restructure the practice of psychology in the Indian setting.

Effects of slide-to-roll ratio and varying velocity on the lubrication performance of grease at low speed

2021 ◽  
pp. 135065012199336
Author(s):  
Yiming Han ◽  
Jing Wang ◽  
Xuyang Jin ◽  
Shanshan Wang ◽  
Rui Zhang
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Industrial Applications ◽  
Transient Effects ◽  
Disintegration Time ◽  
Low Speed ◽  
Existence Time ◽  
Pure Rolling ◽  
Lubrication Performance ◽  
Long Time

Under steady-state pure rolling conditions with low speed, the thickener fiber agglomerations can be maintained for a long time, generating a beneficial thicker film thickness. However, in industrial applications, motions with sliding or transient effects are very common for gears, rolling-element bearings or even chain drives, evaluation of the grease performance under such conditions is vital for determining the lubrication mechanism and designing new greases. In this project, optical interferometry experiments were carried out on a ball-disk test rig to study the disintegration time of the grease thickener agglomerations with the increase of the slide-to-roll ratio under steady-state and reciprocation motions. Under steady-state conditions, the thickener fiber agglomeration can exist for a while and the time becomes shorter with the increase of the slide-to-roll ratio above the critical speed. Below the critical speed, the thickener fiber can exist in the contact in the form of a quite thick film for a very long time under pure rolling conditions but that time is decreased with the increase of the slide-to-roll ratio. The introduction of the transient effect can further reduce the existence time of the thickener.

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

Study of the Cause of Lost Circulation while Drilling Fractured Carbonates

2021 ◽  
Author(s):  
Alexey Ruzhnikov
Keyword(s):  
Success Rate ◽  
Drilling Fluid ◽  
Circulation Zone ◽  
Lost Circulation ◽  
Carbonate Formation ◽  
New Information ◽  
Fractured Carbonate ◽  
Long Time ◽  
The Difference ◽  
Fractured Carbonates

Abstract Fractured carbonate formations are prone to lost circulation, which affects the well construction process and has longtime effect on well integrity. Depending on the nature of losses (either induced or related to local dissolutions) the success rate is different when the induced losses can be cured with a high chance, and the one related to dissolutions may take a long time, and despite multiple attempts, the success rate is normally low. To have a better understanding of the complete losses across the fractured carbonates, a series of studies were initiated. First, to understand the strength of the loss zone, the fracture closing pressure was evaluated studying the fluid level in the annulus and back-calculating the effect of drilling fluid density. Second, the formation properties across the loss circulation zones were studied using microresistivity images, dip data, and imaging of fluid-saturated porous media. The results of the studies brought a lot of new information and explained some previous mysteries. The formation strength across the lost circulation zone was measured, and it was confirmed that it remains constant despite other changes of the well construction parameters. Additionally, it was confirmed that the carbonates are naturally highly fractured, having over 900 fractures along the wellbore. The loss circulation zone was characterized, and it was confirmed that the losses are not related to the fractures but rather to the karst, dissolution, and megafractures. The size and dip of the fractures were identified, and it was proven the possibility to treat them with conventional materials. However, the size of identified megafractures and karst zones exceeding the fractures by 10 times in true vertical depth, and in horizontal wells the difference is even higher due to measured depth. This new information helps to explain the previous unsuccessful attempts with the conventional lost circulation materials. The manuscript provides new information on the fractured carbonate formation characterization not available previously in the literature. It allows to align the subsurface and drilling visions regarding the nature of the losses and further develop the curing mechanisms.

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