Evolution of a Rossby Wave Packet in Barotropic Flows with Asymmetric Basic Current, Topography and δ-Effect

Yang, Huijun

doi:10.1175/1520-0469(1987)044<2267:eoarwp>2.0.co;2

Cited by 25 publications

(22 citation statements)

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“…In addition to the traditional β-plane approximation, there is also the δ-plane approximation (Yang, 1987) which is a second order Taylor expansion of the Coriolis parameter. Our aim in the present study is to use the full expression for the coriolis parameter, but, to ignore the metric terms (and thus, ignore geometric effects).…”

Section: The Mercator Projectionmentioning

confidence: 99%

2009 program of studies : nonlinear waves

Bühler¹,

Helfrich²

2010

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i PrefaceThe fiftieth year of the program was dedicated to Nonlinear Waves, a topic with many applications in geophysical fluid dynamics. The principal lectures were given jointly by Roger Grimshaw and Harvey Segur and between them they covered material drawn from fundamental theory, fluid experiments, asymptotics, and reaching all the way to detailed applications. These lectures set the scene for the rest of the summer, with subsequent daily lectures by staff and visitors on a wide range of topics in GFD. It was a challenge for the fellows and lecturers to provide a consistent set of lecture notes for such a wideranging lecture course, but not least due to the valiant efforts of Pascale Garaud, who coordinated the write-up and proof-read all the notes, we are very pleased with the final outcome contained in these pages. This year's group of eleven international GFD fellows was as diverse as one could get in terms of gender, origin, and race, but all were unified in their desire to apply their fundamental knowledge of fluid dynamics to challenging problems in the real world. Their projects covered a huge range of physical topics and at the end of the summer each student presented his or her work in a one-hour lecture. As always, these projects are the heart of the research and education aspects of our summer study.During the summer we also had a couple of special events, namely the public Sears Lecture given by Geoff Spedding from USC on animal propulsion entitled "Flight at small scales", and a one-day special workshop and celebration in honour of Lou Howard's 80 th birthday entitled "Nonlinear excursions". These well-attended events brought together old and new friends and a good time was had by all.This summer also had its share of unscheduled surprises, but the enthusiasm and tenacity of our fellows was able to overcome all, be it rained-out softball training sessions or advisors that had to disappear abruptly to attend to robbed houses at the other end of the country. At the end it all came together, and the final days were marked by a happy reunion of everyone and a graceful farewell party, despite a somewhat disappointing outcome of the Fellow-Staff softball match.Special thanks go to a number of people who served to make the program flow smoothly. Jeanne Fleming, Kathy Ponti and Penny Foster all helped run the Walsh Cottage office and performed exceptional administrative work for the many visits and lectures. Jeanne Fleming was responsible for assembling and preparing this volume. Janet Fields helped with all aspects of the academic programs for the fellows and as usual did a superb job.We extend our sincere thanks to the National Science Foundation for support for this program under Grant OCE-0824636 and to the Office of Naval Research, Processes and Prediction Division, Physical Oceanography Program, under Grant N00014-09-10844.Oliver Bühler and Karl Helfrich, Co-Directors ii

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Section: The Mercator Projectionmentioning

confidence: 99%

2009 program of studies : nonlinear waves

Bühler¹,

Helfrich²

2010

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“…In simulating the North Polar Hexagon, a high-latitude polar approximation must be used. In order to study high-latitude atmospheric Rossby waves, Yang (1987) proposed a δ-plane approximation. Similar to the development of the β-plane where the β term represents the rate of change in the Coriolis parameter f, the δ-plane (denoted γ -plane by Nof 1990) includes the latitudinal variation of β so that δ = ∂β/∂y and thus allows for the quadratic variation in the Coriolis parameter around the polar regions.…”

Section: Introductionmentioning

confidence: 99%

“…A similar approach was used by Harlander, Schonfeldt & Metz (2000) to investigate flows near the poles with a poleward rigid boundary, thereby only having linear and quadratic change along the north-south y-axis. Unlike the β-plane approximation, higher order approximations such as the δ-plane theories outlined by Yang (1987), Nof (1990) and Harlander et al (2000) cannot be derived from spherical geographic coordinates. However, using a rotated geographic coordinate system, Harlander (2005) was able to derive a δ-plane model from spherical geometry.…”

Section: Introductionmentioning

confidence: 99%

A δ-plane simulation of anticyclones perturbing circumpolar flows to form a transient north polar hexagon

Cosgrove¹,

Forbes²

2017

Monthly Notices of the Royal Astronomical Society

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Saturn's North Polar Hexagon was discovered by Godfrey who pieced together map projections of images captured by the Voyager mission to unveil a hexagonal structure over the north pole of Saturn. This article attempts to answer whether or not a hexagonal structure can be formed through anticyclones impinging on the dominant eastward circumpolar flow and is in part based upon the proposed theory by Allison et al. that the Hexagon may be the result of at least one impinging anticyclone perturbing a circumpolar jet centrally located around the 76 • N latitude. A high-latitude δ-plane approximation is used to simulate the interaction between an initially circular circumpolar jet and at least one perturbing anticyclone. Our simulations with one perturbing anticyclone failed to form a hexagonal structure; yet by including an additional anticyclone it was found that depending on the strength, location and radius of the perturbing anticyclones a hexagonal feature could develop. However, the longevity and drift rate of the actual Hexagon must be attributed to other factors not considered in this paper.

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“…F is the Froud number, a parameter inversely proportional to the static instability of the atmosphere [1,p. 60], B 1 (y, t) and B 2 (x, t) are parameters related to the stability of the basic flow and β 1 (x, y) and β 2 (x, y) are vorticity parameters related to the topography [2]. Neither equation (1) nor equation (2) can be solved exactly.…”

Section: Introductionmentioning

confidence: 99%

“…Karoly and Hoskins [4] and Yang [5], among others, have employed and extended this approach to study Rossby-type equations, i.e., variations of equation (1), and Yang has applied it to study the vorticity equation as well. Near turning or caustic points, the classical WKB technique is not valid [6], e.g., physically, near the "critical layers" where the phase velocity of the wave coincides with the velocity of the large-scale current [7,8] or near sharp topographies [2]. A related approach that is valid at caustics is the Lagrange Manifold formalism developed by Arnol'd [9] and Maslov [10].…”

Section: Introductionmentioning

confidence: 99%