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Rearrangements of vector valued functions, with application to atmospheric and oceanic ows
"... This paper establishes the equivalence of four de nitions of two vector valued functions being rearrangements, and gives a characterisation of the set of rearrangements of a prescribed function. The theory of monotone rearrangement ofavector valued function is used to show the existence and uniquene ..."
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This paper establishes the equivalence of four de nitions of two vector valued functions being rearrangements, and gives a characterisation of the set of rearrangements of a prescribed function. The theory of monotone rearrangement ofavector valued function is used to show the existence and uniqueness of the minimiser of an energy functional arising from a model for atmospheric and oceanic ow. At each xed time solutions are shown to be equal to the gradient of a convex function, verifying the conjecture of Cullen, Norbury and Purser. Key words Rearrangement of functions, semigeostrophic, variational problems, generalised solution.
LegendreTransformable SemiGeostrophic Theories
, 1997
"... For semigeostrophic (SG) theories derived from the Hamiltonian principles suggested by Salmon it is known that a duality exists between the physical coordinates and geopotential, on the one hand, and isentropic geostrophic momentum coordinates and geostrophic Bernoulli function, on the other hand. ..."
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For semigeostrophic (SG) theories derived from the Hamiltonian principles suggested by Salmon it is known that a duality exists between the physical coordinates and geopotential, on the one hand, and isentropic geostrophic momentum coordinates and geostrophic Bernoulli function, on the other hand. The duality is characterized geometrically by a "contact structure". This enables the idealized balanced dynamics to be represented by horizontal geostrophic motion in the dual coordinates while the mapping back to physical space is determined uniquely by requiring each instantaneous state to be the one of minimum energy with respect to volumeconserving rearrangements within the physical domain. It is found that the generic contact structure permits the emergence of topological anomalies during the evolution of discontinuous ows. For both theoretical and computational reasons it is desirable to seek special forms of SG dynamics in which the structure of the contact geometry prohibits such anomalies. We prove that this desideratum is equivalent to the existence of a mapping of geographical position to a Euclidean domain,
Perspectives on Fred Sanders's Research on Cold Fronts
, 2006
"... One characteristic of Fred Sanders's research is his ability to take a topic that is believed to be well understood by the research community and show that interesting research problems still exist. Among Sanders's considerable contributions to synoptic meteorology, those concerned with su ..."
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One characteristic of Fred Sanders's research is his ability to take a topic that is believed to be well understood by the research community and show that interesting research problems still exist. Among Sanders's considerable contributions to synoptic meteorology, those concerned with surface cold fronts have been especially in
uential. After a brief historical review of fronts and frontal analysis, this paper presents three stages in Sanders's career when he performed research on the structure, dynamics, and analysis of surface cold fronts. First, his 1955 paper \An Investigation of the Structure and Dynamics of an Intense Surface Frontal Zone " was the rst study to discuss quantitatively the dynamics of a surface cold front. In the 1960s, Sanders and his students further examined the structure of cold fronts, resulting in the unpublished 1967 report to the National Science Foundation \Frontal Structure and the Dynamics of Frontogenesis. " For a third time in his career, Sanders published several papers in the 1990s and 2000s, revisiting the structure and dynamics of cold fronts. His 1967 and 1990s/2000s work raises the question of the origin and dynamics of the surface pressure trough and/or wind shift that sometimes precedes the temperature gradient (hereafter called a prefrontal trough or prefrontal wind shift, respectively).
Holomorphic structures in hydrodynamical models of nearly geostrophic°ow
"... We study complex structures arising in Hamiltonian models of nearly geostrophic ®ows in hydrodynamics. In many of these models an elliptic Monge{Amp ere equation de nes the relationship between a`balanced' velocity eld, de ned by a constraint in the Hamiltonian formalism, and the materially co ..."
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We study complex structures arising in Hamiltonian models of nearly geostrophic ®ows in hydrodynamics. In many of these models an elliptic Monge{Amp ere equation de nes the relationship between a`balanced' velocity eld, de ned by a constraint in the Hamiltonian formalism, and the materially conserved potential vorticity. Elliptic Monge{Amp ere operators de ne an almostcomplex structure, and in this paper we show that a natural extension of the socalled geostrophic momentum transformation of semigeostrophic theory, which has a special importance in theoretical meteorology, de nes K ahler and special K ahler structures on phase space. Furthermore, analogues of the`geostrophic momentum coordinates' are shown to be special Lagrangian coordinates under conditions which depend upon the physical approximations under consideration. Certain duality properties of the operators are studied within the framework of the K ahler geometry.
NONLINEARITY PII: S09517715(04)697763
, 2004
"... Exact semigeostrophic flows in an elliptical ocean basin* ..."
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Examples of Quaternionic and Kähler Structures in . . .
 J. PHYS. A., 30 (1997), L63L68
, 1997
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CentAUR
, 1994
"... Waveactivity conservation laws and stability theorems for semigeostrophic ..."
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Waveactivity conservation laws and stability theorems for semigeostrophic