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"... A nonparametric Free Disposal Hull (FDH) approach to technical efficiency: an illustration of radial and graph efficiency measures and some sensitivity results BRUNO DE BORGER, KRISTIAAN KERSTENS, WIM MOESEN and JACQUES VANNESTE* ..."
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A nonparametric Free Disposal Hull (FDH) approach to technical efficiency: an illustration of radial and graph efficiency measures and some sensitivity results BRUNO DE BORGER, KRISTIAAN KERSTENS, WIM MOESEN and JACQUES VANNESTE*
The instability of a potential vorticity front
"... Two nearly distinct types of motion are found in the Earth's atmosphere and oceans, namely `balanced ' vortical motions and `unbalanced ' gravitywave motions. The balanced motions are controlled entirely by a materially advected scalar, the potential vorticity (PV), from which all ot ..."
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Two nearly distinct types of motion are found in the Earth's atmosphere and oceans, namely `balanced ' vortical motions and `unbalanced ' gravitywave motions. The balanced motions are controlled entirely by a materially advected scalar, the potential vorticity (PV), from which all other dynamical elds (velocity, pressure, etc.) can be derived via prescribed `inversion relations'. The residual motions are classied as unbalanced motions, and are presumed to be gravity waves. This decomposition is only strictly dened however for the linearised equations about a state of rest. Otherwise, a degree of ambiguity arises (surrounding the choice of inversion relations, for instance), making it impossible to uniquely dene the balanced part of the ow (cf. Mohebalhojeh & Dritschel 2001, Viudez & Dritschel 2004 and references therein). Nevertheless, such a decomposition, even if inexact, is often of great practical utility, particularly in weather forecasting. The actual ambiguity in the denition of balance can be exceedingly small in many circumstances. A longstanding problem in geophysical
uid dynamics concerns the quantication of the coupling between the two types of motion and, in particular, the mechanisms for the generation of gravity waves by balanced motion (e.g. Lorenz & Krishnamurthy 1987, Warn 1997,
Statistical mechanics of Arakawa’s discretizations
, 2007
"... The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization chosen. This is illustrated for quasigeostrophic flow with topographic forcing, for which a well esta ..."
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Cited by 14 (3 self)
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The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization chosen. This is illustrated for quasigeostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa (1966) which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.
Employment
, 2004
"... Chartered Engineer Qualification): a twomonth training course on practical techniques in electrical and ..."
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Chartered Engineer Qualification): a twomonth training course on practical techniques in electrical and
Nonlinear Dynamics Over Rough Topography: Barotropic and Stratified QuasiGeostrophic Theory
"... this paper is the influence of smallscale topography on largescaleflow instability, in particular on baroclinic instability. This can be done straightforwardly by including in the model a largescale, vertically sheared flow and by carrying out a spectral stability analysis. In 5, we apply this ..."
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Cited by 4 (0 self)
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this paper is the influence of smallscale topography on largescaleflow instability, in particular on baroclinic instability. This can be done straightforwardly by including in the model a largescale, vertically sheared flow and by carrying out a spectral stability analysis. In 5, we apply this approach to examine how the simplest model of baroclinic instability of a continuously stratified fluid, namely Eady's model, is a#ected by topography. The results complement those recently obtained by Benilov (2001) who addressed the same issue using Phillips' twolayer model. A remark should be made about the limitations of the asymptotic approach used in this paper. The results are strictly valid when the topography is periodic, but since they involve only the correlation function of the topography height, it is tempting to extend them to random topographies. Di#culties arise, however, in the applications of the multiplescale technique when the topography is defined by a nondegenerate random function (Sengupta, Piterbarg & Reznik 1992). These di#culties, which were already pointed out by Rhines & Bretherton (1973), are associated with the phenomenon of localisation, studied for Rossby waves by Sengupta et al. (1992) and Klyatskin (1996). Here we are not concerned with the e#ect of localisation. It can be excluded by restricting attention to periodic functions or random functions defined by a (discrete) sum of Fourier modes with random amplitudes. More generally, one can also consider random topographies with a continuous spectrum, provided that the spectrum of the topography (i.e. the Fourier transform of the topography correlation function) decreases su#ciently fast at large scales. Two distinct conditions are obtained for the barotropic and quasigeostrophic models. Th...
GRASSMANNIAN SPECTRAL SHOOTING
, 2010
"... We present a new numerical method for computing the purepoint spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifo ..."
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Cited by 10 (5 self)
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We present a new numerical method for computing the purepoint spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In particular, the method avoids representation singularities by, in practice, choosing the best coordinate patch representation for the flow as it evolves. The method is analytic in the spectral parameter and of complexity bounded by the order of the spectral problem cubed. For large systems it represents a competitive method to those recently developed that are based on continuous orthogonalization. We demonstrate this by comparing the two methods in three applications: Boussinesq solitary waves, autocatalytic travelling waves and the Ekman boundary layer.
A SurfaceAware Projection Basis for Quasigeostrophic Flow
, 2012
"... Recent studies indicate that altimetric observations of the ocean’smesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surfacetrapped structure, while the latter are oftenwell represented by the barotropic and first b ..."
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Cited by 3 (1 self)
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Recent studies indicate that altimetric observations of the ocean’smesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surfacetrapped structure, while the latter are oftenwell represented by the barotropic and first baroclinicmodes. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surfacetrapped dynamics are not well represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here the authors derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonormal bases that depend on two parameters; the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics and a series of oscillatingmodes that represent the interior dynamics.Motivated by the ocean, where shears are concentrated near the upper surface, the authors consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. The use and effectiveness of these modes is demonstrated by projecting the energy in a set of simulations of baroclinic turbulence. 1.
COMPUTING STABILITY OF MULTIDIMENSIONAL TRAVELLING WAVES
"... We present a numerical method for computing the purepoint spectrum associated with the linear stability of multidimensional travelling fronts to parabolic nonlinear systems. Our method is based on the Evans function shooting approach. Transverse to the direction of propagation we project the spect ..."
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Cited by 7 (2 self)
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We present a numerical method for computing the purepoint spectrum associated with the linear stability of multidimensional travelling fronts to parabolic nonlinear systems. Our method is based on the Evans function shooting approach. Transverse to the direction of propagation we project the spectral equations onto a finite Fourier basis. This generates a large, linear, onedimensional system of equations for the longitudinal Fourier coefficients. We construct the stable and unstable solution subspaces associated with the longitudinal farfield zero boundary conditions, retaining only the information required for matching, by integrating the Riccati equations associated with the underlying Grassmannian manifolds. The Evans function is then the matching condition measuring the linear dependence of the stable and unstable subspaces and thus determines eigenvalues. As a model application, we study the stability of twodimensional wrinkled front solutions to a cubic autocatalysis model system. We compare our shooting approach with the continuous orthogonalization method of Humpherys and Zumbrun. We then also compare these with standard projection methods that directly project the spectral problem onto a finite multidimensional basis satisfying the boundary conditions.
2009a Ageostrophic instabilities of fronts in a channel in the stratified rotating fluid
 J. Fluid Mech
"... It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby– Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a twolayer rotating shallowwater ..."
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Cited by 4 (2 self)
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It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby– Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149–176) in a twolayer rotating shallowwater model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the twolayer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of smallscale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability. 1.
Results 1  10
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