Energy fluxes in quasi-equilibrium flows

International audienceWe examine the relation between the absolute equilibrium state of the spectrally truncated Euler equations (TEE) predicted by Kraichnan (1973) to the forced and dissipated flows of the spectrally truncated Navier-Stokes (TNS) equations. In both of these idealized systems a finite number of Fourier modes is kept contained inside a sphere of radius kmax but while the first conserves energy in the second energy is injected by a body-force f and dissipated by the viscosity ν. For the TNS system stochastically forced with energy injection rate IE we show, using an asymptotic expansion of the FokkerPlanck equation, that in the limit of small kmaxη (where η = (ν3/IE )1/4 the Kolmogorov lengthscale) the flow approaches the absolute equilibrium solution of Kraichnan with such an effective “temperature” so that there is a balance between the energy injection and the energy dissipation rate. We further investigate the TNS system using direct numerical simulations in periodic cubic boxes of size 2π/k0. The simulations verify the predictions of the model for small values of kmaxη. For intermediate values of kmaxη a transition from the quasi-equilibrium “thermal” state to Kolmogorov turbulence is observed. In particular we demonstrate that, at steady state, the TNS reproduce the Kolmogorov energy spectrum if kmaxη >> 1. As kmaxη becomes smaller then a bottleneck effect appears taking the form of the equipartition spectrum E(k) ∝ k2 at small scales. As kmaxη is decreased even further so that kmaxη << (k0/kmax)11/4 the equipartition spectrum occupies all scales approaching the asymptotic equilibrium solutions found before. If the forcing is applied at small scales and the dissipation acts only at large scales then the equipartition spectrum appears at all scales for all values of ν. In both cases a finite forward or inverse flux is present even for the cases where the flow is close to the equilibrium state solutions. However, unlike the classical turbulence where an energy cascade develops with a mean energy flux that is large compared to its fluctuations, the quasi-equilibrium state has a mean flux of energy that is subdominant to the large flux fluctuations observed

Two-fluid model of the truncated Euler Equations

A phenomenological two-fluid model of the (time-reversible) spectrally-truncated 3D Euler equation is proposed. The thermalized small scales are first shown to be quasi-normal. The effective viscosity and thermal diffusion are then determined, using EDQNM closure and Monte-Carlo numerical computations. Finally, the model is validated by comparing its dynamics with that of the original truncated Euler equation

Boundary layers and emitted excitations in nonlinear Schrodinger superflow past a disk

The stability and dynamics of nonlinear Schrodinger superflows past a two-dimensional disk are investigated using a specially adapted pseudo-spectral method based on mapped Chebychev polynomials. This efficient numerical method allows the imposition of both Dirichlet and Neumann boundary conditions at the disk border. Small coherence length boundary-layer approximations to stationary solutions are obtained analytically. Newton branch-following is used to compute the complete bifurcation diagram of stationary solutions. The dependence of the critical Mach number on the coherence length is characterized. Above the critical Mach number, at coherence length larger than fifteen times the diameter of the disk, rarefaction pulses are dynamically nucleated, replacing the vortices that are nucleated at small coherence length

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Altimetry for the future: building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Dynamique Eulerienne-Lagrangienne généralisée et caractérisation de la reconnexion diffusive

Cette thèse est basée sur la représentation Eulerienne-Lagrangiene de la vitesse, qui nous appelons la transformation de Weber-Clebsch. Constantin a construit en 2002 une extension de la description de Weber-Clebsch des fluides parfaits aux fluides visqueux. La nécessité de réinitialiser périodiquement les coordonnées Lagrangiennes à été interprété par Constantin comme un diagnostique de la reconnexion de la vorticité. Le système de Constantin est contenu dans notre formulation, qui est plus générale, dans une limite singulière. Pour comparer les résultats obtenus en utilisant notre formulation généralisée à ceux qui sont obtenus dans la formulation de Constantin nous avons procédé à des simulations numériques d'un certain nombre d'écoulements obéissants aux équations de Navier-Stokes. Des extensions à la magnéto hydrodynamique et aux fluides compressibles sont également proposées et validées numériquement.PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Stabilité et dynamique d'écoulements de fluides parfaits barotropes autour d'un obstacle en présence de dispersion

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF