On the sampling requirements for measuring moments of eddy variability

The expected errors in first and second moments (means, variances, and covariances) calculated from data records of finite length are analyzed, using formulae based on the spectra. The physical processes from which the data are taken are assumed to be stationary and quasinormal. Asymptotic approximations to these errors (in inverse powers of the record length) are also discussed and compared with the exact expressions...

Generalized Kirchhoff Vortices

A family of exact solutions of the Euler equations is presented: they are generalizations of the Kirchhoff vortex to N confocal ellipses. Special attention is given to the case N=2, for which the stability is analyzed with a method similar to the one used by Love [Proc. London Math. Soc. 1, XXV 18 (1893)] for the Kirchhoff vortex. The results are compared with those for the corresponding circular problem

Filamentation of Unstable Vortex Structures via Separatrix Crossing: A Quantitative Estimate of Onset Time

The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction

Filamentation of Unstable Vortex Structures via Separatrix Crossing: A Quantitative Estimate of Onset Time

The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction

Two-Layer Geostrophic Vortex Dynamics. Part 1. Upper-Layer V-States and Merger

We generalize the methods of two-dimensional contour dynamics to study a two-layer rotating fluid that obeys the quasi-geostrophic equations. We consider here only the case of a constant-potential-vorticity lower layer. We derive equilibrium solutions for monopolar (rotating) and dipolar (translating) geostrophic vortices in the upper layer, and compare them with the Euler case. We show that the equivalent barotropic (infinite lower layer) case is a singular limit of the two-layer system. We also investigate the effect of a finite lower layer on the merger of two regions of equal-sign potential vorticity in the upper layer. We discuss our results in the light of the recent laboratory experiments of Griffiths and Hopfinger (1986). The process of filamentation is found to be greatly suppressed for equivalent barotropic dynamics on scales larger than the radius of deformation. We show that the variation of the critical initial distance for merger as a function of the radius of deformation and the ratio of the layers at rest is closely related to the existence of vortex-pair equilibria and their geometrical properties

The nonlinear dynamics of time-dependent subcritical baroclinic currents

Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 1001-1021, doi:10.1175/jpo3034.1.The nonlinear dynamics of baroclinically unstable waves in a time-dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time-dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear, a symmetry breaking is detected in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time-dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasigeostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded, the inviscid, linear problem is formally stable. However, calculations show that a small degree of nonlinearity is enough to destabilize the flow, leading to large amplitude vacillations and turbulence. When the most unstable wave is not the longest wave in the system, a cascade up scale to longer waves is observed. Indeed, this classically subcritical flow shows most of the qualitative character of a strongly supercritical flow. This result supports previous suggestions of the important role of background time dependence in maintaining the atmospheric and oceanic synoptic eddy field.GRF was supported by NSF Grant OCE-0137023, and JP was supported by NSF Grant OCE- 9901654

Interacting Random Walkers and Non-Equilibrium Fluctuations

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we show indeed that it is mesoscopically described by a Fourier equation with a density dependent diffusivity. A simple mean-field description predicts a critical diffusivity if the hopping amplitude vanishes for a certain walker density. Actually, we evidence that, even if the density equals this pseudo-critical value, the system does not present any criticality but only a dynamical slowing down. This property is confirmed by the fact that, in spite of interaction, the particle distribution at equilibrium is simply described in terms of a product of Poissonians. For mesoscopic systems with a stationary flux, a very effect of interaction among particles consists in the amplification of fluctuations, which is especially relevant close to the pseudo-critical density. This agrees with analogous results obtained for Ising models, clarifying that larger fluctuations are induced by the dynamical slowing down and not by a genuine criticality. The consistency of this amplification effect with altered coloured noise in time series is also proved.Comment: 8 pages, 7 figure

Deficiency in the mouse mitochondrial adenine nucleotide translocator isoform 2 gene is associated with cardiac noncompaction.

The mouse fetal and adult hearts express two adenine nucleotide translocator (ANT) isoform genes. The predominant isoform is the heart-muscle-brain ANT-isoform gene 1 (Ant1) while the other is the systemic Ant2 gene. Genetic inactivation of the Ant1 gene does not impair fetal development but results in hypertrophic cardiomyopathy in postnatal mice. Using a knockin X-linked Ant2 allele in which exons 3 and 4 are flanked by loxP sites combined in males with a protamine 1 promoter driven Cre recombinase we created females heterozygous for a null Ant2 allele. Crossing the heterozygous females with the Ant2(fl), PrmCre(+) males resulted in male and female ANT2-null embryos. These fetuses proved to be embryonic lethal by day E14.5 in association with cardiac developmental failure, immature cardiomyocytes having swollen mitochondria, cardiomyocyte hyperproliferation, and cardiac failure due to hypertrabeculation/noncompaction. ANTs have two main functions, mitochondrial-cytosol ATP/ADP exchange and modulation of the mitochondrial permeability transition pore (mtPTP). Previous studies imply that ANT2 biases the mtPTP toward closed while ANT1 biases the mtPTP toward open. It has been reported that immature cardiomyocytes have a constitutively opened mtPTP, the closure of which signals the maturation of cardiomyocytes. Therefore, we hypothesize that the developmental toxicity of the Ant2 null mutation may be the result of biasing the cardiomyocyte mtPTP to remain open thus impairing cardiomyocyte maturation and resulting in cardiomyocyte hyperproliferation and failure of trabecular maturation. This article is part of a Special Issue entitled 'EBEC 2016: 19th European Bioenergetics Conference, Riva del Garda, Italy, July 2-6, 2016', edited by Prof. Paolo Bernardi

Stability analysis of a class of two-dimensional multipolar vortex equilibria

Published versio

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [Ellis, Haven, Turkington, Nonlin., 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D, 237, 1998 (2008)]. They can provide a small-scale parametrization of 2D turbulence or serve as numerical algorithms to compute maximum entropy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure