Coriolis force in Geophysics: an elementary introduction and examples

We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that reason of pedagogical and practical interest. Our aim is to model them in a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic

Analysis of fast turbulent reconnection with self-consistent determination of turbulence timescale

We present results of Reynolds-averaged turbulence model simulation on the problem of magnetic reconnection. In the model, in addition to the mean density, momentum, magnetic field, and energy equations, the evolution equations of the turbulent cross-helicity $W$, turbulent energy $K$ and its dissipation rate $\varepsilon$ are simultaneously solved to calculate the rate of magnetic reconnection for a Harris-type current sheet. In contrast to previous works based on algebraic modeling, the turbulence timescale is self-determined by the nonlinear evolutions of $K$ and $\varepsilon$, their ratio being a timescale. We compare the reconnection rate produced by our mean-field model to the resistive non-turbulent MHD rate. To test whether different regimes of reconnection are produced, we vary the initial strength of turbulent energy and study the effect on the amount of magnetic flux reconnected in time.Comment: 10 pages, 7 figure

Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate $\gamma$ for the KHI decreases with increasing the width of velocity transition layer ${D_{v}}$ but increases with increasing the width of density transition layer ${D_{\rho}}$. After the initial transient period and before the vortex has been well formed, the linear growth rates, $\gamma_v$ and $\gamma_{\rho}$, vary with ${D_{v}}$ and ${D_{\rho}}$ approximately in the following way, $\ln\gamma_{v}=a-bD_{v}$ and $\gamma_{\rho}=c+e\ln D_{\rho} ({D_{\rho}}<{D_{\rho}^{E}})$, where $a$, $b$, $c$ and $e$ are fitting parameters and ${D_{\rho}^{E}}$ is the effective interaction width of density transition layer. When ${D_{\rho}}>{D_{\rho}^{E}}$ the linear growth rate $\gamma_{\rho}$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].Comment: Accepted for publication in PR

Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates

We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov $k^{-5/3}$ power law over almost a decade of length or wavenumber ($k$) scales. The kinetic energy spectrum of regime (C) exhibits a clear $k^{-3/2}$ power law associated with an inertial range for weak-wave turbulence, and a $k^{-7/2}$ power law for high wavenumbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.Comment: 11 pages, 10 figures. Minor updates to text and figures 1, 2 and

The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present

(abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.Comment: 35 pages, 22 figures, revtex style, submitted to PR

Superparamagnetic Liposomes for MRI Monitoring and External Magnetic Field-Induced Selective Targeting of Malignant Brain Tumors

Magnetic-fluid-loadedliposomes (MFLs) of optimized magnetic responsiveness are newly worked out from the entrapment of superparamagnetic maghemite nanocrystals in submicronic PEG-ylated rhodamine-labelled phospholipid vesicles. This nanoplatform provides an efficient tool for the selective magnetic targeting of malignant tumors localized in brain and non-invasive traceability by MRI through intravascular administration. As assessed by in vivo 7-T MRI and ex vivo electron spin resonance, 4-h exposure to 190-T m–1magnetic field gradient efficiently concentrates MFLs into human U87 glioblastoma implanted in the striatum of mice. The magnetoliposomes are then longer retained therein as checked by MRI monitoring over a 24-h period. Histological analysis by confocal fluorescence microscopy confirms the significantly boosted accumulation of MFLs in the malignant tissue up to the intracellular level. Electron transmission microscopy reveals effective internalization by endothelial and glioblastoma cells of the magnetically conveyed MFLs as preserved vesicle structures. The magnetic field gradient emphasizes MFL distribution solely in the tumors according to the enhanced permeability and retention (EPR) effect while comparatively very low amounts are recovered in the other cerebral areas. Such a selective targeting precisely traceable by MRI is promising for therapeutic applications since the healthy brain tissue can be expected to be spared during treatments by deleterious anticancer drugs carried by magnetically guided MFLs

Growth of non-infinitesimal perturbations in turbulence

We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for non-infinitesimal perturbations, generalizing the usual concept of maximum Lyapunov exponent. We also determine the scaling law for our indicator in the framework of the multifractal approach. We find that the scaling exponent is not sensitive to intermittency corrections, but is an invariant of the multifractal models. A numerical test of the results is performed in the shell model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed with uufile

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We present numerical studies of compressible, decaying turbulence, with and without magnetic fields, with initial rms Alfven and Mach numbers ranging up to five, and apply the results to the question of the support of star-forming interstellar clouds of molecular gas. We find that, in 1D, magnetized turbulence actually decays faster than unmagnetized turbulence. In all the regimes that we have studied 3D turbulence-super-Alfvenic, supersonic, sub-Alfvenic, and subsonic-the kinetic energy decays as (t-t0)^(-x), with 0.85 < x < 1.2. We compared results from two entirely different algorithms in the unmagnetized case, and have performed extensive resolution studies in all cases, reaching resolutions of 256^3 zones or 350,000 particles. We conclude that the observed long lifetimes and supersonic motions in molecular clouds must be due to external driving, as undriven turbulence decays far too fast to explain the observations.Comment: Submitted to Phys. Rev. Letters, 29 Nov. 1997. 10 pages, 2 figures, also available from http://www.mpia-hd.mpg.de/theory/preprints.html#maclo

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200

Statistical Properties of Turbulence: An Overview

We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.Comment: 34 pages, 31 figure