Discussions on the relationships between meteorology and oceanography

G. E. R. DEACON: There must be some of you who, like me, did most of their seagoing 20 to 30 years ago and find it difficult to keep pace with the present urgency of introducing more precise reasoning into oceanography. This afternoon\u27s session dealing mainly with such precise arguments has not been easy to follow, and it is clear that there is much serious hard work ahead...

Particle entrapment as a feedback effect

We consider a suspension of polarizable particles under the action of traveling wave dielectrophoresis (DEP) and focus on particle induced effects. In a situation where the particles are driven by the DEP force, but no external forces are exerted on the fluid, the joint motion of the particles can induce a steady fluid flow, which leads to particle entrapment. This feedback effect is proven to be non-negligible even for small volume concentration of particles.Comment: 4 pages, 4 figures, submitte

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.Comment: 14 pages, 10 figures, published in Physics of Fluid

Weak Wave Turbulence Scaling Theory for Diffusion and Relative Diffusion in Turbulent Surface Waves

We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical results are shown to be in good agreement with experimental results, where a distinct crossover in diffusive behavior is observed at the driving frequency. For gravity waves our results are discussed in the light of ocean wave studies.Comment: 5 pages; for related work visit http://www.imedea.uib.es/~victo

Sensitivity of the Atlantic meridional overturning circulation to South Atlantic freshwater anomalies

The sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) to changes in basin integrated net evaporation is highly dependent on the zonal salinity contrast at the southern border of the Atlantic. Biases in the freshwater budget strongly affect the stability of the AMOC in numerical models. The impact of these biases is investigated, by adding local anomaly patterns in the South Atlantic to the freshwater fluxes at the surface. These anomalies impact the freshwater and salt transport by the different components of the ocean circulation, in particular the basin-scale salt-advection feedback, completely changing the response of the AMOC to arbitrary perturbations. It is found that an appropriate dipole anomaly pattern at the southern border of the Atlantic Ocean can collapse the AMOC entirely even without a further hosing. The results suggest a new view on the stability of the AMOC, controlled by processes in the South Atlantic. <br/

Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main idea is to show that for sufficiently small noise intensity and slow time dependence, the vast majority of paths remain in small space-time sets, typically in the neighbourhood of potential wells. The size of these sets often has a power-law dependence on the small parameters, with universal exponents. The overall probability of exceptional paths is exponentially small, with an exponent also showing power-law behaviour. The results cover time spans up to the maximal Kramers time of the system. We apply our method to three phenomena characteristic for bistable systems: stochastic resonance, dynamical hysteresis and bifurcation delay, where it yields precise bounds on transition probabilities, and the distribution of hysteresis areas and first-exit times. We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure

Turbulence in a free surface

We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. Particles floating on the surface are used to visualize the flow. The effect of surface waves appears to be negligible. The flow is unconventional in that it is confined to two dimensions but does not have squared vorticity as a conservation law, that it is not divergence free and that it inherits scaling features of the mean square velocity differences S_2(R) and the vorticity fluctuations Omega(R) from the bulk 3-d turbulence.Comment: 4 pages, 4 Postscript figure

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Turbulence and passive scalar transport in a free-slip surface

We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. The velocity correlation functions in the 2D surface and in the 3D volume scale with the same exponents. In the viscous subrange the amplitudes are the same, but in the inertial subrange the 2D one is reduced to 2/3 of the 3D amplitude. The surface flow is more strongly intermittent than the 3D volume flow. Geometric scaling theory is used to derive a relation between the scaling of the velocity field and the density fluctuations of a passive scalar advected on the surface.Comment: 11 pages, 10 Postscript figure