37 research outputs found
Bottom-trapped currents as statistical equilibrium states above topographic anomalies
Oceanic geostrophic turbulence is mostly forced at the surface, yet strong
bottom-trapped flows are commonly observed along topographic anomalies. Here we
consider the case of a freely evolving, initially surface-intensified velocity
field above a topographic bump, and show that the self-organization into a
bottom-trapped current can result from its turbulent dynamics. Using
equilibrium statistical mechanics, we explain this phenomenon as the most
probable outcome of turbulent stirring. We compute explicitly a class of
solutions characterized by a linear relation between potential vorticity and
streamfunction, and predict when the bottom intensification is expected. Using
direct numerical simulations, we provide an illustration of this phenomenon
that agrees qualitatively with theory, although the ergodicity hypothesis is
not strictly fulfilled
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
Statistical characterisation of bio-aerosol background in an urban environment
In this paper we statistically characterise the bio-aerosol background in an
urban environment. To do this we measure concentration levels of naturally
occurring microbiological material in the atmosphere over a two month period.
Naturally occurring bioaerosols can be considered as noise, as they mask the
presence of signals coming from biological material of interest (such as an
intentionally released biological agent). Analysis of this 'biobackground' was
undertaken in the 1-10 um size range and a 3-9% contribution was found to be
biological in origin - values which are in good agreement with other studies
reported in the literature. A model based on the physics of turbulent mixing
and dispersion was developed and validated against this analysis. The Gamma
distribution (the basis of our model) is shown to comply with the scaling laws
of the concentration moments of our data, which enables us to universally
characterise both biological and non-biological material in the atmosphere. An
application of this model is proposed to build a framework for the development
of novel algorithms for bio-aerosol detection and rapid characterisation.Comment: 14 Pages, 8 Figure
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
Manifestation of the Berry curvature in geophysical ray tracing
International audienceGeometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial WentzelâKramersâBrillouin ansatz to derive ray- tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallow-water wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for PoincarĂ© wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallow-water model