128 research outputs found
Evolution of the Leading-Edge Vortex over an Accelerating Rotating Wing
AbstractThe flow field over an accelerating rotating wing model at Reynolds numbers Re ranging from 250 to 2000 is investigated using particle image velocimetry, and compared with the flow obtained by three-dimensional time-dependent Navier-Stokes simulations. It is shown that the coherent leading-edge vortex that characterises the flow field at Re~200-300 transforms to a laminar separation bubble as Re is increased. It is further shown that the ratio of the instantaneous circulation of the leading-edge vortex in the accel-eration phase to that over a wing rotating steadily at the same Re decreases monotonically with increasing Re. We conclude that the traditional approach based on steady wing rotation is inadequate for the prediction of the aerodynamic performance of flapping wings at Re above about 1000
Evidence for topological nonequilibrium in magnetic configurations
We use direct numerical simulations to study the evolution, or relaxation, of
magnetic configurations to an equilibrium state. We use the full single-fluid
equations of motion for a magnetized, non-resistive, but viscous fluid; and a
Lagrangian approach is used to obtain exact solutions for the magnetic field.
As a result, the topology of the magnetic field remains unchanged, which makes
it possible to study the case of topological nonequilibrium. We find two cases
for which such nonequilibrium appears, indicating that these configurations may
develop singular current sheets.Comment: 10 pages, 5 figure
Dynamics of the Tippe Top via Routhian Reduction
We consider a tippe top modeled as an eccentric sphere, spinning on a
horizontal table and subject to a sliding friction. Ignoring translational
effects, we show that the system is reducible using a Routhian reduction
technique. The reduced system is a two dimensional system of second order
differential equations, that allows an elegant and compact way to retrieve the
classification of tippe tops in six groups as proposed in [1] according to the
existence and stability type of the steady states.Comment: 16 pages, 7 figures, added reference. Typos corrected and a forgotten
term in de linearized system is adde
Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations
We establish a connection between Optimal Transport Theory and classical
Convection Theory for geophysical flows. Our starting point is the model
designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal
Transport problems. This model can be seen as a generalization of the
Darcy-Boussinesq equations, which is a degenerate version of the
Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate
different variants of the NSB equations (in particular what we call the
generalized Hydrostatic-Boussinesq equations) to various models involving
Optimal Transport (and the related Monge-Ampere equation. This includes the 2D
semi-geostrophic equations and some fully non-linear versions of the so-called
high-field limit of the Vlasov-Poisson system and of the Keller-Segel for
Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model
can be related to the magnetic relaxation model studied by Arnold and Moffatt
to obtain stationary solutions of the Euler equations with prescribed topology
Cross helicity and turbulent magnetic diffusivity in the solar convection zone
In a density-stratified turbulent medium the cross helicity is
considered as a result of the interaction of the velocity fluctuations and a
large-scale magnetic field. By means of a quasilinear theory and by numerical
simulations we find the cross helicity and the mean vertical magnetic field
anti-correlated. In the high-conductivity limit the ratio of the helicity and
the mean magnetic field equals the ratio of the magnetic eddy diffusivity and
the (known) density scale height. The result can be used to predict that the
cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign
is anti-correlated with that of the radial mean magnetic field. Alternatively,
we can use our result to determine the value of the turbulent magnetic
diffusivity from observations of the cross helicity.Comment: 9 pages, 2 figures, submitted to Solar Physic
Nonlinear stabilitty for steady vortex pairs
In this article, we prove nonlinear orbital stability for steadily
translating vortex pairs, a family of nonlinear waves that are exact solutions
of the incompressible, two-dimensional Euler equations. We use an adaptation of
Kelvin's variational principle, maximizing kinetic energy penalised by a
multiple of momentum among mirror-symmetric isovortical rearrangements. This
formulation has the advantage that the functional to be maximized and the
constraint set are both invariant under the flow of the time-dependent Euler
equations, and this observation is used strongly in the analysis. Previous work
on existence yields a wide class of examples to which our result applies.Comment: 25 page
Generalised Gagliardo–Nirenberg inequalities using weak Lebesgue spaces and BMO
Using elementary arguments based on the Fourier transform we prove that for
, if then and there
exists a constant such that
where . In
particular, in we obtain the generalised Ladyzhenskaya inequality
. We also
show that for the norm in can be replaced by the
norm in BMO. As well as giving relatively simple proofs of these inequalities,
this paper provides a brief primer of some basic concepts in harmonic analysis,
including weak spaces, the Fourier transform, the Lebesgue Differentiation
Theorem, and Calderon-Zygmund decompositions
Diffusive transport and self-consistent dynamics in coupled maps
The study of diffusion in Hamiltonian systems has been a problem of interest
for a number of years.
In this paper we explore the influence of self-consistency on the diffusion
properties of systems described by coupled symplectic maps. Self-consistency,
i.e. the back-influence of the transported quantity on the velocity field of
the driving flow, despite of its critical importance, is usually overlooked in
the description of realistic systems, for example in plasma physics. We propose
a class of self-consistent models consisting of an ensemble of maps globally
coupled through a mean field. Depending on the kind of coupling, two different
general types of self-consistent maps are considered: maps coupled to the field
only through the phase, and fully coupled maps, i.e. through the phase and the
amplitude of the external field. The analogies and differences of the diffusion
properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure
- …