Search results for "Vorticity"
showing 10 items of 66 documents
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
2016
We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space $$L_t^\infty L_x^2$$ , satisfying appropriate vorticity estimates. We also obtain impr…
Classical and quantum vortex leapfrogging in two-dimensional channels
2020
The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterizes these systems motivates the study of leapfrogging of vortices within narrow channels. Using the two-dimensional point vortex model, we show that in the constrained geometry of a two-dimensional channel the dynamics is richer than in an unbounded domain: alongsize the known regimes of standard leapfrogging and the absence of it, we identify new regimes of backward leapfrogging and periodic orbits. Moreover, by solving the Gross-Pitaevskii…
SUNRISE/IMaX observations of convectively driven vortex flows in the Sun
2010
We characterize the observational properties of the convectively driven vortex flows recently discovered on the quiet Sun, using magnetograms, Dopplergrams and images obtained with the 1-m balloon-borne Sunrise telescope. By visual inspection of time series, we find some 3.1e-3 vortices/(Mm^2 min), which is a factor of 1.7 larger than previous estimates. The mean duration of the individual events turns out to be 7.9 min, with a standard deviation of 3.2 min. In addition, we find several events appearing at the same locations along the duration of the time series (31.6 min). Such recurrent vortices show up in the proper motion flow field map averaged over the time series. The typical vertica…
The influence of strain localisation on the rotation behaviour of rigid objects in experimental shear zones
2002
Abstract Mica fish and tourmaline fish from natural mylonites were analysed in thin section to determine their orientation distribution. They are oriented with their long axes tilted with respect to the mylonitic foliation, and fish with a small aspect ratio exhibit a slightly larger angle than fish with a large aspect ratio. This orientation seems to be a stable orientation for the mica and tourmaline fish. Analogue experiments with two rheologically different matrix materials were performed to explain the data. One material was PDMS, a linear viscous polymer. The other was tapioca pearls, a granular material with low cohesion and Mohr–Coulomb type behaviour. In contrast to a fairly homoge…
Modelling of segment structures: Boudins, bone-boudins, mullions and related single- and multiphase deformation features
2009
Finite element modelling has been used to simulate the development of segment structures, deformed layer segments separated by veins, such as boudins, mullions, and bone-boudins. A parameter sensitivity analysis is used to compare the influence of the nature of the flow, the relative viscosities of veins in necks and the host rock, and the initial geometry of the layer segments. Parameter fields have been determined for the relative viscosity of veins and layers, and the kinematic vorticity number of flow. Reworked segment structures can have several shapes such as bone-, bulging, shortened bone-boudins and their asymmetric equivalents such as domino- and shearband-boudin geometry. The mode…
The influence of matrix rheology and vorticity on fabric development of populations of rigid objects during plane strain deformation
2002
Abstract The influence of vorticity and rheology of matrix material on the development of shape-preferred orientation (SPO) of populations of rigid objects was experimentally studied. Experiments in plane strain monoclinic flow were performed to model the fabric development of two populations of rectangular rigid objects with object aspect ratios (Rob) 2 and 3. The density of the rigid object populations was 14% of the total area. Objects were dispersed in a Newtonian and a non-Newtonian, power law matrix material with a power law exponent n of 1.2. The kinematic vorticity number (Wn) of the plane strain monoclinic flow was 1, 0.8 and 0.6 with finite simple shear strain of 4.6, 3.0 and 0.9,…
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
2019
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous rando…
Vortex motion in Nb/PdNi/Nb trilayers: new aspects in the flux flow state
2011
We study the dynamics of vortex lines in Supercondutor/Ferromagnet/Superconductor (SFS) heterostructures at microwave frequencies. We have employed swept-frequency, Corbino-disk and resonant, dielectric-resonator techniques to obtain the field and temperature dependence of the vortex-state parameters. We concentrate here on the genuine flux-flow resistivity $\rho_{ff}$, that we access at subcritical currents using a sufficiently high driving frequency. We find that $\rho_{ff}$ does not follow the well-known Bardeen-Stephen model. Instead, it is well described by a full time-dependent Ginzburg-Landau expression at very thin F layer thickness, but changes to a previously unreported field-depe…
Force-free state in a superconducting single crystal and angle-dependent vortex helical instability
2017
Superconducting 2H-NbSe2 single crystals show intrinsic low pinning values. Therefore, they are ideal materials with which to explore fundamental properties of vortices. (V, I) characteristics are the experimental data we have used to investigate the dissipation mechanisms in a rectangular shape 2H-NbSe2 single crystal. Particularly, we have studied dissipation behavior with magnetic fields applied in the plane of the crystal and parallel to the injected currents, i.e. in the force-free state where the vortex helical instability governs the vortex dynamics. In this regime, the data follow the elliptic critical state model and the voltage dissipation shows an exponential dependence.Moreover,…
Stratosphere–Troposphere Exchange and Its Relation to Potential Vorticity Streamers and Cutoffs near the Extratropical Tropopause
2007
Abstract Two distinct dynamical processes near the dynamical tropopause (2-PVU surface) and their relation are discussed in this study: stratosphere–troposphere exchange (STE) and the formation of distinct potential vorticity (PV) structures in the form of stratospheric and tropospheric streamers and cutoffs on isentropic surfaces. Two previously compiled climatologies based upon the 15-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-15) dataset (from 1979 to 1993) are used to establish and quantify the link between STE and these PV structures. An event-based analysis reveals a strong relation between the two processes. For instance, on isentropes below 320 K, 30%–50%…