On the origin of steep edges and filaments in vorticity and potential vorticity fields

High-resolution numerical calculations are shown which capture the fundamental process responsible for the intensification of vorticity gradients in an isolated vortex subject to externally imposed distrubances. Imposition of almost any weak strain or shear field in stripping away the relatively weak vorticity at the edge of the vortex and leaves it with gradients four to six orders of magnitude greater than in the initial state. Calculations displaying such enormous gradients have never been reported previously, because of the artificial eddy diffusivities that always limit such gradients in standard numerical models. The present calculations, which have no such limitations, have been made possible by the development of a novel and robust new numerical technique for vortex dynamics called contour surgery

Vortical control of forced two-dimensional turbulence

A new numerical technique for the simulation of forced two-dimensional turbulence (Dritschel and Fontane, 2010) is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods,making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott (2007), namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k^(−2) is obtained in place of the classical k^(−5/3) prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t^(−1) rather than Kraichnan’s prediction of t^(−3/2). The deviation from Kraichnan’s theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale

Breaking Kelvin: Circulation conservation and vortex breakup in MHD at low Magnetic Prandtl Number

In this paper we examine the role of weak magnetic fields in breaking Kelvin's circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a low magnetic Prandtl number (low $Pm$) fluid. We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation $\Gamma$ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex the loss of circulation depends on the total area swept out by the rotating vortex and so this leads to more efficient circulation loss than for a circular vortex.Comment: 21 pages, 12 figure

On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.PostprintPeer reviewe

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows

Vortex scaling ranges in two-dimensional turbulence

We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.PostprintPeer reviewe

Interaction between a surface quasi-geostrophic buoyancy anomaly jet and internal vortices

This paper addresses the dynamical coupling of the ocean's surface and the ocean's interior. In particular, we investigate the dynamics of an oceanic surface jet, and its interaction with vortices at depth. The jet is induced by buoyancy (density) anomalies at the surface. We first focus on the jet alone. The linear stability indicates there are two modes of instability: the sinuous and the varicose modes. When a vortex in present below the jet, it interacts with it. The velocity field induced by the vortex perturbs the jet and triggers its destabilisation. The jet also influences the vortex by pushing it under a region of co-operative shear. Strong jets may also partially shear out the vortex. We also investigate the interaction between a surface jet and a vortex dipole in the interior. Again, strong jets may partially shear out the vortex structure. The jet also modifies the trajectory of the dipole. Dipoles travelling towards the jet at shallow incidence angles may be reflected by the jet. Vortices travelling at moderate incidence angles normally cross below the jet. This is related to the displacement of the two vortices of the dipole by the shear induced by the jet. Intense jets may also destabilise early and form streets of billows. These billows can pair with the vortices and separate the dipole.PostprintPeer reviewe

Fermion self-trapping in the optical geometry of Einstein-Dirac solitons

Funding: St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1 (P.E.D.L).We analyze gravitationally localized states of multiple fermions with high angular momenta, in the formalism introduced by Finster, Smoller, and Yau [Phys Rev. D 59, 104020 (1999)]. We show that the resulting solitonlike wave functions can be naturally interpreted in terms of a form of self-trapping, where the fermions become localized on shells the locations of which correspond to those of “bulges” in the optical geometry created by their own energy density.Publisher PDFPeer reviewe

Evaluasi Hasil Penjualan Perumahan Bersubsidi Oleh Sales Person Pasca Training Pada PT Paloma Citra Internasional

“EVALUASI HASIL PENJUALAN PERUMAHAN BERSUBSIDI OLEH SALES PERSON PASCA TRAINING PADA PT PALOMA CITRA INTERNASIONAL” YUNIZAR IKA PURNAMANINGTYAS F3214077 Sales person memiliki pengaruh besar dalam memenangkan persaingan pasar. Sebagai ujung tombak perusahaan sales person harus memiliki keahlian dan ketrampilan yang khusus. Ketrampilan dan kinerja tenaga penjual memiliki fungsi tersendiri yaitu menjembatani hubungan antara perusahaan dengan konsumen. Kinerja tenaga penjual yang baik juga berperan sebagai keunggulan bersaing perusahaan. Penelitian ini bertujuan untuk mengukur kinerja sales person setelah diadakannya training. Dasar interpersonal skill, salesmanship skill, dan technical skill juga penting. Evaluasi yang dilakukan dengan mengukur hasil penjualan. Pengukuran diadakan sebelum pelatihan dan setelah pelatihan. Hasil penjualan tiap sales person akan diukur dan di bandingkan sebelum dan sesudah pelatihan. Metode penelitian yang digunakan dalam penyusunan tugas akhir ini adalah penelitian deskriptif yaitu peneliti akan membuat gambaran atau deskripsi mengenai evaluasi hasil penjualan pada PT Paloma Citra Internasional. Data yang diperoleh melalui dua sumber yaitu data primer dan data sekunder. Data primer diperoleh dari jawaban direktur perusahaan melalui wawancara. Data sekunder diperoleh dari sumber lain seperti buku referensi yang mendukung dan beberapa data dari perusahaan. Hasil rata-rata presentase penjualan sebelum pelatihan adalah 8,81% dengan total rumah yang ditawarkan 116 unit rumah. Sedangkan setelah pelatihan penjualan menjadi 14,53%. Penjualan meningkat sebesar 5,72%. Perusahaan mengalami keuntungan dari hasil penjualan. Presentase kehadiran para sales person juga meningkat. Kesimpulan yang dapat diambil dari analisa data tersebut bahwa kompetensi sales person memang penting bagi perusahaan. Meningkatkan ketrampilan dengan pelatihan menjadikan penjualan perusahaan meningkat. Diharapkan dapat diadakan pelatihan yang lebih inovatif agar sales person lebih meningkat penjualannya. Kata Kunci : sales person, training, evaluasi penjualan

The interaction of two asymmetric quasi-geostrophic vortex patches

Herein we study the general interaction of two vortex patches in a single-layer quasi-geostrophic shallow-water flow. Steadily-rotating equilibrium states are found over a wide parameter space spanning the Rossby deformation length, vortex area ratio, potential vorticity ratio, and gap between their innermost edges. A linear stability analysis is then used to identify the critical gap separating stable and unstable solutions, over the entire range of area and potential vorticity ratios, and for selected values of the Rossby deformation length. A representative set of marginally unstable equilibrium states are then slightly perturbed and evolved by an accurate contour dynamics numerical algorithm to understand the long-term fate of the instabilities. Not all instabilities lead to vortex merger; many in fact are characterised by weak filamentation and a small adjustment of the vortex shapes, without merger. Stronger instabilities lead to material being torn from one vortex and either wrapped around the other or reduced to ever thinning filamentary debris. A portion of the vortex may survive, or it may be completely strained out by the other.PostprintPeer reviewe