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The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of n antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases n = 2, 3 are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations. [ABSTRACT FROM AUTHOR]

For a number of years the fundamental processes behind rotating turbulence have been debated. Whilst the Coriolis force appears as a linear term in the Navier-Stokes equation, many believe that the columnar eddies, which are so evident in experiments and simulations, are created by non-linear mechanisms. However, new findings have recently re-established the importance of linear processes, suggesting that, under typical laboratory situations, linear inertial waves play an important role in the formation of columnar eddies. These findings are both analytical and experimental. Analytical work, conducted in the limit Ro → 0, shows that an initially compact eddy evolves into two separate elongated structures, which propagate along the rotation axis. This change in the morphology of the eddy is achieved through inertial wave propagation, a prediction that has now been confirmed experimentally. Our laboratory experiment consisted of a single grid oscillation in the bottom of a rotating tank of water. This created a cloud of turbulence from which elongated columnar structures emerged. These propagate linearly with time into the quiescent region above. The distance travelled by these structures was then tracked over a sequence of images, and the speed of propagation is found to be proportional to both the speed of rotation and the bar size of the grid, which is consistent with structure formation due to linear wave propagation. [ABSTRACT FROM AUTHOR]

A wavelet-based method to extract coherent vortices is applied to data of three-dimensional incompressible homogeneous isotropic turbulence with the Taylor micro-scale Reynolds number 471 in order to examine contribution of the vortices to statistics on the turbulent flow. We observe a strong scale-by-scale correlation between the velocity field induced by them and the total velocity field over the scales retained by the data. We also find that the vortices almost preserve statistics of nonlinear interactions of the total flow over the inertial range. [ABSTRACT FROM AUTHOR]

Several features of decaying and forced two-dimensional turbulent flows confined between no-slip walls are addressed, with emphasis put on the crucial role played by the solid walls. Such walls are essential in that they act as sources of vorticity filaments and in that they provide shear and normal stresses that exert torques on the fluid, hence possibly changing its net angular momentum. In the case of decaying 2D turbulence on a square domain this may result in an increase of the fluid's absolute angular momentum. Numerical simulations of forced 2D flow have revealed that sign reversal of the total angular momentum may occur, owing to breakdown of the organized central cell as a result of erosion by wall-induced vorticity filaments and the subsequent re-establishment of a cell (of either sign). [ABSTRACT FROM AUTHOR]

The task of period multiplying cascade detection in some dynamical systems is a rather complicated problem. The presence of bifurcation chain is not a guarantee that this chain will continue ad infinitum. The indirect confirmation of infinite period multiplying cascade presence is self-duplication of the period muliplying "tree" and convergence of its characteristics to certain universal values. The goal of the present work is to study different period multiplying sequences, e.g. period tripling as well as numerical determination and their Feigenbaum and scaling constants. [ABSTRACT FROM AUTHOR]

The characteristics of the motion of A + 1 point vortices with A symmetry planes in a two-layer fluid are studied. The central vortex belongs to the upper layer, and an A-gonal configuration of vortices with equal intensity — is located in the bottom one. The analysis of the theoretically possible stationary movements at A ≥ 2 is carried out. Preliminary numerical results are obtained for the stability of symmetrical configurations in the particular case of A = 2. [ABSTRACT FROM AUTHOR]

We address two research lines, continuing our work in [11]. The first uses the affine connection introduced by Cartan at the 1928 International Congress of Mathematicians. We classify here the 2-3-5 nonholonomic geometries. The maximum symmetry case, 6-dimensional, has two branches. We describe the most interesting and quite surprising one, that ocurs in the celebrated 3:1 sphere-sphere distribution (a shadow of Cartan's exceptional Lie group G2). In the second part we study the dynamics of a "rubber coated" body rolling without slipping nor twisting on a surface. If the latter is a sphere one has a SO(3) Chaplygin system [14], and the dynamics reduces to T* S2. The sphere-sphere problem is conformally symplectic. Details and further results will be published elsewhere (for the dynamic part, see [16]), and posted on Arxiv. [ABSTRACT FROM AUTHOR]

The system of two interacting dynamically 2D rigid circular cylinders in an infinite volume of perfect fluid was considered in [4, 5], while the pioneering contribution is due to Hicks [1, 2]. An allied problem—the motion of two spheres in perfect fluid—was studied by Stokes, Hicks, Carl and Vilhelm Bjerknes, Kirhhoff, and Joukowski (the references can be found in [3] and [7]). Assuming the circulations around the cylinders to be constant and making the radii of the cylinders infinitely small result in new 2D hydrodynamic objects called mass vortices [5]. The equations of motion for mass vortices expand upon the classical Kirhhoff equations governing the motion of ordinary point vortices. In this paper the motion of two mass vortices is examined in greater detail (some results have been obtained already in [5]). A reduction of order is performed; using the Poincaré surface-of-section technique the system is shown to be generally non-integrable. Some integrable cases are indicated. In conclusion the motion of a single mass vortex and the motion of cylinder in a half-plane are briefly investigated. [ABSTRACT FROM AUTHOR]

The motion of two vortex rings on a sphere is considered. This motion generalizes the well-known centrally symmetrical solution of the equations of point vortex dynamics on a plane derived by D. N. Goryachev, N. S. Vasiliev and H. Aref. The equations of motion in this case are shown to be Liouville integrable, and an explicit reduction to a Hamiltonian system with one degree of freedom is described. Two particular cases in which the solutions are periodical are presented. Explicit quadratures are given for these solutions. Phase portraits are described and bifurcation diagrams are shown for centrally symmetrical motion of four vortices on a sphere. [ABSTRACT FROM AUTHOR]

The nonlinear stability of stratified quasi-geostrophic background currents streaming isolated seamount on f- and β-plane is investigated. Arnol'd theory (1966) and it's implications for quasi-geostrophic flows by McIntyre and Shepherd (1987) are used. The realistic situation in the ocean when the background flow is not homogeneous and has a vertical shift in velocity, whereas the Brunt-Väisälä frequency is not constant, is considered. The hyperbolic law is used for the approximation of the Brunt-Väisälä frequency. Sufficient conditions of the stability are proved. In particularly the stability of the important type of stratified shear currents represented by two-layer flow with differently directed flow in different layers is considered. The topographic eddy in this current has the form of a vortex lens. As it was shown some of two-layer background currents are stable and hence the new type of topographic eddies in the form of a vortex lens is a stable formation. [ABSTRACT FROM AUTHOR]

An asymptotic model for long large-amplitude internal solitary waves with a trapped core, propagating in a narrow layer of nearly uniformly stratified fluid embedded in an infinitely deep homogeneous fluid is presented. The case of a mode one asymmetric wave with an amplitude slightly greater than the critical amplitude, for which there is incipient overturning, is considered. A vortex core located near the point at which this incipient breaking occurs is then incorporated. The effect of the vortex core is to introduce into the governing equation for the wave amplitude an extra nonlinear term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude. The result is that as the wave amplitude increases above the critical amplitude, the wave broadens, which is in marked contrast to the case of small amplitude waves where a sharpening of the wave crest normally occurs. The limiting form of the broadening wave is a deep fluid bore. The wave speed is found to depend nonlinearly on the wave amplitude. [ABSTRACT FROM AUTHOR]

As a development of the work [2], we give a short analysis of regular and chaotic regimes in an idealized periodical current over a submerged obstacle of Gaussian shape. [ABSTRACT FROM AUTHOR]

The linearized Shallow Water Equations (LSWE) on a tangent (x, y) plane to the rotating spherical Earth with Coriolis parameter f(y) that depends arbitrarily on the northward coordinate y is considered as a spectral problem of a self-adjoint operator. This operator is associated with a linear second-order equation in x — y plane that yields all the known exact and approximate solutions of the LSWE including those that arise from different boundary conditions, vanishing of some small terms (e.g. the β-term and frequency) and certain forms of the Coriolis parameter f(y) on the equator or in mid-latitudes. The operator formulation is used to show that all solutions of of the LSWE are stable. In some limiting cases these solutions reduce to the well-known plane waves of geophysical fluid dynamics: Inertia-gravity (Poincaré) waves, Planetary (Rossby) waves and Kelvin waves. In addition, the unified theory yields the non-harmonic analogs of these waves as well as the more general propagating solutions and solutions in closed basins. [ABSTRACT FROM AUTHOR]

Using four models for which the relationship between the degree of phase space chaotization and external excitation frequency was studied earlier we propose the explanation of this relationship on the basis of analysis of circulation time for unperturbed trajectories. [ABSTRACT FROM AUTHOR]

In this article gas-dynamic analogy for shallow water equations is generalized in the case when initial conditions depend on vertical coordinate. Simple parametrization of advective term allowing full theoretical analysis of solutions of simple waves of Riemann problem for modified shallow water equations is suggested. The simple wave solutions obtained have permitted to find dimensionless parameter, which restricts limits of applicability of classical shallow water equations and neglecting advective impulse transfer. Solution of the initial discontinuity decay problem for modified shallow water equations is found. [ABSTRACT FROM AUTHOR]

The interaction of two identical point vortices in an unsteady shear and strain field is studied in a two-dimensional incompressible flow. Their equilibria and stability are computed. Their resonant interaction with the forcing is analyzed. Transition to chaos is presented. [ABSTRACT FROM AUTHOR]

The motion of a localized vortex on the beta-plane, in the presence of a long Rossby wave, is studied with an asymptotic theory and via numerical simulations in an equivalent-barotropic quasi-geostrophic model. The initial phase of the wave is chosen to obtain maximum horizontal shear on the vortex core. This shear modifies the vortex drift via the nonlinear interaction of azimuthal modes one (responsible for the vortex drift) and two (leading to elliptical deformation). The resulting advection of potential vorticity in the background sheared flow by the beta-gyres can be understood in terms of shear-induced distortion of the beta-gyres. [ABSTRACT FROM AUTHOR]

A Lagrangian approach is formulated for rotating stratified axisymmetric flows. The moment of inertia for compact flows with finite energy is shown to oscillate with inertial frequency. In particular, any steady axisymmetric solution for a finite volume inviscid anticyclonic vortex with outcropping isopycnals corresponds to a set of self-similar analytical time-periodic pulson solutions with linear profile of radial velocity which is not affected by horizontal friction. The amplitude of pulsations with inertial frequency can be within a range limited by the intensity of the stationary vortex. If the initial conditions deviate from the pulson solution, inertiagravity waves propagate inside the vortex and may form shocks at the vortex edge calculated by a Lagrangian numerical model. After shocks dissipate due to small friction added near the edge, the solution tends to the pulson solution with linear radial velocity. [ABSTRACT FROM AUTHOR]

This study considers the evolution of long nonlinear Rossby waves in a sheared zonal current in the régime where a competition sets in between weak nonlinearity and weak dispersion. The traditional assumption of a weak amplitude breaks down when the wave speed equals the mean-flow velocity at a certain latitude, due to the appearance of a singularity in the leading order equation, which strongly modifies the flow in the critical layer. Here, nonlinear effects are invoked to resolve this singularity, since the relevant geophysical flows have high Reynolds numbers. Viscosity is introduced in order to render the nonlinear critical-layer solution unique, but the inviscid limit is eventually taken. By the method of matched asymptotic expansions, this inner flow is matched at the edges of the critical layer with the outer flow. This theory is relevant for the phenomenon of Rossby wave breaking and eventual saturation into a nonlinear wave. Spatially localized solutions are described by a Korteweg-de Vries equation, modified by new nonlinear terms, depending on the critical-layer shape. These lead to depression or elevation solitary waves. [ABSTRACT FROM AUTHOR]

The governing equations of motion of two point vortices in an ideal fluid in the plane has a Hamiltonian formulation that is completely integrable, so the dynamics are regular in the sense that one has quasiperiodic solutions confined to invariant two-dimensional tori accompanied by periodic orbits. Moreover, it is well known that the same is true of the dynamics of two point vortices in an ideal fluid in a standard half-plane (with a straight line boundary). It is natural to ask if this is also the case for half-planes whose boundaries are perturbations of a straight line. We prove here that there are such Hamiltonian perturbations of two vortex dynamics in the half-plane that generate chaotic — and a fortiori nonintegrable — dynamics, thereby answering an open question of rather long standing. Our proof, like most demonstrations of this kind, is based on Melnikov's method. [ABSTRACT FROM AUTHOR]

We consider equations describing nonstationary motion of ideal liquid with free boundary in a gravitational field. Existence of analytic solutions of the above equations for a sufficiently small time interval is proved. Solutions from Sobolev spaces of finite order are also investigated. [ABSTRACT FROM AUTHOR]

New models and properties of piezoceramic transducer due to the interaction with the excitation device of limited power-supply are built and investigated in details. The special attention is given to examination of origin and development of the deterministic chaos in this system. It is shown, that a major variety of effects typical for problems of chaotic dynamics is inherent in the system. The presence of several types of chaotic attractors is established and the existence of hyper-chaos is revealed. [ABSTRACT FROM AUTHOR]

Shocks with regular and stochastic structures are observed in numerical solutions for various systems of nonlinear equations with dispersion. Analytical methods to predict the type of the shock are developed. Averaging methods are used for analysis of these solutions. [ABSTRACT FROM AUTHOR]

A new mechanism of transition to instability is treated arising for vertical motions with phase transition in horizontally infinite two dimensional domains of a porous medium. Destabilization of a plane interface takes place at zero wave number being accompanied by reversible bifurcations indicating the formation of a secondary flow with a shifted phase transition interface. Sub- and supercritical structures in a neighborhood of the threshold of instability obey the weakly nonlinear diffusion equation. Homoclinic solutions of this equation corresponding to the horizontally nonhomogeneous phase transition interface and bifurcating from the basic state are found to be unstable both in subcritical as well as in supercritical cases. We consider two examples of motion in a porous medium: the first one describes vertical flows with phase transition in a high-temperature geothermal reservoirs, consisting of two high-permeability layers, which are separated by a low-permeability stratum. The second example relates to to the Rayleigh-Taylor instability of a water layer located over an air-vapor layer in a porous medium under isothermal condition in presence of capillary forces at the phase transition interface. [ABSTRACT FROM AUTHOR]

In the present study, the stability of a helical vortex triplet has been predicted theoretically for the first time, and its existence proven experimentally as well as numerically. As basic flow configuration, swirling flows induced by a rotating cover in a closed cylinder have been considered. The experimental investigation was carried using simultaneously two diagnostics methods: Particle Image Velocimetry (PIV) to determine velocity fields by particle tracks and Laser Doppler Anemometry (LDA) to establish time-histories. The flow was systematically investigated for flow structures and, as a result, the existence of a stable vortex triplet was found at operating conditions corresponding to those predicted by the theoretical stability analysis. For the same flow regime, the 3D unsteady Navier-Stokes equations were solved numerically to identify the 3D structure of the vortex triplet. [ABSTRACT FROM AUTHOR]

Efficient experimental technique and tools for study of the physical processes in view are developed, as well as experimental equipment and new methods for measurements of turbulent fluctuations in the turbulent boundary layer. The fluctuating wall pressures that develop beneath a turbulent boundary layer have received extensive analytical and experimental investigation over the past few decades. In fluid mechanics and hydrodynamical acoustics the principal interest in turbulent pressure fluctuations lies in their role as a source of structural excitation and reradiation of acoustic noise. We developed a new experimental method for study the dynamics of near-wall turbulence problems is based on the higher moments investigation. The models that most adequately describe the spatial structure of turbulent pressure are the continual statistical models specified by a characteristic functional which provide a complete statistical description of the random field of pressure fluctuations. In this paper, we analyze simple analytical representations of the characteristic functional of turbulent wall-pressure fluctuations. The functional approach to measuring turbulent pressures provides an almost exhaustive description of the random field on the basis of the experimentally measured characteristic functional of the turbulent fields. A method for the experimental study of the characteristic functional and multidimensional distributions of parameters of the field of turbulent pressure fluctuations is described. [ABSTRACT FROM AUTHOR]

We describe a new effect of floaters clustering by surface waves. This clustering is a result of the surface tension force, which for small particles becomes comparable with their weight. Surface tension creates a difference between the masses of a particle and displaced liquid making the particle effectively inertial. Inertia, positive for hydrophobic or negative for hydrophilic particles, causes particle clustering in the nodes or antinodes of a standing wave and leads to chaotic mixing in random waves. Here we show experimentally that in a standing wave the clustering rate is proportional to the squared wave amplitude. In the case of random waves we demonstrate that inertia effects change statistics of floater distribution and particles concentrate on a multifractal set. [ABSTRACT FROM AUTHOR]

Tripolar vortices have been observed to emerge in two-dimensional flows from the evolution of unstable shielded monopoles. They have also been obtained from a stable Gaussian vortex with a large quadrupolar perturbation. In this case, if the amplitude of the perturbation is small, the flow evolves into a circular monopolar vortex, but if it is large enough a stable tripolar vortex emerges. This change in final state has been previously explained by invoking a change of topology in the co-rotating stream function. We find that this explanation is insufficient, since for all perturbation amplitudes, large or small, the co-rotating stream function has the same topology; namely, three stagnation points of centre type and two stagnation points of saddle type. In fact, this topology lasts until late in the flow evolution. However, the time-dependent Lagrangian description can distinguish between the two evolutions, as only when a stable tripole arises the hyperbolic character of the saddle points manifests persistently in the particle dynamics (i.e. a hyperbolic trajectory exists for the whole flow evolution). [ABSTRACT FROM AUTHOR]

Translating point vortex street configurations model asymptotic states of wakes in a two-dimensional fluid. In this paper such configurations are found with the aid of a multilinear differential equation analogous to the one used in the non-periodic case. Arrangements of point vortex streets with circulations +1/-1 or +1/-2, arbitrary translation velocity and arbitrary numbers of vortex streets (consistent with zero total circulation) are found; the polynomials describing these arrangements have free complex parameters and hence describe a continuum or family of translating states. A similar family with three circulation values is also exhibited. [ABSTRACT FROM AUTHOR]

A version of the theoretical design of a size distribution function for mixed-layer thermals is proposed. In the framework of this approach, classical Boltzmann statistics is supplemented with a hydrodynamic invariant that describes the motion of isolated thermals. The gamma distribution that we have derived agrees with numerous experimental data obtained earlier for size distribution of thermals in the convective boundary layer. [ABSTRACT FROM AUTHOR]

Numerical solutions of the kinetic equation for deep water wind waves (the Hasselmann equation) for various functions of external forcing are analyzed. For wave growth in spatially homogeneous sea (the so-called duration-limited case) the numerical solutions are related with approximate self-similar solutions of the Hasselmann equation. These self-similar solutions are shown to be considered as a generalization of the classic Kolmogorov-Zakharov solutions in the theory of weak turbulence. Asymptotic law of wave growth that relates total wave energy with net total energy input (energy flux at high frequencies) is proposed. Estimates of self-similarity parameter that links energy and spectral flux and can be considered as an analogue of Kolmogorov-Zakharov constants are obtained numerically. [ABSTRACT FROM AUTHOR]

A system of equations determining average velocity of ideal incompressible fluid is derived from the assumption that fluid motion is ergodic. Two flows are considered: one vortex line in a bounded cylindrical domain and a flow of almost circular vortex lines. In the first case the averaged equations have the form of an eigenvalue problem similar to that for Schrődinger's equation. [ABSTRACT FROM AUTHOR]

Recent advances in experimental techniques have opened a window on real time dynamical behavior in molecular systems. This necessitates the development of new theoretical, modeling, and computational techniques to both interpret and model the data and to use the models to predict new phenomena. We argue that the framework of the geometrical theory of nonlinear dynamical systems is ideal for the development of such a program. In this paper we discuss recent theoretical and computational issues and results along these lines. [ABSTRACT FROM AUTHOR]

From a physical viewpoint the assumption of flow's non-divergence, which greatly simplifies the Shallow Water Equations, is justified by the addition of a virtual "rigid lid" that overlies the surface of the fluid and which supplies the pressure gradient forces that drive the (non-divergent) velocity field. In the presence of rotation any initial vorticity field generates divergence by the Coriolis force in the same way that any initial horizontal velocity component generates the other component in finite time, which implies that an initial non-divergent flow is bound to become divergent at later times. Using a particular scaling of the Shallow Water Equations it can be shown that non-divergent flows are regular limits of the Shallow Water Equations when the layer of fluid is sufficiently thick (high) even though the required surface pressure is not determined by the height of the fluid. These analytical considerations are supported by numerical calculations of the instability of a shear flow on the f-plane that show how the non-divergent instability is the limit of the divergent instability when the mean layer thickness becomes large. [ABSTRACT FROM AUTHOR]

When helical neutral modes propagate on a vortex with a continuous velocity profile the inviscid equation governing linear stability theory may have a singular critical point at some value of r, the radial coordinate. Viscosity or temporal evolution can be restored locally to treat the critical layer centered on this singular point. Nonlinearity, however, is a more appropriate choice in applications where the Reynolds number is large. The associated theory is outlined in this paper and new solutions to the eigenvalue problem are presented. [ABSTRACT FROM AUTHOR]

A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic find coupled to a massive rotating sphere. The angular momentum of the fluid component changes under complex torques that are not resolved and the kinetic energy of the fluid is not a conserved Hamiltonian in these models. These models are used in a statistical equilibrium formulation for the energy — relative enstrophy theory of the coupled barotropic fluid — rotating sphere system, known as Kac's spherical model, to study the interactions between the energy cascade to large scales and angular momentum transfer. Exact solution of this model provides critical temperatures and amplitudes of the ground modes — superrotating solid body flows — in the BECondensed phase. [ABSTRACT FROM AUTHOR]

This paper provides a new insight to the classical Björknes's problem. We examine a mechanical system "solid+fluid" consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton's) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical high-frequency pulsations (vibrations) of the singlet. In order to construct the high-frequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the "slow" Lagrangian for the averaged motions directly from Hamilton's principle. We derive such a "slow" Lagrangian for a general solid. In details, we study the "slow" dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the "Björknes's dynamic buoyancy" for a solid of general form. [ABSTRACT FROM AUTHOR]

The notions of a heton and baroclinic modon had been brought into use in geophysical find dynamics more than two decades ago; the concept of a hetonic quartet is a new one. A heton is a two-layer quasigeostrophic (generally, translating) point-vortex pair. Two aligned hetons with properly fitted circulations and separations form a steadily translating collinear ensemble of four discrete vortices, termed a hetonic quartet. Baroclinic modons, i.e., localized regular steady-state solutions to the nonlinear equations of potential vorticity (PV) conservation in a (differentially) rotating stratified fluid, represent a paradigm for coherent structures in geophysical flows. Hetons and hetonic quartets share some traits with baroclinic modons and, therefore, offer a finite-dimensional model for exploring the modon stability and transitions. A baroclinic modon appears as two oppositely signed PV chunks that reside at different depths (one in the upper layers and the other in the lower layers) and are shifted relative to each other in the north-south direction. A hetonic quartet is a discrete counterpart of a two-layer modon whose upper- and lower-layer PV chunks overlap considerably, while a heton models a nonoverlapping modon. The phenomenon of transition of baroclinic modons from overlapping to nonoverlapping states (observed in numerical simulations) is explained in terms of stability of hetonic quartets and their breakdown into two noninteracting hetons. [ABSTRACT FROM AUTHOR]

Motion of an elliptic vortex ring is considered as an example of unsteady 3D vortex motion. The Local Induction Equation is used for the analysis. By keeping the self-induction constant and changing its value in the equation, different features of particle motion around an elliptic vortex ring, corresponding to thin and fat vortex rings, can be observed numerically. [ABSTRACT FROM AUTHOR]

An unstable periodic flow (UPF), which represents the characteristics of a minimal Couette turbulence, is applied for the study of stretching rate of passive vectors for the purpose of understanding the mixing mechanism in turbulence. It is shown that any two passive vectors, which start from a same position but with different directions in UPF, tend to align with each other in a few periods of UPF. This property of alignment guarantees that the direction (therefore the stretching rate as well) of passive vectors is uniquely determined by the spatio-temporal structure of UPF (perhaps of turbulence too). That is, the fields of direction and stretching rate of passive vectors can be defined for a given UPF, which enables us to directly compare the stretching rate of passive vectors and the instantaneous structure of the flow. The fields of various physical quantities associated with passive vectors can be constructed by a long-term particle simulation. By taking the spatio-temporal correlation between these fields of passive vectors and the rate-of-strain field of UPF, we find that there is a strong correlation between the stretching rate of passive vectors and the first eigenvector of the rate-of-strain tensor, and that not only the magnitude of the first eigenvalue but also the direction of the first eigenvector are relevant to the strong stretching of passive vectors. [ABSTRACT FROM AUTHOR]

We consider destruction of adiabatic invariance in volume-preserving systems due to separatrix crossings, scattering on and capture into resonances. These mechanisms result in mixing and transport in large domains of phase space. We consider several examples of systems where these phenomena occur. [ABSTRACT FROM AUTHOR]

Motion of a vortex filament with axial flow in the core, i.e. a vortex-jet filament, is governed, in the localized induction approximation, by the first two terms of the localized induction hierarchy. Permanent form of a steadily translating vortexjet filament is found to be identical with equilibrium form of a thin inextensible elastic rod of circular cross section, and, as a dynamical extension, traveling waves on an extensible rod is sought. We establish a variational principle for motion of an elastic rod with respect to material frames. [ABSTRACT FROM AUTHOR]

Filamented surfaces are invariant surfaces, with respect to the Hamiltonian dynamics, that are wound by trajectories and that have topological genus more than one. Dynamics along the surfaces is not integrable (V. Kozlov, 1979), and numerous examples of such surfaces can be found in hydro- and magneto-hydrodynamics. Using the renormalization group approach we study transport of particles along such surfaces and show that the kinetics is superdiffusive. Other discussed features of the dynamics are Poincaré recurrences, stickiness of trajectories, and connection to dynamics in billiards. [ABSTRACT FROM AUTHOR]

The issues discussed in this paper relate to the description of developed two-dimensional turbulence, when the mean values of characteristics of steady flow stabilize. More exactly, the problem of a weak limit of vortex distribution in two-dimensional flow of an ideal fluid at time tending to infinity is considered. Relations between the vorticity equation and the well-known Vlasov equation are discussed. [ABSTRACT FROM AUTHOR]

The year 2007 will mark the centenary of the death of William Thomson (Lord Kelvin), one of the great nineteenth-century pioneers of vortex dynamics. Kelvin was inspired by Hermann von Helmholtz's [7] famous paper "Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen", translated by P. G. Tait and published in English [17] under the title "On Integrals of the Hydrodynamical Equations, which Express Vortex-motion". Kelvin conceived his "Vortex theory of Atoms" (1867-1875) on the basis that, since vortex lines are frozen in the flow of an ideal fluid, their topology should be invariant. We now know that this invariance is encapsulated in the conservation of helicity in suitably defined Lagrangian fluid subdomains. Kelvin's efforts were thwarted by the realisation that all but the very simplest three-dimensional vortex structures are dynamically unstable, and his vortex theory of atoms perished in consequence before the dawn of the twentieth century. The course of scientific history might have been very different if Kelvin had formulated his theory in terms of magnetic flux tubes in a perfectly conducting fluid, instead of vortex tubes in an ideal fluid; for in this case, stable knotted structures, of just the kind that Kelvin envisaged, do exist, and their spectrum of characteristic frequencies can be readily defined. This introductory lecture will review some aspects of these seminal contributions of Helmholtz and Kelvin, in the light of current knowledge. [ABSTRACT FROM AUTHOR]

Several problems related to the dynamics of vortex patterns as observed in wake flows are addressed. These include: The universal Strouhal-Reynolds number relation. The Hamiltonian dynamics of point vortices in a periodic strip, both the classical two-vortices-in-a-strip problem, which gives the structure and self-induced velocity of the traditional vortex street, and the three-vortices-in-a-strip problem, which is argued to be relevant to the wake behind an oscillating body. The bifurcation diagram for wake structure found experimentally by Williamson and Roshko is addressed theoretically. [ABSTRACT FROM AUTHOR]

We study the nonlinear evolution of an elliptical flow by weakly nonlinear analysis. Two sets of amplitude equations are derived for different situations. First, the weakly nonlinear evolution of helical modes is considered. Nonlinear selfinteraction of the two base Kelvin waves results in cubic nonlinear terms, which causes saturation of the elliptical instability. Next, the case of triad interaction is considered. Three Kelvin waves, one of which is a helical mode, form a resonant triad thanks to freedom of wavenumber shift. As a result three-wave equations augmented with linear terms are obtained as amplitude equations. They explain the numerical results on the secondary instability obtained by Kerswell (1999). [ABSTRACT FROM AUTHOR]

The purpose of this study is to clarify the boundary layer transition process influenced by anisotropic and low-level free stream turbulence generated by a turbulence grid mounted upstream from a contraction. Flow visualization experiments in the boundary layer revealed the appearance of wave packets with streamwise wave numbers that transform into ‘A' shaped structures and immediately break down into turbulent spots. The wave packets were mapped out around the upper branch of the neutral curve in a linear stability diagram, suggesting the modal disturbance is dominant and triggers transition to turbulence in the boundary layer subject to relatively low-level free stream turbulence on the boundary layer scale. [ABSTRACT FROM AUTHOR]

The interaction between a columnar vortex and external turbulence is investigated numerically. The formation of turbulent eddies around the columnar vortex and the vortex-core deformations are studied in detail by visualizing the flow field. In the marginally case with q = -1.5, small thin spiral structures are formed inside the vortex core. In the unstable case with q = -0.45, the linear unstable modes grow until the columnar vortex completes one turn. Its growth rate agrees with that of the linear analysis of Mayer and Powell. After the vortex completes two turns, a secondary instability is excited which causes the collapse of the columnar q-vortex, after which many fine scale vortices appear spontaneously. [ABSTRACT FROM AUTHOR]

The statistics of quasi-gestrophic point vortices and spherical vortex patches are investigated theoretically and numerically, in order to understand fundamental aspects of quasi-geostrophic turbulence. The numerical computations are performed using the fast special-purpose computer for molecular dynamics simulations, MDGRAPE-2/3. The most probable distributions are determined based on the maximum entropy theory. The theoretical predictions agree well with the numerical results. [ABSTRACT FROM AUTHOR]