bluuebunny/crossref_metadata_2025_split huggingface dataset:
Three-dimensionalization of barotropic vortices on the f-plane
Authors: Smyth W. D. , Peltier W. R. 
Published: April 2006

We examine the stability characteristics of a two-dimensional flow which consists initially of an inflexionally unstable shear layer on an f-plane. Under the action of the primary instability, the vorticity in the shear-layer initially coalesces into two Kelvin–Helmholtz vortices which subsequently merge to form a single coherent vortex. At a sequence of times during this process, we test the stability of the two-dimensional flow to fully three-dimensional perturbations. A somewhat novel approach is developed which removes inconsistencies in the secondary stability analyses which might otherwise arise owing to the time-dependence of the two-dimensional flow.In the non-rotating case, and before the onset of pairing, we obtain a spectrum of unstable longitudinal modes which is similar to that obtained previously by Pierrehumbert & Widnall (1982) for the Stuart vortex, and by Klaassen & Peltier (1985, 1989, 1991) for more realistic flows. In addition, we demonstrate the existence of a new sequence of three-dimensional subharmonic (and therefore ‘helical’) instabilities. After pairing is complete, the secondary instability spectrum is essentially unaltered except for a doubling of length- and timescales that is consistent with the notion of spatial and temporal self-similarity. Once pairing begins, the spectrum quickly becomes dominated by the unstable modes of the emerging subharmonic Kelvin–Helmholtz vortex, and is therefore similar to that which is characteristic of the post-pairing regime. Also in the context of non-rotating flow, we demonstrate that the direct transfer of energy into the dissipative subrange via secondary instability is possible only if the background flow is stationary, since even slow time-dependence acts to decorrelate small-scale modes and thereby to impose a short-wave cutoff on the spectrum.The stability of the merged vortex state is assessed for various values of the planetary vorticity f. Slow rotation may either stabilize or destabilize the columnar vortices, depending upon the sign of f, while fast rotation of either sign tends to be stabilizing. When f has opposite sign to the relative vorticity of the two-dimensional basic state, the flow becomes unstable to new mode of instability that has not been previously identified. Modes whose energy is concentrated in the vortex cores are shown to be associated, even at non-zero f, with Pierrehumbert's (1986) elliptical instability. Through detailed consideration of the vortex interaction mechanisms which drive instability, we are able to provide physical explanations for many aspects of the three-dimensionalization process.
Dynamical properties of vortical structures on the beta-plane
Authors: Sutyrin G. G. , Hesthaven J. S. , Lynov J. P. , Rasmussen J. Juul 
Published: April 2006

The long-time evolution of monopolar and dipolar vortices influenced by the largescale gradient of the ambient potential vorticity (the β-effect) is studied by direct numerical solutions of the equivalent barotropic quasi-geostrophic equation. Translation and reorganization of vortical structures are shown to depend strongly on their intensity. Transport of trapped fluid by vortical structures is illustrated by calculating particle trajectories and by considering closed isolines of potential vorticity and the streamfunction in a co-moving reference frame.The initial behaviour of strong monopoles is found to be well described by a recent approximate theory for the evolution of azimuthal mode one, even for times longer than the linear Rossby wave period. In the long-time limit, strong monopoles transport particles mainly westward, although the meridional displacement is several times larger than the initial vortex size. The appearance of an annulus with opposite radial gradient of the potential vorticity around the vortex core is demonstrated. This annulus forms owing to the meridional vortex drift on the β-plane and results in reorganization of a strong monopolar vortex into a rotating tripole. A critical value of the vortex intensity is found, below which the tripolar structure does not appear even in the case of an initially shielded vortex. Weak monopolar vortices are able to trap particles and provide some west-meridional fluid transport, even in the case when they decay like a linear Rossby wave packet.The evolution of initial f-plane dipoles on the β-plane is strongly dependent on the initial direction of propagation. Strong dipoles adjust to steadily propagating modon solutions either accelerating (westward case), decelerating (eastward case) or oscillating with a decaying amplitude (meridional case), thereby carrying trapped particles predominantly eastward. A steady state is not reached if the dipole intensity is below a critical value which depends on the initial direction of propagation. Weak dipoles either decay and shrink owing to Rossby wave radiation (westward case), gradually separate and split (eastward case), or disintegrate (meridional case) without longdistance fluid transport. Thus, on the β-plane monopoles provide mainly westward transport of trapped fluid, whereas dipoles provide mainly eastward transport. Only strong monopoles are found to provide significant meridional fluid transport.
An analytical theory of distributed axisymmetric barotropic vortices on the β-plane
Authors: Reznik G. M. , Dewar W. K. 
Published: April 2006

An analytical theory of barotropic β-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonlinearity. In particular, a solution of the initial value problem is given, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its interaction with the so-called ‘β-gyres’ which, in turn, are generated by the vortex circulation. Comparisons of analytical and numerical predictions for vortex motion are presented and demonstrate the utility of the present theory for times comparable to the ‘wave’ timescale. The latter exceeds the temporal limit derived from formal considerations. The properties of the far-field planetary wave radiation are also computed.This theory differs from previous calculations by considering more general initial vortex profiles and by obtaining a more complete solution for the perturbation fields. Vortex trajectory predictions accrue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.
The stability of a trailing-line vortex in compressible flow
Authors: Stott Jillian A. K. , Duck Peter W. 
Published: April 2006

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (azimuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, whilst a new ‘centre mode’ forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex.Throughout the paper comparison is made between our numerical results and results obtained from the various asymptotic theories.
The nucleation, growth and settling of crystals from a turbulently convecting fluid
Authors: Jarvis Richard A. , Woods Andrew W. 
Published: April 2006

We present a new model to describe the thermal and compositional evolution of a binary alloy which is cooled from above. Explicit account is taken of the nucleation of crystals in the cold upper thermal boundary layer, the growth of crystals in the turbulently convecting interior, and their subsequent gravitational settling to the floor of the chamber. The crystallization of one solid phase only is considered. When the residence time of a typical crystal within the convecting bulk is short compared with the overall cooling time of the fluid, the crystal size distribution loses memory of earlier conditions in the fluid and the number density simply decays exponentially with the cube of the crystal size. A quasi-steady state exists in which the rate of crystal production is balanced by the rate of sedimentation at the floor, allowing the volume fraction of suspended crystals to remain small until convection ceases to be vigorous.We focus on the situation in which the latent heat released by solidification would far exceed the heat flux extracted through convection if the melt undercooling were maintained equal to the initial temperature difference applied at the cold upper boundary. In this case, either the growth or nucleation of crystals must be limited in order that the fluid continues to cool. Both the growth-limited and nucleation-limited regimes may develop during the cooling of an individual fluid body, depending upon the thermal boundary condition at the upper boundary of the convecting portion of the fluid.We calculate how the mean crystal size within the sedimented crystal pile evolves as the fluid cools. During the growth-limited regime, the mean crystal size in the crystal pile typically decreases with height, owing to the decrease in the extracted heat flux and the greater efficiency of crystal settling as the fluid layer becomes shallower. In contrast, during the nucleation-limited regime, the fluid undercooling may increase significantly as the fluid cools, and inverse grading (large crystals over small) is possible. We discuss the possible application of our theory to the cooling of large igneous intrusions.
Active vorticity control in a shear flow using a flapping foil
Authors: Gopalkrishnan R. , Triantafyllou M. S. , Triantafyllou G. S. , Barrett D. 
Published: April 2006

It is shown experimentally that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow.First, flow-visualization experiments are conducted in Kalliroscope fluid at Reynolds number 550. A foil is placed in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process. The foil performs a heaving and pitching oscillation at a frequency close to the Strouhal frequency of the cylinder, while cylinder and foil also move forward at constant speed. By varying the phase of the foil oscillation, three basic interaction modes are identified. (i) Formation of a street of pairs of counter-rotating vortices, each pair consisting of one vortex from the initial street of the cylinder and one vortex shed by the foil. The width of the wake is then substantially increased. (ii) Formation of a street of vortices with reduced or even reverse circulation compared to that of oncoming cylinder vortices, through repositioning of cylinder vortices by the foil and interaction with vorticity of the opposite sign shed from the trailing edge of the foil. (iii) Formation of a street of vortices with circulation increased through merging of cylinder vortices with vortices of the same sign shed by the foil. In modes (ii) and (iii) considerable repositioning of the cylinder vortices takes place immediately behind the foil, resulting in a regular or reverse Kármán street. The formation of these three interaction patterns is achieved only for specific parametric values; for different values of the parameters no dominant stable pattern emerges.Subsequently, the experiments are repeated in a different facility at larger scale, resulting in Reynolds number 20000, in order to obtain force and torque measurements. The purpose of the second set of experiments is to assess the impact of flow control on the efficiency of the oscillating foil, and hence investigate the possibility of energy extraction. It is found that the efficiency of the foil depends strongly on the phase difference between the oscillation of the foil and the arrival of cylinder vortices. Peaks in foil efficiency are associated with the formation of a street of weakened vortices and energy extraction by the foil from the vortices of the vortex street.
Pressure-driven flow of suspensions: simulation and theory
Authors: Nott Prabhu R. , Brady John F. 
Published: April 2006

Dynamic simulations of the pressure-driven flow in a channel of a non-Brownian suspension at zero Reynolds number were conducted using Stokesian Dynamics. The simulations are for a monolayer of identical particles as a function of the dimensionless channel width and the bulk particle concentration. Starting from a homogeneous dispersion, the particles gradually migrate towards the centre of the channel, resulting in an homogeneous concentration profile and a blunting of the particle velocity profile. The time for achieving steady state scales as (H/a)3a/〈u〉, where H is the channel width, a the radii of the particles, and 〈u〉 the average suspension velocity in the channel. The concentration and velocity profiles determined from the simulations are in qualitative agreement with experiment.A model for suspension flow has been proposed in which macroscopic mass, momentum and energy balances are constructed and solved simultaneously. It is shown that the requirement that the suspension pressure be constant in directions perpendicular to the mean motion leads to particle migration and concentration variations in inhomogeneous flow. The concept of the suspension ‘temperature’ – a measure of the particle velocity fluctuations – is introduced in order to provide a nonlocal description of suspension behaviour. The results of this model for channel flow are in good agreement with the simulations.
Vortex dynamics of viscous fluid flows. Part 1. Two-dimensional flows
Authors: Ostrikov N. N. , Zhmulin E. M. 
Published: April 2006

The method of product integration is applied to the vortex dynamics of two-dimensional incompressible viscous media. In the cases of both unbounded and bounded flows under the no-slip boundary condition, the analytic solutions of the Cauchy problem are obtained for the Helmholtz equation in the form of linear and nonlinear product integrals. The application of product integrals allows the generalization in a natural way of the vortex dynamics concept to the case of viscous flows. However, this new approach requires the reconsideration of some traditional notions of vortex dynamics. Two lengthscales are introduced in the form of a micro- and a macro-scale. Elementary ‘vortex objects’ are defined as two types of singular vortex filaments with equal but opposite intensities. The vorticity is considered as the macro-value proportional to the concentration of elementary vortex filaments inhabiting the micro-level. The vortex motion of a viscous medium is represented as the stochastic motion of an infinite set of elementary vortex filaments on the micro-level governed by the stochastic differential equations, where the stochastic velocity component of every filament simulates the viscous diffusion of vorticity, and the regular component is the macro-value induced according to the Biot–Savart law and simulates the convective transfer of vorticity.In flows with boundaries, the production of elementary vortex filaments at the boundary is introduced to satisfy the no-slip condition. This phenomenon is described by the application of the generalized Markov processes theory. The integral equation for the production intensity of elementary vortex filaments is derived and solved using the no-slip condition reformulated in terms of vorticity. Additional conditions on this intensity are determined to avoid the many-valuedness of the pressure in a multi-connected flow domain. This intensity depends on the vorticity in the flow and the boundary velocity at every time instant, together with boundary acceleration.As a result, the successive and accurate application of the product-integral method allows the study of vortex dynamics in a viscous fluid according to the concepts of Helmholtz and Kelvin.
Theoretical and experimental studies of three-dimensional wavemaking in narrow tanks, including nonlinear phenomena near resonance
Authors: Yao Yitao , Tulin Marshall P. , Kolaini Ali R. 
Published: April 2006

In view of several practical ramifications of this problem, computational-analytical techniques for calculating waves induced by heaving arbitrary bodies in narrow tanks have been developed, including nonlinear wave groups produced near tank resonance. These feature computational near-field solutions matched with appropriate far-field solutions. In the linear case, the far field is provided by linear mode superposition. In the nonlinear case, the far field is described by a suitable nonlinear evolution equation of the cubic Schrödinger type. Matching techniques were developed. Calculations were successfully carried out and the results confirm the important effect of tank walls on added mass and damping.Results of computations have been compared with some data obtained with a conical wavemaker in a narrow tank. Pronounced nonlinear wave groups were obtained near resonance, and these are well reproduced in some detail by the nonlinear theory and computations, without considering any effects of dissipation.The related problem of resonant wave groups produced by a segmented paddle wavemaker has also been treated by analysis and subject to computation, with good general agreement with past experiments. The technique features matching near- and far-field computations using energy considerations.
Plume formation and resonant bifurcations in porous-media convection
Authors: Graham Michael D. , Steen Paul H. 
Published: April 2006

The classical boundary-layer scaling laws proposed by Howard for Rayleigh–Bénard convection at high Rayleigh number extend to the analogous case of convection in saturated porous media. We computationally study two-dimensional porous-media convection near the onset of this scaling behaviour. The main result of the paper is the observation and study of instabilities that lead to deviations from the scaling relations.At Rayleigh numbers below the scaling regime, boundary-layer fluctuations born at a Hopf bifurcation strengthen and eventually develop into thermal plumes. The appearance of plumes corresponds to the onset of the boundary-layer scaling behaviour of the oscillation frequency and mean Nusselt number, in agreement with the classical theory. As the Rayleigh number increases further, the flow undergoes instabilities that lead to ‘bubbles’ in parameter space of quasi-periodic flow, and eventually to weakly chaotic flow. The instabilities disturb the plume formation process, effectively leading to a phase modulation of the process and to deviations from the scaling laws. We argue that these instabilities correspond to parametric resonances between the timescale for plume formation and the characteristic convection timescale of the flow.
Interaction of a potential vortex with a local roughness on a smooth surface
Authors: Ryzhov Oleg S. , Timofeev Sergey V. 
Published: April 2006

Disturbances generated by a potential vortex moving past a small hump or dent on the otherwise smooth flat plate are considered. Features peculiar to this problem derive from the fact that the vortex is stuck with a fixed fluid particle; hence the nonlinear dependence of the pressure on the induced velocity field ensues even if the vortex intensity tends to zero. Formulation of the problem on a flow in the viscous wall sublayer given in canonical variables involves four similarity parameters for any particular shape of a roughness. The parallels between the process at hand and sound scattering from a boundary layer with a small obstacle at the bottom are indicated. Results from numerical integration of the boundary-value problem posed allow us to trace the evolution of the wave-packet structure depending on the potential vortex intensity. Overlapping of the peak wings and formation of an almost continuous spectrum in the Fourier decomposition of the signal serve as a guide for explaining the explosive development of the wave packet as distinct from the Tollmien–Schlichting wavetrain that has been registered experimentally.The theory developed is applied to discussing the so-called bypass mode of transition provoked by external turbulence. Special emphasis is laid on flows in gas turbine engines where bypass transition plays a dominant role owing to extremely high free-stream turbulence levels.
Numerical and theoretical solutions for a drop spreading below a free fluid surface
Authors: Koch Dorothy M. , Koch Donald L. 
Published: April 2006

Numerical solutions are derived for a viscous, buoyant drop spreading below a free fluid surface. The drop has zero interfacial tension, and we consider viscosity contrasts 0.1 < λ < 10 with the surrounding fluid half-space. The density contrast between the drop and outer fluid is assumed to be small compared with the density contrast at the fluid surface. The numerical solutions for the approach and initial spread of the drop below the fluid surface are obtained using the boundary integral method. To facilitate an investigation over a larger range of viscosity contrasts and for longer time periods, we solve for the motion of gravity currents at the fluid surface. For this geometry we also solve the boundary integral equations for the cases λ = 0 and 1/λ = 0.For extensive drop spreading, the motion is described by asymptotic solutions. Three asymptotic solutions are derived, which apply for different values of the viscosity contrast relative to the aspect ratio ((radial extent R)/(drop thickness a)). For very low-viscosity drops (λ [Lt ] a/R[ln(R/a)]-1), the greatest resistance to spreading occurs at the drop rim, and the asymptotic solution is found using slender body theory. Drops with intermediate viscosity contrast (a/R [Lt ] λ [Lt ] R/a) are slowed primarily by shear stresses at the lower drop surface, and a lubrication solution (Lister & Kerr 1989) applies. The greatest resistance to the spread of very viscous drops (λ [Gt ] R/a) comes from the radial stresses within the drop, and the asymptotic solution is independent of the outer fluid. All drops having 0 [Lt ] λ [Lt ] ∞ will eventually spread according to lubrication theory, when their aspect ratio becomes sufficiently large relative to viscosity contrast.Theoretical results are compared with numerical and experimental results for drops and gravity currents spreading at a fluid surface. The solutions can be applied to aspects of planetary mantle flow where temperature variations cause significant viscosity contrasts. The low-viscosity solution has been applied to study the encounter of a hot, low-viscosity upwelling plume with a planet surface (Koch 1994). Here we apply the high-viscosity asymptotic solution to study how cold downwelling slabs spread at a depth of neutral buoyancy in the Earth's mantle.