bluuebunny/crossref_metadata_2025 huggingface dataset:
Prepotentials of N=2 SU(2) Yang–Mills theories coupled with massive matter multiplets
Authors: Ohta Yűji
Published: July 2002

We discuss N=2 SU(2) Yang–Mills gauge theories coupled with Nf(=2,3) massive hypermultiplets in the weak coupling limit. We determine the exact massive prepotentials and the monodromy matrices around the weak coupling limit. We also study that the double scaling limit of these massive theories and find that the massive Nf−1 theory can be obtained from the massive Nf theory. New formulae for the massive prepotentials and the monodromy matrices are proposed. In these formulae, Nf dependences are clarified.
A sufficient condition for the existence of bound states in a potential
Authors: Chadan K. , Kobayashi R.
Published: July 2002

For a wide class of purely attractive potentials, we obtain a new sufficient condition for the existence of bound states for any angular momentum. Applied to some exactly soluble cases, the condition gives good results as compared to exact results.
Generalization of Shannon’s theorem for Tsallis entropy
Authors: dos Santos Roberto J. V.
Published: July 2002

By using the assumptions that the entropy must (i) be a continuous function of the probabilities {pi}(pi∈(0,1)∀i), only; (ii) be a monotonic increasing function of the number of states W, in the case of equiprobability; (iii) satisfy the pseudoadditivity relation Sq(A+B)/k=Sq(A)/k+Sq(B)/k+(1−q)Sq(A)Sq(B)/k2 (A and B being two independent systems, q∈R and k a positive constant), and (iv) satisfy the relation Sq({pi})=Sq(pL,pM)+pL qSq({pi/pL})+pM qSq({pi/pM}), where pL+pM=1(pL=∑i=1WLpi and pM=∑i=WL+1Wpi), we prove, along Shannon’s lines, that the unique function that satisfies all these properties is the generalized Tsallis entropy Sq=k(1−∑i=1Wpiq)/(q−1).
Effects of spin-torsion in gauge theory gravity
Authors: Doran Chris , Lasenby Anthony , Challinor Anthony , Gull Stephen
Published: July 2002

The spin-torsion sector of a new gauge-theoretic formulation of gravity is analyzed and the relationship to the Einstein–Cartan–Kibble–Sciama theory of gravity is discussed. The symmetries of the Riemann tensor and the conservation laws of the theory are derived. This formalism is applied to the problem of a Dirac field coupled self-consistently to gravity. The equations derived from a minimally coupled gauge-invariant Lagrangian naturally give the gauge-theoretic analogs of the Einstein–Cartan–Dirac equations. Finally, a semiclassical model for a spinning point-particle moving in a gravitational background with torsion is considered.
Differential geometry on SU(3) with applications to three state systems
Authors: Byrd Mark
Published: July 2002

The left and right invariant vector fields are calculated in an “Euler angle”-type parametrization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This enables the calculation of the invariant volume element or Haar measure. These are then used to describe the density matrix of a pure state and geometric phases for three state systems.
Hirota bilinear approach to a new integrable differential-difference system
Authors: Hu Xing-Biao , Wu Yong-Tang , Geng Xian-Guo
Published: July 2002

A new integrable differential-difference system is proposed. By the dependent variable transformation, the system is transformed into multilinear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation for it is obtained. Furthermore a nonlinear superposition formula is presented. As an application of the obtained results, soliton solutions to the system are derived.
High-frequency soliton-like waves in a relaxing medium
Authors: Vakhnenko V. O.
Published: July 2002

A nonlinear evolution equation is suggested to describe the propagation of waves in a relaxing medium. It is shown that for low-frequency approach this equation is reduced to the KdVB equation. The high-frequency perturbations are described by a new nonlinear equation. This equation has ambiguous looplike solutions. It is established that a dissipative term, with a dissipation parameter less than some limit value, does not destroy these looplike solutions.
A coupled AKNS–Kaup–Newell soliton hierarchy
Authors: Ma Wen-Xiu , Zhou Ruguang
Published: July 2002

A coupled AKNS–Kaup–Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS–Kaup–Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup–Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.
On characteristic equations, trace identities and Casimir operators of simple Lie algebras
Authors: Macfarlane A. J. , Pfeiffer Hendryk
Published: July 2002

Two approaches are developed to exploit, for simple complex or compact real Lie algebras 𝔤, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for “small” Lie algebras, but also to be suitable for treatment by computer algebra. A very large body of new results emerges in the forms of (a) identities of a tensorial nature, involving structure constants etc. of 𝔤, (b) trace identities for powers of matrices of the adjoint and defining representations of 𝔤, (c) expressions of nonprimitive Casimir operators of 𝔤 in terms of primitive ones. The methods are sufficiently tractable to allow not only explicit proof by hand of the nonprimitive nature of the quartic Casimir of g2, f4, e6, but also, e.g., of that of the tenth order Casimir of f4.
Dynamics of axial channeling in quasicrystals: An averaging-theory approach
Authors: Sáenz A. W.
Published: July 2002

A mathematically rigorous Hamiltonian theory of nonrelativistic axial channeling of positively charged particles in simply decorated icosahedral quasicrystals (IQCs) is developed in this paper on the basis of first-order averaging theory. The main result is an error estimate for the approximation of replacing the relevant Hamiltonian by that of the corresponding axial-continuum model to calculate suitable phase-space orbits. The derivation of this result makes essential use of a rigorous version of a theorem of Besjes on single-phase first-order averaging theory and of an asymptotic formula for the distribution of quasilattice points along arbitrary quasilattice axes of the considered IQC model. A deep number-theoretic result of Niederreiter is used to obtain this formula.
Isoperimetric problems for the helicity of vector fields and the Biot–Savart and curl operators
Authors: Cantarella Jason , DeTurck Dennis , Gluck Herman , Teytel Mikhail
Published: July 2002

The helicity of a smooth vector field defined on a domain in three-space is the standard measure of the extent to which the field lines wrap and coil around one another. It plays important roles in fluid mechanics, magnetohydrodynamics, and plasma physics. The isoperimetric problem in this setting is to maximize helicity among all divergence-free vector fields of given energy, defined on and tangent to the boundary of all domains of given volume in three-space. The Biot–Savart operator starts with a divergence-free vector field defined on and tangent to the boundary of a domain in three-space, regards it as a distribution of electric current, and computes its magnetic field. Restricting the magnetic field to the given domain, we modify it by subtracting a gradient vector field so as to keep it divergence-free while making it tangent to the boundary of the domain. The resulting operator, when extended to the L2 completion of this family of vector fields, is compact and self-adjoint, and thus has a largest eigenvalue, whose corresponding eigenfields are smooth by elliptic regularity. The isoperimetric problem for this modified Biot–Savart operator is to maximize its largest eigenvalue among all domains of given volume in three-space. The curl operator, when restricted to the image of the modified Biot–Savart operator, is its inverse, and the isoperimetric problem for this restriction of the curl is to minimize its smallest positive eigenvalue among all domains of given volume in three-space. These three isoperimetric problems are equivalent to one another. In this paper, we will derive the first variation formulas appropriate to these problems, and use them to constrain the nature of any possible solution. For example, suppose that the vector field V, defined on the compact, smoothly bounded domain Ω, maximizes helicity among all divergence-free vector fields of given nonzero energy, defined on and tangent to the boundary of all such domains of given volume. We will show that (1) |V| is a nonzero constant on the boundary of each component of Ω; (2) all the components of ∂Ω are tori; and (3) the orbits of V are geodesics on ∂Ω. Thus, among smooth simply connected domains, none are optimal in the above sense. In principal, one could have a smooth optimal domain in the shape, say, of a solid torus. However, we believe that there are no smooth optimal domains at all, regardless of topological type, and that the true optimizer looks like the singular domain presented in this paper, which we can think of either as an extreme apple, in which the north and south poles have been pressed together, or as an extreme solid torus, in which the hole has been shrunk to a point. A computational search for this singular optimal domain and the helicity-maximizing vector field on it is at present under way, guided by the first variation formulas in this paper.
Dilatation dissipation: The concept and application in modeling compressible mixing layers
Authors: Zeman Otto
Published: July 2002

In this paper a concept of dilatation dissipation εd for high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for εd is found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second-order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach number Mc in accordance with Papamoschou–Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses at Mc=0.5–0.86. Finally, the physical implications of the new model and results obtained are discussed and compared with other existing explanations of the Mach number effect on mixing layer dynamics.
An eigenfunction approach to large scale transitional structures in jet flow
Authors: Sirovich L. , Kirby M. , Winter M.
Published: July 2002

The Karhunen–Loève procedure is applied to the analysis of digitally imaged two-dimensional gas concentration fields obtained for a seeded axisymmetric jet. Large scale structures observed in the transitional region of a low Reynolds number jet are characterized in terms of an optimal basis. The essential features are captured by retaining roughly 30 parameters in the expansion. By retaining more terms smaller scales of the flow can be resolved.
Boundary-layer analysis of the dynamics of axisymmetric capillary bridges
Authors: Borkar Abhay , Tsamopoulos John
Published: July 2002

Small-amplitude oscillations of capillary bridges are examined in the limit of large modified Reynolds number. The contact line between the free surface of the bridge and the upper and lower supporting walls is allowed to undergo a restrained motion by taking its velocity to be proportional to the slope of the free surface there. It is found that the oscillation frequency and damping rate depend on the aspect ratio of the bridge, the mode being excited, the motion of the contact line, and the modified Reynolds number. Very good agreement with other studies is obtained for Re>100.
On the condition of streak formation in a bounded turbulent flow
Authors: Lam K. , Banerjee S.
Published: July 2002

Flow between two surfaces at which no-slip and free-slip conditions can be imposed has been investigated numerically with a Fourier–Chebyshev pseudospectral method. Different mean shear rates have been applied to each boundary to study the effect of shear and boundary condition on the streaky structures that have been observed near walls in many previous investigations. In addition to the streaks found near the no-slip wall, the computations also reveal streaky structures when the free-slip surface is under a sufficiently high shear. The low-speed streaks observed near the free-slip surface, although appearing somewhat more pronounced, have much the same characteristics as the wall-layer streaks—e.g., the average spanwise spacing between the streaks both near the wall and the free surface is about 100 when normalized by the kinematic viscosity and the appropriate shear velocity (at the wall or at the free-slip surface). The results show that shear is much more important than the nature of the boundary in determining the dominant flow structure, rather unexpected since vortex lines can attach at a free-slip boundary whereas they cannot at a no-slip one. The formation of streaks appears to be governed by a local nondimensional shear parameter defined as S̃≡S‖〈u′w′〉‖/ε, where S is the mean shear rate, and 〈u′w′〉 and ε are the kinematic turbulent shear stress and rate of dissipation of turbulent kinetic energy, respectively. It is found that S̃≂1.0 is the condition at which the elongated low-speed streaky regions first appear.
Temperature and suction effects on the instability of an infinite swept attachment line
Authors: Lasseigne D. G. , Jackson T. L. , Hu F. Q.
Published: July 2002

It is known that the incompressible, infinite swept attachment line flow is unstable to streamwise disturbances that originate in the boundary layer when the cross-flow exceeds a critical magnitude. Furthermore, a small degree of suction at the surface has a significant stabilizing influence while a small degree of blowing has a considerable destabilizing influence. This paper investigates the stabilizing and destabilizing effects of, respectively, cooling or heating the plate and the competing or enhancing effects of suction or blowing. A nonorthogonal flow with respect to the attachment line is also considered by adding a component of shear to the mean flow.
Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow
Authors: Lee Sangsan , Lele Sanjiva K. , Moin Parviz
Published: July 2002

For the numerical simulation of inhomogeneous turbulent flows, a method is developed for generating stochastic inflow boundary conditions with a prescribed power spectrum. Turbulence statistics from spatial simulations using this method with a low fluctuation Mach number are in excellent agreement with the experimental data, which validates the procedure. Turbulence statistics from spatial simulations are also compared to those from temporal simulations using Taylor’s hypothesis. Statistics such as turbulence intensity, vorticity, and velocity derivative skewness compare favorably with the temporal simulation. However, the statistics of dilatation show a significant departure from those obtained in the temporal simulation. To directly check the applicability of Taylor’s hypothesis, space-time correlations of fluctuations in velocity, vorticity, and dilatation are investigated. Convection velocities based on vorticity and velocity fluctuations are computed as functions of the spatial and temporal separations. The profile of the space-time correlation of dilatation fluctuations is explained via a wave propagation model.
Intrinsic chaos in a plasma wave
Authors: Uma R. , Subbarao D.
Published: July 2002

The linear plasma response to an electrostatic wave is described by the Van Kampen–Case–Siewert (VCS) modal structure using Lie transform techniques. The VCS structure, which is well known to give rise to Landau damping, is also proved to be responsible for chaotic particle response and diffusion in phase space in the quasilinear limit.
Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas
Authors: Bécoulet A. , Gambier D. J. , Samain A.
Published: July 2002

The question of heating a tokamak plasma by means of electromagnetic waves in the ion cyclotron range of frequencies (ICRF) is considered in the perspective of large rf powers and in the low collisionality regime. In such a case, the quasilinear theory (QLT) is validated by the Hamiltonian dynamics of the wave–particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows derivation of the rf diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker–Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. The Fokker–Planck equation is then given a variational form from which a solution is derived in the form of a semianalytical trial function of three parameters: the percentage of resonant particles contained in the tail, an isotropic width ΔT, and an anisotropic width ΔP. This solution is successfully tested against real experimental observations. It is shown that in the case of the JET tokamak [Plasma Phys. Controlled Fusion 30, 1467 (1988)] the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that from a bounce-averaged prediction. This may actually be an advantage for machines like JET [Plasma Phys. Controlled Fusion 30, 1467 (1988)] considering the energy range required to simulate the α-particle behavior in a relevant fusion reactor.
Sensitivity of the kink instability to the pressure profile
Authors: Howl W. , Turnbull A. D. , Taylor T. S. , Lao L. L. , Helton F. J. , Ferron J. R. , Strait E. J.
Published: July 2002

The stability of the n=1 ideal kink in DIII-D-like [Fusion Technol. 8, 441 (1985)] configurations is found to depend critically on the details of the current density and pressure profiles. The maximum stable normalized β, βN=β/(I/aB) (I in MA, a in meters, and B0 in tesla), is found to increase dramatically as the peak in the pressure gradient is shifted from the central region toward the plasma boundary. Further, for peaked pressure profiles, the β limit is insensitive to the internal inductance, li, whereas for broad pressure profiles, the β limit depends more strongly on li and can increase with li almost up to the point where the q profile becomes hollow. With broad pressure profiles and a conducting wall at 1.5 minor plasma radii, kink-stable βN values of 5.8−significantly above both the Troyon limit and the ballooning limit−have been found.
Forced reconnection and current sheet formation in Taylor’s model
Authors: Wang Xiaogang , Bhattacharjee A.
Published: July 2002

The problem of forced reconnection in Taylor’s model, first investigated by Hahm and Kulsrud [Phys. Fluids 28, 2412 (1985)], is revisited. After the linear phases A, B, and C, described by Hahm and Kulsrud, the plasma enters a nonlinear phase W with a current sheet, described by Waelbroeck [Phys. Fluids B 1, 2380 (1989)]. After the W phase, the plasma passes into the Rutherford regime. The reconnected flux at the separatrix increases monotonically from zero to its asymptotic value in the Rutherford regime. Analytical expressions for the reconnected flux and the island width are given.
Action principles for the Vlasov equation
Authors: Ye Huanchun , Morrison P. J.
Published: July 2002

Five action principles for the Vlasov–Poisson and Vlasov–Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov–Maxwell equations are altered so as to produce the Vlasov–Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov–Poisson equation is altered to produce the Vlasov–Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables.
Poloidal magnetic field dependence of the edge electric field layer width in the H mode in tokamaks
Authors: Shaing K. C.
Published: July 2002

It is shown that when the complete effects of orbit squeezing are taken into account, the width of the edge radial electric field layer in the H mode as estimated from the ion orbit loss model does not depend explicitly on the poloidal magnetic field.
Two-electron temperature model of a laser-driven implosion
Authors: Sanmartín J. R. , Ramis R. , Montañés J. L. , Sanz J.
Published: July 2002

The plasma ejected by a pellet irradiated with moderately intense laser light (Icrλ2 ∼1015 W cm−2 μm2, Icr and λ being intensity and wavelength) is analyzed. Both hot electrons caused by resonant absorption, and cold or thermal electrons are considered; no appeal is made to heat-flux saturation. The cold (hot) population controls the overdense (underdense) plasma flow. Ingoing hot electrons at the critical surface are found to thermalize before reaching the ablation surface. Results obtained are compared with a model that assume one electron temperature, and a saturated flux; agreement requires using a range of saturation factors: 0.1≲f≲0.3. The validity of the model is discussed.
Scattering of ion-acoustic solitons
Authors: Raychaudhuri Santwana , Chang Hong-Young , Tsikis Eugene K. , Lonngren Karl E.
Published: July 2002

A series of experiments is described that is designed to ascertain the properties of the scattering of planar ion-acoustic solitons from objects of various shapes. The scattered solitons are compared with those radiated from the same objects.
Self-organization process in three-dimensional compressible magnetohydrodynamics
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

A three-dimensional self-organization process in a compressible dissipative plasma is investigated in detail by means of a variational method and a magnetohydrodynamic (MHD) simulation. In the closed system where the total energy and total mass are conserved, the compressible MHD plasma relaxes to a maximum entropy state under the constraint that the total magnetic helicity is constant. This state is equivalent to a force-free equilibrium in which the pressure distribution is uniform. Magnetic reconnection converts the magnetic energy into the thermal energy in the vicinity of the reconnection points where the selective dissipation of magnetic energy effectively takes place owing to the generation of magnetic bubbles [R. Horiuchi and T. Sato, Phys. Fluids 29, 1161 (1986)]. The enchanced thermal energy is carried away all over the system by the fast MHD waves. The swift expansion of the thermal energy leads to a uniform distribution of the pressure profile in the transit time scale of the fast MHD wave. Numerical simulation shows that the system tends to self-organize to a force-free state where the physical quantities are almost exactly the same as those of the zero pressure case. It is also observed that the magnetic energy spectrum cascades toward the high wavenumber region while the helicity spectrum inversely cascades toward the low wavenumber region.
Theory of beat-resonant coupling of electrostatic modes
Authors: Crawford John David , Johnston Shayne , Kaufman Allan N. , Oberman Carl
Published: July 2002

A general expression is derived for the beat-resonant coupling electrostatic modes in a Vlasov plasma. The result for the coupling of two modes has a simple structure: the appropriate momentum gradient of the equilibrium particle distribution is weighted by a positive coupling coefficient and averaged over the resonance surface in momentum space. The contributions of all the resonance surfaces are then summed. This basic structure had been previously exhibited only for specific homogeneous plasma models. The present theory, which unifies and greatly simplifies these individual treatments, is based on a variational formulation of the Vlasov–Poisson equations. Using Lie transforms, the variational principle is reexpressed in oscillation-center variables, and then the nonlinear wave dynamics are obtained from the independent variations of the wave phase and the wave amplitude. The power of the method is then applied to a strongly magnetized, strongly inhomogeneous, non-neutral plasma model.
Turbulent magnetic reconnection
Authors: Matthaeus W. H. , Lamkin S. L.
Published: July 2002

The effects of turbulence on magnetic reconnection are investigated by two-dimensional spectral method magnetohydrodynamic computations. The nonlinear evolution of the periodic sheet pinch configuration is studied as an initial value problem. Turbulence is initiated by including a low level of broadband fluctuations in the initial data. Nonlinear features of the evolution, appropriately described as turbulence, are seen early in the solutions and persist throughout the runs. Small-scale, unsteady coherent electric current and vorticity structures develop in the reconnection zone, resulting in enhanced viscous and resistive dissipation. Unsteady and often spatially asymmetric fluid flow develops. Large-scale magnetic islands produced by reconnection activity, undergo internal pulsations. Small-scale magnetic islands, or ‘‘bubbles’’ develop near the reconnection zone, prodcing multiple X points. Large-amplitude electric field fluctuations, often several times larger than the reconnection electric field, are produced by large island pulsations and by motion of magnetic bubbles. Spectral analysis of the fluctuations show development of broad band excitations, reminiscent of inertial and dissipation range spectra in homogeneous turbulence. Two-dimensional spectra indicate that the turbulence is broadband in both spatial directions. It is suggested that the turbulence that develops from the randomly perturbed sheet pinchbears a strong resemblence to homogeneous magnetohydrodynamic turbulence, and that analytical theories of reconnection must incorporate these effects.
Large-eddy simulations of axisymmetric excitation effects on a row of impinging jets
Authors: Rizk Magdi H. , Menon Suresh
Published: July 2002

Numerical simulations of a row of impinging jets are performed. Both the impinging jets and the fountains caused by the collision of the wall jets are modeled in the simulation. The problem considered contains the essential features of twin jets impinging on the ground, simulating the hovering configuration of a vertical takeoff and landing (VTOL) aircraft. The flow is assumed to be governed by the time-dependent, incompressible Navier–Stokes equations. The large-eddy simulation approach is followed. The present study focuses on the motion and dynamics of large-scale structures that have been experimentally observed in jet flows. The behavior of the jets and the fountain caused by the introduction of axisymmetric disturbances at the jet exits are investigated.
The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers
Authors: Monkewitz Peter A.
Published: July 2002

The linear parallel and incompressible stability of a family of bluff-body wake profiles is studied at Reynolds numbers close to the onset of Kármán vortex shedding. The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness. The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number. A comparison of this survey with experimental data shows that in bluff-body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one-half the critical value for Kármán vortex shedding. Hence, at the onset of the global response (Kármán vortex shedding), a substantial region of local absolute instability already exists in the wake. This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys. Rev. Lett.] and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number.
Spectral transfer of self-similar passive scalar fields in isotropic turbulence
Authors: Yeung P. K.
Published: July 2002

The spectral transfer of passive scalars in a self-similar state is studied by direct numerical simulations of stationary isotropic turbulence. At high wave numbers the dominant process is forward cascading local transfer as a result of nonlocal triadic interactions that couple together two similarly high wave-number scalar modes by one low wave-number velocity mode. This indicates that advection by the energy-containing eddies transfers the scalar fluctuations towards smaller scales.
Numerical simulation of vortices with axial velocity deficits
Authors: Ragab Saad , Sreedhar Madhu
Published: July 2002

Axial velocity deficit is a source of instability in vortices that may otherwise be stable. Temporal large-eddy simulation is performed to study the response of vortices with axial velocity deficits to random and controlled disturbances at high Reynolds numbers. The q vortex [Batchelor, J. Fluid Mech. 20, 321 (1964)] is used as a model of such vortices. When the vortex is linearly unstable, the disturbances grow and result in the appearance of large-scale helical sheets of vorticity. Later, these large-scale helical structures break up into small-scale filaments. Associated with the formation of the large-scale structures is a redistribution of both angular and axial momentum between the core and the surroundings. The redistribution weakens the axial velocity deficit in the core while strengthens the rigid-body-like rotation of the core. The emerging mean velocity profiles drive the vortex core to a stable configuration. The vortex eventually returns to a laminar state, with an insignificant decay in the tangential velocity, but with a much weakened axial velocity deficit. A direct numerical simulation obtained at a lower Reynolds number confirms the above conclusions.
The collapse of a cavitation bubble in shear flows—A numerical study
Authors: Yu Po-Wen , Ceccio Steven L. , Tryggvason Grétar
Published: July 2002

The collapse of a cavitation bubble is examined by direct numerical simulations of the Navier–Stokes equations, using a finite difference/front tracking technique. Bubbles in both a quiescent fluid as well as shear flows are examined. For quiescent fluid, the results are compared with theoretical and previous computational results. For bubbles in a shear flow it is shown that large shear can increase the rate of collapse, and for bubbles near boundaries shear can eliminate the re-entrant jet seen for bubbles in a quiescent flow.
Experimental study of incompressible Richtmyer–Meshkov instability
Authors: Jacobs J. W. , Sheeley J. M.
Published: July 2002

The Richtmyer–Meshkov instability of a two-liquid system is investigated experimentally. These experiments utilize a novel technique that circumvents many of the experimental difficulties that have previously limited the study of Richtmyer–Meshkov instability. The instability is generated by vertically accelerating a tank containing two stratified liquids by bouncing it off of a fixed coil spring. A controlled two-dimensional sinusoidal initial shape is given to the interface by oscillating the container in the horizontal direction to produce standing waves. The motion of the interface is recorded during the experiments using standard video photography. Instability growth rates are measured and compared with existing linear theory. Disagreement between measured growth rates and the theory are accredited to the finite bounce length. When the linear stability theory is modified to account for an acceleration pulse of finite duration, much better agreement is attained. Late time growth curves of many different experiments seem to collapse to a single curve when correlated with the circulation deposited by the impulsive acceleration. A theory based on modeling the late time evolution of the instability using a row of vortices is developed. The growth curve given by this model has similar shape to those measured, but underestimates the late-time growth rate.
On the linear stability of channel flow over riblets
Authors: Ehrenstein Uwe
Published: July 2002

In the present study channel flow with the lower wall mounted with streamwise riblets is considered. The laminar flow state is computed and its stability is investigated by superimposing infinitesimal perturbations, which leads to a hydrodynamic stability problem in a complex geometry. Linear stability characteristics for riblets with several scalloped cross sections are computed. The computations show that at the primary instability level the laminar flow in the presence of riblets is more unstable than channel flow with smooth walls.
The flow structure around a surface piercing strut
Authors: Pogozelski E. M. , Katz J. , Huang T. T.
Published: July 2002

The flow near a surface piercing, symmetric body with a long draft is examined. The experiments are performed in a towing tank at 0.05⩽FrL⩽0.51, primarily focusing on FrL=0.25, and include velocity measurements using PIV as well as video and film photography above and below the free surface. The bow wave is mild (no bubble entrainment) for Froude numbers below 0.35; however, bow wave breaking and vorticity entrainment at the toe of the wave occur. Energy dissipation in the bow wave is significant and affects the flow behind it. At FrL⩾0.15, impingement of the flow on the model near x/L=0.41 generates a turbulent, bubbly wake. On the mid-body just behind this impingement is the origin of a second wave, containing several regions of counter-rotating vorticity which entrain bubbles from the free surface. The wave crest becomes milder and eventually irrotational with increasing distance from the model. At x/L=0.64, boundary layer separation begins at the intersection of the model and the free surface. The separated region grows, but never extends far from the free surface. The separation process originates from secondary flows associated with impingement and breaking at the root of the mid-body wave. At FrL=0.25, there is no reverse flow within the separated region, but at FrL>0.30, flow reversal does occur.
Large eddy simulations of a forced semiconfined circular impinging jet
Authors: Olsson M. , Fuchs L.
Published: July 2002

Large eddy simulations (LES) of a forced semiconfined circular impinging jet were carried out. The Reynolds number was 104 and the inflow was forced at a Strouhal number of 0.27. The separation between the jet inlet and the opposing wall was four jet inlet diameters. Four different simulations were made. Two simulations were performed without any explicit sub-grid-scale (SGS) model using 1283 and 963 grid points, respectively. Two simulations were performed with two different SGS-models using 963 grid points; one with a dynamic Smagorinsky based model and one with a stress-similarity model. The simulations were performed to study the mean velocity, the turbulence statistics, the SGS-model effects, the dynamic behavior of the jet with a focus on the near wall region. The existence of separation vortices in the wall jet region was confirmed. These secondary vortices were found to be related to the radially deflected primary vortices generated by the circular shear layer of the jet. It was also shown that the primary vortex structures that reach the wall were helical and not axisymmetric. A quantitative gain was found in the simulations with SGS-models. The stress-similarity model simulation correlated slightly better with the higher resolution simulation than the other coarse grid simulations. The variations in the results predicted by the different simulations were larger for the turbulence statistics than for the mean velocity. However, the variation among the different simulations in terms of the turbulence intensity was less than 10%.
Dynamics of the velocity gradient tensor invariants in isotropic turbulence
Authors: Martı́n Jesús , Ooi Andrew , Chong M. S. , Soria Julio
Published: July 2002

The evolution of the invariants (R and Q) of the velocity gradient tensor in homogeneous isotropic turbulence is investigated using data from direct numerical simulation (DNS). The concepts of conditional average time rate of change of the invariants and conditional mean trajectories (CMT) in invariant phase space are introduced to study the dynamics of this flow. The resulting dynamical system in the (R,Q) phase space is a clockwise spiral with a stable focus at the origin, illustrating that in the mean, the cyclic sequence of topological evolution following a fluid particle is unstable-node/saddle/saddle (UN/S/S)→stable-node/saddle/saddle (SN/S/S)→stable-focus/stretching (SF/S)→unstable-focus/contracting (UF/C). The mean rates of change of R and Q, i.e., Ṙ, Q̇, are found to be negligible near the right branch of the null discriminant (D=0) curve, indicating that this curve is an attractor in the (R,Q) space. The effects of both the diffusion term and the anisotropic part of the pressure Hessian term on the dynamics of the invariants have also been analyzed using the conditional averages. Both contributions are found to be important in the dynamics of the velocity gradient invariants. Based on these results the extent of the validity of the model equations governing the evolution of R and Q proposed by Cantwell [Phys. Fluids A 4, 782 (1992)] and Dopazo et al. [“Velocity gradients in turbulent flows. Stochastic models,” Ninth Symposium on “Turbulent Shear Flows,” Kyoto, Japan, 1993, pp. 26-2-1–26-2-5] are discussed.
Three-dimensional Floquet instability of the wake of square cylinder
Authors: Robichaux J. , Balachandar S. , Vanka S. P.
Published: July 2002

In this study we investigate the onset of three-dimensionality in an otherwise two-dimensional periodic wake of a square cylinder. Floquet stability analysis is employed to extract the different modes of three-dimensional instabilities. It is observed that the three-dimensional transition process for a square cylinder is similar to that of a circular cylinder. Most notably, there is a long-wavelength (mode A) three-dimensional disturbance that becomes unstable first at a Reynolds number of about 161, followed by a short-wavelength (mode B) three-dimensional disturbance that becomes unstable at a Reynolds number of about 190. In addition, a third intermediate-wavelength mode is also observed to become unstable at around Re=200. Unlike modes A and B, the intermediate-wavelength mode is subharmonic with a period of twice the shedding period of the two-dimensional base state. This mode also breaks the reflection translation symmetry observed in the other two modes and as a result appears with multiplicity two. The space–time symmetries of the three modes are explored in detail.
Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries
Authors: Clercx H. J. H. , Maassen S. R. , van Heijst G. J. F.
Published: July 2002

We report results of direct numerical simulations of decaying two-dimensional (2D) turbulence inside a square container with rigid boundaries. It is shown that the type of boundary condition (no-slip or stress-free) determines the flow evolution essentially. During the initial (0⩽t⩽0.2Re) and intermediate (0.2Re⩽t⩽3Re) stages of decaying 2D turbulence (t≅1 is comparable with an eddy turnover time, Re is the Reynolds number of the flow), the decay scenario for simulations with no-slip boundary conditions can be understood from turbulent spectral transfer and selective decay. A third mechanism can be recognized for t⩾3Re: A decay stage where diffusion dominates over nonlinear advection, i.e., spectral transfer is then absent in favor of self-similar decay. The present results show that at presently accessible Reynolds numbers and computation times, laboratory experiments cannot be accurately compared with quasi-stationary states from ideal maximum-entropy theories or with computed solutions of flows in containers with stress-free boundaries. The decay which results in rectangular containers with no-slip boundaries does not yet yield anything that is meaningfully comparable with these formulations. The evolution of the number of vortices V, the average vortex radius a, the ratio of enstrophy Ω over energy E, and the extremum of vorticity (normalized by E) have been computed based on ensemble averaging of the no-slip runs. An algebraic regime has been observed with V(t)∼t−0.90, a(t)∼t0.31, Ω(t)/E(t)∼t−0.63, and ωext(t)/E(t)∼t−0.30. Finally, quantities such as a measure of the viscous stresses near the boundaries have been computed in order to analyze the decay of 2D turbulence in containers with rigid boundaries.
Scattering and radiation of water waves by permeable barriers
Authors: Lee M. M. , Chwang A. T.
Published: July 2002

The two-dimensional problems of scattering and radiation of small-amplitude water waves by thin vertical porous plates in finite water depth are considered using the linear water wave theory. Applying the method of eigenfunction expansion, these boundary value problems are converted to certain dual series relations. Solutions to these relations are then obtained by a suitable application of the least squares method. For the scattering problem, four different basic configurations of the barriers are investigated, namely, (I) a surface-piercing barrier, (II) a bottom-standing barrier, (III) a totally submerged barrier, and (IV) a barrier with a gap. The performance of these types of barriers as a breakwater are examined by studying the variation of their reflection and transmission coefficients, hydrodynamic forces and moments for different values of the porous effect parameter defined by Chwang [J. Fluid Mech. 132, 395–406 (1983)], or the Chwang parameter. For the radiation problem, three types of wavemakers, which resemble types (I), (II), and (III) of the above-mentioned configuration, are analyzed. The dependence of the amplitude to stroke ratio on other parameters is also investigated to study the features of these wavemakers.
A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation
Authors: Voelkl Tobias , Pullin D. I. , Chan Daniel C.
Published: July 2002

A physical-space version of the stretched-vortex subgrid-stress model is presented and applied to large-eddy simulations of incompressible flows. This version estimates the subgrid-kinetic energy required for evaluation of the subgrid-stress tensor using local second-order structure-function information of the resolved velocity field at separations of order the local cell size. A relation between the structure function and the energy spectrum is derived using the kinematic assumptions of the stretched-vortex model for locally homogeneous anisotropic turbulence. Results of large-eddy simulations using this model are compared to experimental and direct numerical simulation data. Comparisons are shown for the decay of kinetic energy and energy spectra of decaying isotropic turbulence and for mean velocities, root-mean-square velocity fluctuations and turbulence-kinetic energy balances of channel flow at three different Reynolds numbers.
Steady free-surface thin film flows over topography
Authors: Kalliadasis Serafim , Bielarz Catherine , Homsy G. M.
Published: July 2002

We consider the slow motion of a thin viscous film flowing over a topographical feature (trench or mound) under the action of an external body force. Using the lubrication approximation, the equations of motion simplify to a single nonlinear partial differential equation for the evolution of the free surface in time and space. It is shown that the problem is governed by three dimensionless parameters corresponding to the feature depth, feature width and feature steepness. Quasi-steady solutions for the free surface are reported for a wide range of these parameters. Our computations reveal that the free surface develops a ridge right before the entrance to the trench or exit from the mound and that this ridge can become large for steep substrate features of significant depth. Such capillary ridges have also been observed in the contact line motion over a planar substrate where the buildup of pressure near the contact line is responsible for the ridge. For flow over topography, the ridge formation is a manifestation of the effect of the capillary pressure gradient induced by the substrate curvature. In addition, the minimum film thickness is always found near the concave corner of the feature. Both the height of the ridge and the minimum film thickness are found to be strongly dependent on both the profile depth and steepness. Finally, it is found that either finite feature width or a significant vertical component of gravity can suppress these effects in a way that is made quantitative and which allows the operative physical mechanism to be explained.
Nonlinear theory of the free-electron laser based upon a coaxial hybrid wiggler
Authors: Freund H. P. , Jackson R. H. , Pershing D. E. , Taccetti J. M.
Published: July 2002

A three-dimensional nonlinear formulation of a free-electron laser based upon a coaxial hybrid iron (CHI) wiggler is described. The CHI wiggler is created by insertion of a central rod and an outer ring [composed of alternating ferrite and dielectric spacers in which the ferrite (dielectric) spacer on the central rod is opposite to the dielectric (ferrite) spacer on the outer ring] along the axis of a solenoidal. An analytic model of the CHI wiggler is developed which is in good agreement with the Poisson/Superfish group of codes. The free-electron laser (FEL) formulation is a slow-time-scale analysis of the interaction of an annular electron beam with the CHI wiggler in a coaxial waveguide. The electromagnetic field is represented as the superposition of the vacuum transverse electric (TE), transverse magnetic (TM), and transverse electromagnetic (TEM) modes of the waveguide, and a set of nonlinear second-order differential equations is derived for the amplitudes and phases of these modes. These equations are solved simultaneously with the three-dimensional Lorentz force equations for the combined magnetostatic and electromagnetic fields. An adiabatic taper is used to model the injection of the beam, and an amplitude taper is included for efficiency enhancement. Simulations are presented for Ka-, Ku- and W-band operation. Multimode operation is also studied. The results indicate that operation over a wide bandwidth is practical with the CHI wiggler, and that the bandwidth in the tapered-wiggler cases is comparable to that for a uniform wiggler. Therefore, relatively high field strengths can be achieved with the CHI wiggler at shorter wiggler periods than is possible in many other conventional wiggler designs.