Terms Of Velocity Field Research Articles

Passive velocity field control of mechanical manipulators

Two concepts are advocated for the task specification and control of mechanical manipulators: 1) coding tasks in terms of velocity fields; 2) designing controllers so that the manipulator when under feedback control, interacts in an energetically passive manner with its physical environment. Based on these two concepts, a new passive velocity field controller is proposed which mimics the behavior of a passive energy storage element, such as a flywheel or a spring. It stores and releases energy while interacting with the manipulator, but does not generate any. The controller has the interesting property that it stabilizes any multiple (positive or negative) of the desired velocity field, and exponentially stabilizes the particular multiple of the desired velocity field which is determined by the total kinetic energy of the manipulator control system.

Steady Waves and Forces About a Yawing Flat Plate

An analysis of the flow about a free-surface-piercing yawed plate in steady drift, or in steady turning motion, is presented. The problem is studied by means of an inviscid rotational flow model, based on an integral representation for the velocity field in terms of source and surface vorticity distributions. The related integral equations are numerically solved by coupling a source panel technique together with the vortex lattice method for treating the surface vorticity integrals. The free surface conditions are linearized with respect to the double model lifting flow, and the vortex shedding has been modeled in a simple but effective manner. A special effort has been put in the validation of the present approach by comparing the obtained results with several experimental data and previous numerical computations. The keel vortex shedding, as was expected by virtue of the low draft-to-length ratio typically encountered in naval architecture, has been found crucial for the prediction of the hydrodynamic forces on a maneuvering ship.

Transonic wing flow computations using the field-panel method with a shock-fitting technique

An integral equation field-panel scheme for solving the full-potential equation for compressible flows with and without shocks is presented. The full-potential equation is written in the form of the Poisson's equation. Compressibility is treated as non-homogeneity. The integral equation solution in terms of velocity field is obtained by Green's theorem. The solution consists of wing (or a general body) surface integral term(s) of vorticity/source distribution(s), wake surface integral term(s) of free-vortex sheet(s), a volume integral term of compressibility over a small limited domain around the source of disturbance, and a shock surface integral term of source distributions for the shock-fitting purpose. Solutions are obtained through an iterative procedure. Instead of using a grid (field-panel) refinement procedure, a shock-fitting technique is used to fit the shock. The present scheme is applied to non-lifting flows around both sharp and round leading edge rectangular wings at high-subsonic and transonic flow conditions.

Boundary Surface Dynamics: An Algorithm for Stratified Geostrophic Flows

Assuming three-dimensional stratified geostrophic vortices of finite volume and potential vorticity of arbitrary vertical structure but piecewise-constant distribution in the horizontal direction, we derive equations for the velocity field in terms of surface integrals over the boundary of the vortex regions. Using conservation of quasigeostrophic potential vorticity and the concepts of contour dynamics, the three-dimensional problem is reduced to the Lagrangian evolution of the boundary surface enclosing the vortex region, thus decreasing the number of dimensions by one. The equations are discretized in space and time giving a simple and robust algorithm for the evolution of the flow with specified initial conditions. The model is used to study the interaction of two identical cylindrical vortices of finite height in a spatially unbounded fluid. For vortices at the same level the simulations show that if the horizontal scale is larger than the internal radius of deformation, filamentation is virtually suppressed and the resulting structure is a compact cylindrical vortex of ellipse-like cross section. For vortices at different levels the interaction results in a structure of considerable horizontal and vertical complexity due to the combined effects of merger and alignment processes acting together.

Optimal monopole dynamics in nuclei

A generator coordinate method with variationally determined generating functions is used in order to investigate the optimal ground-state correlations and monopole collective excitations in nuclei4He,16O and40Ca with Skyrme-type effective interaction. Simulating collective deformations by generalized scaling ansatz, we look for the optimal collective paths in terms of velocity fields. It is found that nuclear characteristics as the binding energy and the ground-state root-mean-square (r.m.s.) radius are not very sensitive to the choice of the path. On the contrary, radial density oscillations, ground-state nucleon momentum distributions, monopole excitation energies and the corresponding energy-weighted sum rules are sensitive to this choice.

The nature of triad interactions in homogeneous turbulence

Nonlinear interactions in homogeneous turbulence are investigated using a decomposition of the velocity field in terms of helical modes. There are two helical modes per wave vector and thus eight fundamental triad interactions. These eight elementary interactions fit in only two classes, ‘‘R’’ (for ‘‘reverse’’) and ‘‘F’’ (for ‘‘forward’’), depending on whether the small-scale helical modes have helicities of the same or of the opposite sign. In a single-triad interaction, the large scale is unstable when the small-scale helical modes have helicities of opposite signs (class ‘‘F’’), and the medium scale is unstable otherwise (class ‘‘R’’). It is proposed that, on average, the triple correlations in a turbulent flow correspond to these unstable states. In the limit of nonlocal triads, where one leg is much smaller than the other two, the triadic interscale energy transfer is largest for interactions of class ‘‘R.’’ In that case, most of the energy flows locally in wave number, from the medium scale to the smallest, with a comparatively small feedback on the large scale. However, integrating over all scales in an inertial range, the net effect of nonlocal interactions of class ‘‘R’’ is a reverse energy cascade from small to large scales. All other interactions transfer energy upward in wave number. In local triads, this upward energy transfer occurs primarily between modes with helicities of the same sign, through catalytic interactions with a mode whose helicity has the opposite sign. The class ‘‘F’’ interactions transfer energy to the small scales and exist only in three dimensions. The physical processes associated to both classes of interactions are discussed. It is shown that the large local transfers due to nonlocal ‘‘R’’ interactions appear in pairs of opposite signs that nearly cancel each other and the net effect corresponds to an advection in wave space.

Unsteady transonic wing flow computations using field-boundary element methods

An unsteady integral equation (or called field-panel, field-boundary element) scheme for solving the full-potential equation for transonic unsteady wing flows has been developed. The unsteady full-potential equation has been written in a moving frame of reference, in the form of the Poisson's equation. Compressibility and unsteadiness have been treated as non-homogeneity. The integral equation solution in terms of velocity field is obtained by the Green's theorem. The solution consists of a wing surface (boundary elements) integral term of vorticity distribution, a wake surface (boundary elements) integral term of free-vortex sheet and a volume (field-elements) integral term of compressibility and unsteadiness over a small limited domain around the wing. Numerical solutions are obtained by a time-marching, iterative procedure. Time-derivative term is calculated by a second-order backward finite-difference scheme. To be consistent with the mixed-nature of flows, the Murman-Cole type-difference scheme is used to compute the derivatives of the density. The present scheme is applied to flows around a rectangular wing at transonic speed undergoing acceleration motion and transient pitching motion, respectively. The time history of wing surface pressure distributions has been presented.

On the convection of a passive scalar by a turbulent Gaussian velocity field

Through the use of the Novikov-Furutsu formula for Gaussian processes an equation is obtained for the diffusion of the ensemble average of a passive scalar in an incompressible turbulent velocity field in terms of the two-point, two-time correlator of this field. The equation is valid for turbulence which is not necessarily homogeneous or stationary and thus generalizes previous work.

Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase variance

A numerical technique for simulating the behavior of an acoustic wave propagating through a turbulent medium is introduced. The technique involves two elements: the generation of 3-D, random, hypothetical, isotropic velocity fields in terms of a collection of discrete Fourier velocity modes; and the integration of the ray-trace equations to describe the trajectories of points tagging an acoustic wave front. The propagation times for these points to travel fixed distances through each of an ensemble of random velocity fields are recorded, and the variance of travel time (or acoustic phase) over the ensemble is calculated. In numerical ray-trace experiments through fields having average perturbation indices ≊0.01, acoustic travel-time variances are obtained that have a higher-order dependence on travel distance R than the classical Chernov prediction—a linear increase with R. The Chernov result is obtained, however, when the rays are confined to axial trajectories. Additional numerical experiments integrating the stochastic Helmholtz equation and its parabolic approximation yield time-variance estimates consistent with the ray-trace results. Predictions from these simulations are then applied to the laboratory experiments of Blanc-Benon and found to be in qualitative agreement. Finally, a set of 2-D travel-time experiments are presented to identify differences between source–receiver eigenray propagation and preassigned initial direction ray propagation.

Eulerian kinematics of flow through spatially periodic models of porous media

For spatially periodic models of porous media, and incompressible fluids, we consider here in detail thephysical interpretation of averaged velocity fields in terms of a purely continuum-level Eulerian seepage flux relation involving the mass flow across an arbitrarily oriented ‘macroscale’ surface element. We prove that the appropriately averaged microscale velocities do indeed satisfy a macroscale Eulerian flux relation (albeit to some approximation), provided that the surface ‘element’ is large compared with the pore lengthscale (microscale). A quantitative discussion of an ‘intermediate scale’ (lying between the pore scale and a characteristic macroscale) is achieved through the use of locally periodic velocity fields. Within the context of seepage velocity kinematics, our developments provide a conceptual foundation that renders continuum theories of flow of incompressible fluids through (periodic) porous media entirely selfcontained on the macroscale—free from any details of the discrete microscale structure (inaccessible to macroscopic observers) from which this continuum theory sprang. The error bounds and scaling laws derived are of special interest when the macroscale/microscale disparity is not very ‘wide’. With reference to current rational mechanical theories of ‘immiscible mixtures,’ our analysis provides aconstructive existence proof, at least for periodic models of porous media, for phase-specific velocities; heretofore, such velocities were usually accepted, in a Lagrangian sense, on an axiomatic basis. Thus, clarification and quantification of thekinematical aspects of the continuum hypothesis for certain classes of multiphase systems can be effecteda priori by our arguments, independently of any subsequent macroscaledynamical modelling. Our analysis, whereby we systematically proceed from a discrete picture of the underlying geometry to a purely continuum picture, may be likened to that achieved in classical statistical mechanics. As in that case, we hope that the general results obtained transcend the underlying discrete (i.e. spatially periodic) model of the subcontinuum structure.

Coastal-Trapped Waves behind a Large Continental Shelf Island, Southern Great Barrier Reef

The salient features of subinertial frequency fluctuations of current, sea level, temperature and wind stress observed within the Capricornia section of the Great Barrier Reef are interpreted by comparison with coastal-trapped wave (CTW) theories Near-coastal currents and sea levels are modeled with some success by a theory of first-mode wind-forced barotropic continental shelf waves with geographical origin at Fraser Island, the southern across-shelf boundary of the study region. However, current and temperature variations of period 8–10 days on the continental slope are observed to have energy far in excess of that generated by the local wind. Decomposition of the observed alongshore velocity field in terms of baroclinic CTW modes indicates the signal is predominantly a second- or third-mode wave propagating equatorward at 0.4–0.6 m s−1. These modes have most of their energy flux propagating along the continental slope, and the energy levels indicate that the source region lies to the south of Fraser Island. The possible biological and geological relevance of CTW activity within the study region is briefly discussed.

Simplified transonic integral equations for lifting profiles and wings

The basic small perturbation integral equations for steady inviscid transonic flow past a thin cambered profile at small incidence have been simplified here using Oswatitsch substitution for the velocity field in terms of that on the profile axis. The resulting equations contain only one-dimensional singular integrals. These equations represent simplification of the equations of Nixon and Hancock [3], from which the two-dimensional camber integrals have been eliminated. Also the corresponding simplified equations for a thin lifting wing have been derived, which contain only two-dimensional singular integrals.

流体現象における臨界点の分類とその気象力学への応用

Motivated by appearances of multiple equilibrium states in some models of atmospheric flows (Charney and DeVore (1979), Matsuda (1980)), we classify critical points (transition points) appearing in steady problems of fluid dynamics in connection with symmetry break-down in the velocity field.For this purpose, we rewrite the Navier-Stokes equations in a spectral form. In the expansion of the velocity field in terms of normal modes, we divide the modes into two groups; the first group consists of modes which have the same symmetry as the external conditions imposed on the system, while the second group consists of other asymmetric modes. By postulating that there exists always a steady solution which has the same symmetry as the external conditions in the system, we restrict nonlinear coupling between the two groups of modes in the spectral equations.Using the spectral equations obtained in this way, we examine structure of critical points. If the symmetry breaks down in the velocity field, critical points of two types can appear in a fluid system. The first type is the critical point at which a symmetric solution is destabilized and other solutions with lowered symmetry branch from it. The second type is the critical point at which a symmetric solution and an asymmetric solution exchange its stability. If the degree of symmetry is preserved, the critical point of another type can appear in a fluid system; this type of critical point is characterized by coalescence of a stable solution and an unstable one and its subsequent disappearence in the phase space as the relevant parameter is varied.By constructing a local potential in the vicinity of each critical point, we examine the correspondence of critical points examined in this study to Thom's (1972) elementary catastrophes.In the last section, in the light of our classification theory we re-examine multiplicity and stability of the equilibrium states obtained in Charney and DeVore's model (1979) of blocking phenomena.

Experiments on a turbulent cylindrical wall jet

The investigation described here is an experimental study directed toward determining flow field and surface friction characteristics of a cylindrical wall jet. The flow configuration is obtained by placing a cylindrical rod along the axis of a converging nozzle. The flow field thus produced consists of a developing turbulent boundary layer co-existing with an outer fluid layer that mixes freely with quiescent surroundings. Direct measurements of fluid friction at the rod surface, performed with a hot-film element, revealed a significant effect of transverse surface curvature on the local friction factor. Velocity profiles at various axial stations exhibited similarity in the outer mixing layer, but not in the boundary layer adjacent to the surface. Representations of the velocity field in terms of law of the wall variables and defect-law variables revealed significant transverse curvature effects. The measured wall-jet velocity profiles could be satisfactorily represented in terms of a law of the wake, wherein the wake function depends on a transverse curvature parameter. In the outer mixing layer, the eddy viscosity data correspond closely to those of free jets.

QUASI-CYLINDRICAL SURFACES WITH PRESCRIBED THICKNESS DISTRIBUTIONS

A formula for the supersonic velocity field in terms of a given surface distribution of sources is applied to points lying in the surface. An equation giving the camber shape of a quasi circular-cylindrical surface in terms of a prescribed thickness distribution is derived and the half ring wing with prescribed thickness distribution is discussed as an example.