On the steadiness of separating meandering currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

Tephra fallout hazard assessment for a Plinian eruption scenario at Volcán de Colima (Mexico)

Volcanic ash fallout associated with renewal of explosive activity at Colima, represents a serious threat to the surrounding urbanized area. Here we assess the tephra fallout hazard associated with a Plinian eruption scenario. The eruptive history of Volcán de Colima shows that Plinian eruptions occur approximately every 100 years and the last eruption, the 1913, represents the largest historic eruption of this volcano. We used the last eruption as a reference to discuss volcanic hazard and risk scenarios connected with ash fallout. Tephra fallout deposits are modeled using HAZMAP, a model based on a semi-analytical solution of the advection– diffusion–sedimentation equation for volcanic particles. Based on a statistical study of wind profiles at Colima region, we first reconstructed ash loading maps and then computed ground load probability maps for different seasons. The obtained results show that a Plinian eruptive scenario at Volcán de Colima, could seriously damage more than 10 small towns and ranches, and potentially affect big cities located at tens of kilometers from the eruptive center. The probability maps obtained are aimed to give support to the risk mitigation strategies

Predicting natural ventilation in a two-zone building driven by combined forces.

Natural ventilation relies on less controllable natural forces so that it needs more artificial control, and thus its prediction, design and analysis become more important. This paper presents both theoretical and numerical simulations for predicting the natural ventilation flow in a two-zone building with multiple openings which is subjected to the combined natural forces. To our knowledge, this is the first analytical solutions obtained so far for a building with more than one zones and in each zone with possibly more than 2 openings. The analytical solution offers a possibility for validating a multi-zone airflow program. A computer program MIX is employed to conduct the numerical simulation. Good agreement is achieved. Different airflow modes are identified and some design recommendations are also provided.

Processes controlling atmospheric dispersion through city centres

We develop a process-based model for the dispersion of a passive scalar in the turbulent flow around the buildings of a city centre. The street network model is based on dividing the airspace of the streets and intersections into boxes, within which the turbulence renders the air well mixed. Mean flow advection through the network of street and intersection boxes then mediates further lateral dispersion. At the same time turbulent mixing in the vertical detrains scalar from the streets and intersections into the turbulent boundary layer above the buildings. When the geometry is regular, the street network model has an analytical solution that describes the variation in concentration in a near-field downwind of a single source, where the majority of scalar lies below roof level. The power of the analytical solution is that it demonstrates how the concentration is determined by only three parameters. The plume direction parameter describes the branching of scalar at the street intersections and hence determines the direction of the plume centreline, which may be very different from the above-roof wind direction. The transmission parameter determines the distance travelled before the majority of scalar is detrained into the atmospheric boundary layer above roof level and conventional atmospheric turbulence takes over as the dominant mixing process. Finally, a normalised source strength multiplies this pattern of concentration. This analytical solution converges to a Gaussian plume after a large number of intersections have been traversed, providing theoretical justification for previous studies that have developed empirical fits to Gaussian plume models. The analytical solution is shown to compare well with very high-resolution simulations and with wind tunnel experiments, although re-entrainment of scalar previously detrained into the boundary layer above roofs, which is not accounted for in the analytical solution, is shown to become an important process further downwind from the source.

Thermal wave scattering by two overlapping and parallel cylinders

In this paper an analytical solution of the temperature of an opaque material containing two overlapping and parallel subsurface cylinders, illuminated by a modulated light beam, is presented. The method is based on the expansion of plane and cylindrical thermal waves in series of Bessel and Hankel functions. This model is addressed to the study of heat propagation in composite materials with interconnection between inclusions, as is the case of inverse opals and fiber reinforced composites. Measurements on calibrated samples using lock-in infrared thermography confirm the validity of the model.

The role of an insulating surface layer on the relaxation time of the ionic redistribution in an electrolytic cell

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

Experimental and theoretical investigation of compression of a cylinder using a rotating platen

A rig was constructed to carry out compression of an aluminum cylinder with a monotonically rotating platen. The tests carried out showed that the compression load decreased and the side wall bulge severity reduced when the die was rotated. Not all the work supplied by the rotating dies was transferred to the work-piece; circumferential slippage was frequently observed at the die/material interface. This slippage was quantified by comparing measurements made during interrupted testing with the angular velocity of the die. A compound velocity field based on an exponential cusp description of the barreling was employed in an upper bound analysis. An approximate analytical solution was obtained for the degree of barreling and the compression pressure. The model is able to reproduce the decrease in barreling and compression loads with increasing die rotation.

Deformation behaviour of a cylinder under simultaneous compression and torsion

A number of experiments involving the compression of an Aluminum cylinder with concurrent die rotation were carried out. Two important features were observed: one was that die rotation reduced the degree of bulging and the other was that the compression load decreased. An upper bound analysis with a velocity field consisting of a compound exponential cusp representation was utilized to obtain an approximate analytical solution in a closed form. The theoretical result reproduced the reduction in bulging severity with die rotation as well as the changes in compression pressure.

Analysis of the inverse kinematics problem for 3-DOF axis-symmetric parallel manipulators with parasitic motion

 Determining an analytical solution to the inverse kinematics problem for a parallel manipulator is typically a straightforward problem. However, lower mobility parallel manipulators with 2-5 degrees of freedom (DOFs) often suffer from an unwanted parasitic motion in one or more DOFs. For such manipulators, the inverse kinematics problem can be significantly more difficult. This paper contains an analysis of the inverse kinematics problem for a class of 3-DOF parallel manipulators with axis-symmetric arm systems. All manipulators in the studied class exhibit parasitic motion in one DOF. For manipulators in the studied class, the general solution to the inverse kinematics problem is reduced to solving a univariate equation, while analytical solutions are presented for several important special cases.

Spacecraft's attitude prediction: solar radiation torque and the Earth's shadow

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite, under the influence of torque due to the solar radiation pressure, and taking into account the influence of Earth's shadow. Using Andoyer variables the equations for the rotational motion are presented in extended Hamiltonian form. In order to get a solution for the state variables close to an actual motion, the considered model for the shadow function takes into account physical and geometric factors and three specific regions: shadow, penumbra and full light. A mapping for the shadow function is proposed and a semi-analytical process is applied. When the satellite is totally illuminated or it is inside the penumbra, a known analytical solution is used to compute the satellite's attitude. A numerical simulation shows, when the penumbra region is included, the attenuation of the rotational motion during the transition from the shadow to the illuminate region and vice versa. (c) 2005 Published by Elsevier Ltd on behalf of COSPAR.

Optimal attitude corrections for cylindrical spacecraft

A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

Attitude propagation using non-singular canonical variables

Three sets of non-singular canonical variables for the rotational motion are analyzed. These sets are useful when the angle between z-axis of a coordinate system fixed in artificial satellite ( here defined by the directions of principal moments of inertia of the satellite) and the rotational angular momentum vector is zero or when the angle between Z-inertial axis and rotational angular momentum vector is zero. The goal of this paper is to compare all these sets and to determine the benefits of their uses. With this objective, the dynamical equations of each set were derived, when mean hamiltonian associate with the gravity gradient torque is included. For the torque-free rotational motion, analytical solutions are computed for symmetrical satellite for each set of variables. When the gravity gradient torque is included, an analytical solution is shown for one of the sets and a numerical solution is obtained for one of the other sets. By this analysis we can conclude that: the dynamical equation for the first set is simple but it has neither clear geometrical nor physical meaning; the other sets have geometrical and physical meaning but their dynamical equations are more complex.

Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of J(2). The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

CHARGED PARTICLE DYNAMICS IN TIME DEPENDENT MAGNETIC FIELDS

In this work we study the behavior of charged particles immersed in a peculiar configuration of magnetic fields, which has a main constant field B(0) and a superimposed, transversal perturbation field B(1) sin(omega(p)t), with B(1) << B(0). By taking Cartesian coordinates and placing B(0) along the z axis and B(1) sin (omega(p)t) on the x axis, an analytical solution for y(t) may be obtained by solving an integrodifferential equation. Besides, the solution z(t) also exhibits a very interesting dynamics, and the entire system is conditioned by resonances between the particle orbit frequencies and the frequency of the magnetic transversal perturbation, omega(p). In this work we also discuss numerical simulations for the related particle trajectories, as well as potential applications in the context of separation phenomena.