Experimental and Theoretical Advances in Fluid Dynamics

The flutter that spontaneously appears when a flexible plate is immersed in a parallel flow is addressed both experimentally and theoretically. Linear stability of the plate is analyzed using a model of one-dimensional flutter coupled with a three-dimensional potential flow. The analysis leads to results in quantitative agreement with the experiments. The coupled flutter of parallel plates is also considered. A similar, but simplified, model shows that the problem is then reduced to a system of linearly coupled oscillators which is in agreement with the coupled flutter modes observed in the experiments.

Sky dancers are long vertical flexible tubes which fluctuate above an air blower. These systems involve fluid-structure interactions that can give rise to complex dynamics. Air flow which passes through the tube deforms the tube wall which in turn modifies the flow hydrodynamical properties, and so on. We present in this article an experiment which models a sky dancer. The blown air speed can be varied and tubes of low rigidity and of different dimensions are used. The critical values of the flow velocity for which each tube begins “dancing” are measured. Comparisons with previous theoretical studies conducted for much more rigid tubes (Païdoussis, J Sound Vib 33:267–294, 1970) allow us to show that for tubes of low rigidity, the mechanism of destabilization is different.

Structures and self-diffusion coefficients of Gay-Berne (GB) mesogens with parameterizations GB(3.0, 5.0, 2.0, 1.0) and GB(4.4, 20.0, 1.0, 1.0) were extracted from

NVT

Molecular Dynamics simulations. These parameterizations are commonly used in the study of mesogenic systems. Structural features of accessible phases were characterized through translational [

$$g_{\parallel}(r_{\parallel})$$

] and positional [

$$g_{\perp}(r_{\perp})$$

] radial distribution functions. Translational self-diffusion coefficients parallel (

$$D_{\parallel}$$

) and perpendicular (

$$D_{\perp}$$

) to the global director were determined. Upon cooling a mesogenic system with parameterization GB(3.0, 5.0, 2.0, 1.0), a solid-like phase forms (as deduced from diffusivity) without attaining a smectic phase. Instead, the GB(4.4, 20.0, 1.0, 1.0) parameterization yields a range of liquid crystalline phases that follows the sequence isotropic

$$\to$$

nematic

$$\to$$

smectic A

$$\to$$

smectic B, for which the smectic B phase exhibits small, but measurable diffusivity. Collectively, results point to the GB(4.4, 20.0, 1.0, 1.0) parameterization as being a better candidate in capturing the typical gamut of liquid crystalline phases.

The random motion of mono-dispersed particles in a liquid fluidized bed was measured and processed from video recordings, using a refractive index matching method. 3D trajectories of coloured particles have been collected in a wide range of solid fraction, and statistical quantities have been derived in the range of high particle Reynolds number (

O

(10) <

Re

p

<

O

(10

3

)) and intermediate Stokes number (

O

(1) <

St

<

O

(10)). The evolution of the particle velocity variance as a function of solid fraction has been determined for different concentrations.

Although massive stars play a dominant role in shaping galactic structure and evolution, their origin and early evolution are not well understood mainly because of the lack of a good observational guidance. One major conceptual problem in massive star formation arises from the radiation pressure they exert on the surrounding dust and gas, which could be strong enough to halt further accretion and impose a limit to the mass of a star. Radiation hydrodynamic collapse calculations of massive protostars have suggested an upper limit of ~40

$${M}_\odot$$

before radiation pressure can exceed the star’s gravitational pull and block the infall of dusty gas. However, observational evidence for an upper mass limit near to 150

$${M}_\odot$$

has been found in young massive clusters (>10

4

$${M}_\odot$$

) in the Galactic Center. This cut-off seems to be unrelated to the heavy-element content of the star-forming gas, implying that radiation pressure may not be the physical mechanism that determines how massive stars can become. Here we find using frequency-dependent radiation transfer calculations, coupled to a frequency-dependent dust model, that stellar masses in excess of 100

$${M}_\odot$$

may well form by runaway accretion in a collapsing, pressure-bounded logatrope. The radii and bolometric luminosities (~10

6

$${L}_\odot$$

) of the produced stars are in good agreement with the figures reported for known candidates of massive stars.

Godunov-type methods relying on Riemann solvers have performed spectacularly well on supersonic compressible flows with sharp discontinuities as in the case of strong shocks. In contrast, the method of standard smoothed particle hydrodynamics (SPH) has been known to give a rather poor description of strong shock phenomena. Here we focus on the one-dimensional Euler equations of gas dynamics and show that the accuracy and stability of standard SPH can be significantly improved near sharp discontinuities if the bandwidth (or smoothing length,

h

) of the interpolating kernel is calculated by means of an

adaptive density estimation

procedure. Unlike existing adaptive SPH formulations, this class of estimates introduces less broad kernels in regions where the density is low, implying that the minimum necessary smoothing is applied in these regions. The resolving power of the method is tested against the strong shock-tube problem and the interaction of two blast waves. The quality of the solutions is comparable to that obtained using Godunov-type schemes and, in general, superior to that obtained from Riemann-based SPH formulations.

We study the large scale structure formation in the Universe using a dark matter model steaming from a scalar–tensor theory of gravitation. We present the equations that govern the evolution of the scale factor of the Universe and also the appropriate Newtonian equations to follow the non-linear evolution of the structures. Results are given in terms of the power spectrum that gives quantitative information on the structure formation. The initial conditions we have used are consistent with the so called concordance

$$\Uplambda$$

CDM model.

The present review is intended to give a general background of the main issues involving the oil spill that occurred on April 20, 2010 in the Deepwater Horizon platform owned by British Petroleum. A general description of the zone is provided, as well as the chronology of the facts that occurred since the spill began, including the different attempts to stop it, until the date of its complete control which occurred on July 15. Beside the efforts to stop the spill (on the surface and in deep waters), there were many governmental organizations, universities and scientific societies which contributed with diverse proposal of control, mitigation and prevention activities, such as, retaining and diminishing the amount of oil which could arrive to the coast, forecasting and tracking the behavior of the slick by means of satellite imagery, measurements and models. Finally, this work includes a brief description of possibilities of some influence on the Mexican coasts.

This article documents long-term characteristics of tropical cyclones (TCs) in the eastern Pacific Ocean from 1970 through 2009. This basin is relatively active during the summer and the presence of TCs may result in significant changes in atmospheric moisture and convective activity over populated areas along the west coast of Mexico. Because of its length and geographical location, the Baja California Peninsula received more than 30 landfalls during the period considered. To demonstrate their impact, four case studies from recent seasons were selected for further analysis. The analysis includes examination of TC position and intensity records, satellite imagery, meteorological gridded fields, and surface rainfall observations that are used to illustrate the evolution of these cyclones prior to and during landfall.

This article discusses some of the challenges that Mexico is facing on climate change issues. Mexico’s leadership on the United Nations Framework Convention on Climate Change (UNFCCC) and Conference of the Parties 16 (COP16) celebrated in Cancun, Mexico on December 2010 was a real challenge. In spite of the low expectations of this climate summit, a multilateral agreement was signed by the Parties. The major outcomes of the Cancun Agreement are described here. Funding derived from this agreement is expected to flow (hopefully) soon to underdeveloped countries to support mitigation and adaptation strategies. However, even if Mexico receives international funding through the Cancun Agreement, there are some major challenges that need to be resolved: (1) to understand the causes and impacts of climate change at regional scale and in different sectors, (2) to be able to identify adequate and feasible adaptation and mitigation strategies to build a more resilient country, and (3) to the have the financial support and the political will to implement them at regional scale by order of social importance.

The hydrographic and hydrodynamic structure of the Campeche Canyon (Southern Gulf of Mexico), was studied using oceanographic data obtained from PROMEBIO 3 on board of the R/V Justo Sierra of the UNAM. The sampling was performed during 24 days, in spring 2000. The hydrographic analysis was based on temperature, conductivity and pressure data obtained with a CTD profiler. Current speeds were recorder with a 75 kHz Acoustic Doppler Current Profiler (ADCP). The vertical velocity component (

w

) and the vertical component of the vorticity (

?

z

) were calculated using the horizontal velocity field registered by the ADCP. An objective analysis was applied to obtain homogeneous fields of hydrodynamic parameters such as currents, vorticity, and the Froude and Rossby numbers. Results shows horizontal speeds of the order of 3 × 10

?1

ms

?1

; positive vorticity to the Southwest of the study area and negative vorticity toward the Western side of the domain with a magnitude of the order of 10

?6

s

?1

. An upward and downward flow pattern was observed over the canyon in agreement with the positive and negative vorticity values, at different deeps. Finally, the Froude number with values below one indicated the existence of internal waves and a hydraulic jump within the Campeche Canyon.

This paper deals with the dynamics of two or more toroidal filamentary vortices—i.e. thin tubular vortices coiled on an immaterial torus—in an otherwise quiescent, ideal fluid. If the vortices are identical and equally spaced on a meridional section of the torus, the flow evolution depends on the torus aspect ratio (

$$r_1/r_0,$$

where

$$r_0$$

is the radius of the centreline and

$$r_1$$

is the radius of the cross section), the number of vortices (

N

), and the vortex topology (

$$V_{p,q},$$

denoting a vortex that winds

p

times round the torus symmetry axis and

q

times round the torus centreline). The evolution of sets of

$$NV_{1,2}$$

vortices was computed using the Rosenhead–Moore approximation to the Biot–Savart law to evaluate the velocity field and a fourth-order Runge–Kutta scheme to advance in time. It was found that when a small number of vortices is coiled on a thin torus the system progressed along and rotated around the torus symmetry axis in an almost steady manner, with each vortex approximately preserving its shape.

The Buenavista shallow aquifer, in Leon central Mexico is polluted with hexavalent chromium, Cr(VI). The soil and groundwater contamination by it has a significant problem in this area, which must be studied given the importance that represents the shallow aquifer for the drinking water supply at the local level. The real system state of the wells and piezometers in the Buenavista shallow aquifer was revised to design a scheme of P&T and select the sites, wells number and pumping flow most appropriate for the system. The best well location and pumping flow was chosen to capture and reduce the Cr(VI) groundwater concentration. A remediation strategy based on P&T system has been designed by the mathematical approximation optimization simulation (O/S) and a single period of planning, it was used as a tool to identify the sites appropriate to extract Cr(VI) contaminated groundwater, they have the potential to reduce Cr(VI) concentrations with an actual cost for remediation. The strategy was built using a simulation-optimization tool, combining the answer function with a genetic algorithm.

In this paper we present computer simulations of interstellar cloud collisions that for a given range of initial conditions could favor stellar cluster formation. We first construct a single spherical molecular hydrogen cloud with the Plummer radial density distribution with rigid rotation and an

m

= 2 density perturbation. The isolated cloud collapses into a filament with no sign of fragmentation. We then place two clouds for a head-on collision, and for an oblique collision characterized by an impact parameter that depends on the initial radius of the cloud. The approaching velocity of the clouds is changed from zero up to thirty times the gas sound speed. We have found that for certain values of our parameter space fragmentation into a stellar cluster is possible.

We examine the problem of the collapse and fragmentation of molecular clouds with a Gaussian density distribution with high resolution, double precision numerical simulations using the GADGET-2 code. To describe the thermodynamic properties of the cloud during the collapse—to mimic the rise of temperature predicted by radiative transfer—we use a barotropic equation of state that introduces a critical density to separate the isothermal and adiabatic regimes. We discuss the effects of this critical density in the formation of multiple systems. We confirm the tendency found for Plummer and Gaussian models that if the collapse changes from isothermal to adiabatic at earlier times that occurs for the models with a lower critical density, the collapse is slowed down, and this enhances the fragments’ change to survive. However, this effect happens up to a threshold density below which single systems tend to form. On the other hand, by setting a bigger initial perturbation amplitude, the collapse is faster and in some cases a final single object is formed.

The question about the existence of dark matter in the Universe is nowadays an open problem in cosmology. In this work we will present how we can build a hydrodynamic model in order to study dark matter halos of galaxies. The theoretical general idea is to start with the Einstein–Hilbert Lagrangian in which we have added a complex scalar field minimally coupled to the geometry. Then, by making variations of the corresponding action we come up with the Einstein field equations for the geometry and a Klein–Gordon equation for the scalar field. This set of coupled partial differential equations is non-linear. If we assume that dark matter halos can be described in the Newtonian limit we obtain a set of equations known as Schrödinger–Poisson equations. This set of equations can be written in the form of Euler equations for a fluid by making a Madelung transformation, where the self-interaction potential of the fluid is present. Also, there appears a quantum-like potential which depends non-linearly on the density of the fluid. We present results on the Jeans’ instability of the fluid model for dark matter and show how the physical parameters of the model can be determined, in particular, we compute the mass of the scalar field.

This paper shows the parallel implementation of the Linked Cell Method using CUDA and MPI. The so called Linked Cell method is employed in particle simulations with short range interactions. The method divides the physical domain into uniform sub domains while limiting the interactions to particles occupying the same cell and the flanking ones. In CUDA the Graphic Processing Units (GPUs) can be used for general purpose calculations. In the present case, the MPI standard allows the distribution of the sub domains into the available GPUs. Achieving an optimum GPU interchange process is crucial for system scaling. Results here presented will be used in the operation of a multi-GPUs system for fluid dynamics simulations using Smoothed Particle Hydrodynamics (SPH).

Multiphase phenomena identification in frequency domain through an electrical impedance sensor (EIS) in air–water pipes were analyzed experimentally. The electrical properties between the components were used to settle on the relative volumes of both phases. The selection of the appropriate a.c. frequency is well known to eliminate the capacitive impedance. The EIS is a device whose variable size electrodes were used to measure void fraction and its fluctuations. Measurements were carried out with six electrodes, when air was flowed into a standing water column, producing a bubble chain. Analysis in frequency domain of the electrical impedance signals allowed the spectral power density. This analysis was correlated with observed phenomena through video recording, in order to show that low frequency peaks can be associated to dynamic phenomena, while high frequency peaks could not be clearly correlated to flow particularities.

We present a two-dimensional numerical study of the dynamic interaction of bubbles. The simulation is made by solving the conservation equations in a regular Cartesian coordinate system and using the front tracking technique to follow the position of the bubbles. The qualitative properties of the flow are described in terms of the Reynolds (

Re

) and Bond (

Bo

) numbers. The values explored for these parameters are

Re

= 399 and

Bo

= 0.54 which represent realistic experimental conditions. Initially, we give a brief description of the trajectory of a bubble and the flow of the liquid produced by the displacement of a single bubble. It is found that the bubble motion generates of a chain of vortices similar to a von Kármán vortex street. The details of the motion of a second bubble that interacts with the first through the surrounding liquid, critically depend on the relative initial positions of the two bubbles. In general, it can be said that in the early stages of the motion, the two bubbles follow roughly the same path, but at a certain point where the interaction is particularly strong, the paths of the two bubbles diverge.

The interaction between two spherical bubbles rising in-line in a stagnant Newtonian liquid was studied. A model was proposed to relate the flow structure in the wake of a leading bubble with the hydrodynamic force and the rise velocity of a trailing bubble, at separation distances of the order of its diameter (2 ?

s/d

B

? 14) and moderate particle Reynolds numbers (20 ?

Re

1

? 200). To this end, a force balance on the trailing bubble was used as a starting point. The flow character in the axisymmetric laminar wake of a spherical bubble was analyzed, and an equation for the axial velocity profile was proposed in the modified form of an analytical approximation, which was fitted to numerical data. This equation, once substituted in the force balance, allowed obtaining a predictive model explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. The predictions of the proposed models show a good agreement with numerical and experimental data for the hydrodynamic force and the rise velocity of a trailing bubble, respectively.

In this work, a one-dimensional, thermal, transient two-fluid mathematical model for “Bubbly gas-Intermittent oil” (Bg-Io) upward flow is presented. The model was developed under the hypothesis that the Bg-Io flow pattern can be approached by two different flow patterns, each one in neighboring regions: water–gas bubbly flow through the annular region and heavy oil-gas-water bubbly flow in the slug body region. The model consists of mass, momentum and energy conservation equations for every phase whose numerical solution is based on the finite difference technique in the implicit scheme. The model is able to predict pressure, temperature, volumetric fraction and velocity profiles for each phase. For accurate modeling, a liquid slug length was proposed and used. Various oil interfacial and wall-water shear stresses correlations proposed in literature were also evaluated. The predictions are in agreement with experimental data reported in literature.

A one-dimensional, isothermal, transient model for the stratified flow of heavy oil, water and gas, in horizontal pipelines, is presented. The two-fluid mathematical model consists of mass, momentum and energy conservation equations for every phase. The model takes into account: (1) the hydrostatic pressure, (2) wall shear stress, (3) interfacial shear stress, (4) gas–oil interfacial roughness, and (5) the non-Newtonian oil behavior. The model is able to predict pressure, volumetric fraction, temperature, and velocity profiles for every phase. The numerical solution is based on the finite differences technique in an implicit scheme. The model is validated using experimental data reported in literature, for a light oil (32°API), and a heavy oil (14°API); in both cases the pressure drop calculated by the model is reasonably close to the experimental data.

Slug flow is the flow pattern that more often is presented in two-phase flow. It has a complex physical configuration which has not been totally understood. For decades slug flow has been modeled by mechanistic approach with the use of the slug-unity concept. For this, slug length must be known. This parameter affects the determination of shear stresses and then the pressure drop calculations. In this work data are presented from experiments carried out in a two-phase flow equipment. Equipment has a pipe of 12 m length and a diameter of 0.01905 m, which can be inclined from 0 to 90°. The measured data were: (1) angle for which the Taylor bubble breaks contact with the pipe wall, (2) the characteristic lengths of the slug-unit, (3) pressure drop, and (4) presence of bubbles by means of optical sensors. It was found that Taylor bubbles break contact with the wall pipe at 45°. With the voltage signal from optical sensors it was possible to quantify velocities, lengths and frequency for the Taylor bubbles.

A transient one-dimensional two fluid model to simulate slug flow through pipes was developed. It is formed by the conservation equations of mass, momentum and energy averaged in space and time for a water-air system. It was considered that water is incompressible, air is compressible and the unit-slug concept was used. For angles smaller than 45° the Taylor bubble region was modeled as a stratified flow, otherwise it was modeled as annular flow. The liquid slug region was modeled as a bubbly flow for all inclination angles. The model was solved numerically using the finite differences technique. An implicit upstream scheme was used for temporal derivatives and an implicit downstream scheme was used for spatial derivatives. The model allows predicting the profiles of pressure, liquid fraction, velocities and temperatures for the gas and liquid. The predictions present good agreement with experimental data.

In this work a transient, isothermal, mixture model for one and two fluid flows through pipes is presented. The model is formed by mass, momentum and energy conservation equations, which include leak term. The model is solved numerically using the finite difference technique and allows to simulate pressure and flow rate in steady and transient state. The hydraulic grade line is experimentally obtained and compared against predictions from the model. The result shows a good agreement with experimental data. It was found that (1) leaks induce inlet pressure changes, which are directly proportional to the leak location and magnitude; and (2) the outlet flow rate diminishes directly with the leak.

Some modeling aspects concerning large industrial pipelines are briefly outlined in this paper. The crucial identification of the dominant process during the model development stage is emphasized. The discussion is illustrated with examples of an application to a concrete oil-production system.

Migration and mass transfer of radionuclides through a saturated porous media taking into account the retention in the solid matrix as a function of the pH, is studied using the Darcy’s law equation for the effective velocity, and solving the contaminant transport diffusion equation within a porous media by the finite element method. The retardation coefficient

R

is obtained directly from the distribution constant

K

d

which depends strongly on the media physicochemical characteristics such as ionic strength and pH. A logarithmic dependence of

K

d

with pH and its effect over the

232

Th transport is analyzed in two different porous media: homogeneous and heterogeneous. By means of this model we obtained the concentration for the contaminant at different positions and the retardation in the migration originated by the differences in the pH values that was analyzed. We obtain the total concentration in different substrates and the effect of the changes in the media in the final distribution of the contaminant.

In this work a volume average mathematical model for multiphase flow of oil, water and gas through a homogeneous, isotropic and rigid porous media was developed, and proposed to simulate an in situ combustion problem. Such model consists of mass, momentum and energy equations. The gas is considered ideal and incompressible and the following processes were taken into account: (1) the formation of coke due to an oil chemical reaction, (2) formation of gas due to a combustion reaction between coke and oxygen, and (3) mass transfer due to oil and water phase change. The closure relationships for the water phase change, the formation of coke and the combustion of coke, were taken from the work of Gottfried and Mustafa (

1978

). However, the oil phase change equation, presented by Chu (1964), was modified as function of the partial pressure of the oil vapor in the gas phase and the vapor pressure of oil. The model is solved using the finite differences technique with explicit scheme for the mass equations and the Crack-Nicholson scheme for energy equation. The model allows predicting the profiles of: (1) temperature, (2) pressure, (3) oil, water and gas saturations, (4) oxygen, oil vapor, and steam mass fractions, and (5) cumulative oil recovery. The predictions are in agreement with experimental data reported in literature.

This work presents the mathematical formalism of a numerical model used for the simulation of

226

Ra migration and decay in saturated porous layers. The simulation methodology employs Darcy’s law for calculating the velocity field; it is subsequently used as input data for solving the transport equation. The latter includes advection, diffusion and hydrodynamic dispersion processes. The interactions with the medium are represented by a retention coefficient of the solid matrix, and a term associated to the radioactive decay. For the computational system we consider a vertical cross section composed of five saturated porous stratums. The hydrodynamic system of equations is solved by the finite element numerical technique.

Experiments in natural porous media such as

Eicchornia crassipes

biomass for determining the sorption of arsenic are compared with numerical simulations done with the COMSOL Multiphysics code. The close agreement between the experimental and numerical results suggest that the theoretical model of hydrodynamic dispersion can be used to model the transport of arsenic in unsaturated porous media composed of

Eichhornia crassipes

biomass. The aim of this work was to find the best fitting between the experimental breakthrough curve and the simulated curve, during the arsenic sorption through the biomass.

This work uses Particle Swarm Optimization (PSO) for estimating the heat generation function of a Guarded Hot-Plate Apparatus (GHPA). The device is used for the determination of thermal conductivity of insulating materials. The problem is one-dimensional in cylindrical coordinates. The geometry includes a disc (Hot-Plate) and an annulus (Guard). The heat generation function is estimated from a one to five parameters polynomial series. The capability of the method for recovering the analytical function is tested. Results are good enough for this kind of problem.

We present an easy, fast and inexpensive method to produce micron-sized bubbles using a low power laser diode operating in CW mode. The technique is based on light absorption by a thin layer of carbon nanostructures (nanotubes and nanoparticles) deposited on the tip of an optical fiber. Through flow visualization techniques and thermal imaging, we have observed evidence of the thermal and pressure gradients that appear in this process. With this method, micron-sized bubbles can be generated. These effects might be of significance for cavitation studies as well as for laser surgery.

We present a model for calculating the heat transfer by convection and radiation inside a cubic box with high density thermal radiation incident on a small window. The box is filled with a participating fluid and thermal radiation is absorbed by the bulk of the fluid. The numerical method used to integrate the resulting system of integro-differential equations is described and a particular example is discussed. The system analyzed is proposed as the fundamental concept of a heat exchanger that is specifically designed to absorb and store efficiently high density radiation as required in solar energy absorption in Central Receiver Systems.

We derive the Oberbeck-Boussinesq approximation using a rigorous thermodynamic approach, within the framework of one of the simplest implicit constitutive theories.

This paper focuses on the resonance frequencies in a membrane. We plot the amplitude response of the cantilever when it is subjected to a sinusoidal force in its clamped extreme. We took into account the presence of air and a damping coefficient to quantify the resonant frequency shifts and the quality factors of the resonant peaks. Theoretical calculations were also developed. Despite this, the experimental results did not correlate well with the theoretical results. We therefore infer that other energy dissipations must be taken into account.

The shear thickening behavior and flow instabilities of an equimolar semidilute aqueous solution of cetylpyridinium chloride and sodium salicylate were studied in this work by using rheometry coupled with flow visualization. The experiments were conducted at 25°C in a stress controlled Couette rheometer with a transparent flow cell. A detailed flow curve was obtained for this solution, which includes five different regimes. At very low shear rates a Newtonian behavior was found, followed by a shear thinning one in the second regime. In the third regime, a strong orientation of the micelles consistent with shear banding served as a precursor of the shear induced structures (SIS) and shear thickening. The fourth and fifth regimes in the flow curve were separated by a spurt-like behavior, and they clearly evidenced the existence of shear thickening accompanied by stick–slip oscillations at the rotating cylinder. The use of the combined method allowed the detection of SIS. The visualization of this solution in the shear thickening regime showed the build-up of SIS (turbid fluid) in the shear banding regime followed by large variations in shear rate and viscosity, corresponding to the oscillation of clear and turbid bands stacked in the vorticity direction. These alternating bands and shear rate variations are in agreement with the presence of the vorticity banding instability as well as with the creation and destruction of SIS.

When a jet of a thinning fluid is poured over a perpendicular surface covered with the same fluid, under certain circumstances it is observed that a small jet seems to bounce out of the surface very close to the incident jet. This phenomenon was first described by Kaye in 1963. In this work, the same type of fluid was used but the surface of incidence was inclined between 10 and 45 degrees. To better visualize the flow, the fluid was seeded with metallic flakes and illuminated with a sheet of light. The speed of the incident jet was kept constant. For each angle of incidence several videos at 240 frames per second were captured. It was observed that initially, a column of the falling liquid is formed. When the column breaks down, a jet comes out of it. The length of contact between the surface and the jet gets longer as the angle of inclination is increased. A critical angle

$$ \theta c $$

was found for which the terminal speed is larger than the falling speed of the incident jet. This cannot be explained by any of the mathematical models that have been proposed. The thinning characteristic of the fluid is not taken into account in any of the models.

In this work we present a theoretical study, based on the continuum approach, of the traction forces on the wall of the silo and on a cylindrical rod located at its center when the silo is filled with a dry, non cohesive granular material. We derive expressions for the traction forces by using the Janssen model and the modified, two-parameter Janssen model in order to take into account the existence of dead zones, i.e., the existence of zones without traction occurring during the incipient filling of the silos. Comparison between both models allow understand important aspects observed in experiments.

Squash is a highly competitive racquet sport. Professional players can answer most shots, regardless of how near the ball is to the wall. Only one shot is unanswerable. When the ball collides against the `nick’ formed by a vertical and a horizontal wall, under certain conditions, it rolls instead of bouncing, loosing most of its vertical momentum; hence, a reply is impossible. In this investigation, we study the conditions for this process to occur. We conducted visualizations with a high speed camera, throwing a squash ball to a corner to reproduce the nick shot in a controlled manner. Balls were thrown with a sling shot at different positions and angles in the vicinity of the corner. We determined the conditions for which a ball can loose all of its vertical bouncing motion. In this paper, we present some results, and a simple model to explain the phenomenon.

Simulations of steady state fluid dynamics and heat transfer in a two-dimensional flow inside a channel with main and secondary inlet flows were carried out in this work for a Reynolds number of

Re

= 1,562. The main cool jet was injected by a submerged inlet at the top while the secondary hot jets were injected at the vertical walls. The analysis was done by the finite element method for three different positions of the lateral entrance and three different velocities ratios of the main and secondary jets. The vortex formation and heat fluxes were analyzed and the temperature, streamline and velocity fields were obtained. The simulations have shown that is possible to control the dynamics and formation of vortices inside a channel with the variation of the secondary jet position.

In this work a numerical solution for the flow in a system of two basins connected by a channel is presented. The flow rate is assumed to be time dependent. With this assumption we intend to model the effect of tides in coastal systems. Our results show the formation of a vortex dipole at the channel outlet. Evolution of dipole depends strongly on the period of flow rate, as already noted by previous works. Using the velocity field obtained with the numerical method we calculate trajectories of fluid particles and show that dipole has an effect of suction in the region it pass. On the other hand the process of vortex formation and further evolution are well described.

The motion of the upper free surface of a liquid column released from rest in a vertical container, whose cross-section opens slowly in the downward direction, is analyzed theoretically. An inviscid, one-dimensional model, for a slightly expanding pipe’s radius, describes how the recently reported super free fall of liquids occurs in liquids of very low viscosity.

A saline oscillator is a device that consists of a small container with salt water and a tiny hole in the bottom. The small container is partially submerged into a larger container with distilled water. First, as expected, a jet of salt water falls into the larger container, but after a certain time the jet becomes unstable, a jet of distilled water starts going up, and an apparently periodic motion is installed. The global structure of the flow has been visualized using a technique sensitive to the density gradients, called shadowgraph. The velocity fields have been measured using particle image velocimetry (PIV). The flow rate has been measured as a function of time. Not all instabilities lead to a change of direction of the flow, so different flow patterns can be observed. With a pair of electrodes inserted in each container, a voltage signal with the same period of oscillation as the flow has been obtained. The interval of time when the flow goes down is always larger than the interval of time going up. Some experimental results that do not agree with other authors are presented.

This a review of the main issues involving the oil spill that occurred on April 20, 2010 in the Deepwater Horizon platform owned by British Petroleum. A general description of the main facts that occurred, supported by images and a brief description, since the spill began to the date when it was finally controlled on July 15. It contains brief comments on future consequences.

Groups of bubbles were collected and released in an associative polymer (HASE 1.5%,

H

ydrophobically modified

A

ssociative

S

oluble Polym

E

r). The bubbles (volume ?18 mm3) rising in this highly viscous fluid tend to form clusters. The images show clusters formed by different number of bubbles; the number below each image indicates the number of individual bubbles (N) in each cluster. In agreement with what has been observed in the case of settling particles (Jayaweera et al. J Fluid Mech 20:121, 1964; Hocking, J Fluid Mech 20:129, 1964), the bubbles form regular polyhedrons for N < 7. Surprisingly, the bubble clusters do not experience the velocity jump (Soto et al. Phys Fluids 18:121510, 2006) observed for the case of single bubbles having an equivalent total volume. However, the appearance of the characteristic cusped tail is observed on the bubbles near the trailing edge of the cluster.

An air stream is injected into a packed bed immersed in water. The refractive index of the water and the packed bed is closely matched; yet, the edges of the spherical particles can be seen. Two distinctive regimens can be observed. The first one, for low air flow rates, is characterized by the percolation of the air through the interstitial spaces among particles, which remain fixed in space. The second one, for high air flow rates, is characterized by the accumulation of air inside the packed bed without percolation; in this case the bubble causes significant agitation of the surrounding particles.

Dipolar vortex in an anticlockwise rotating platform. The mean depth is 0.85 m and the rotating period of the system is 30 s. The radius of the visible cyclonic part is 0.80 m. The anticyclonic part is formed due to potential vorticity conservation as fluid columns are squeezed over an obstacle at the bottom (not visible). The flow is visualized with small particles floating on the free surface and illuminated with a horizontal laser sheet. The experiments were performed at the Coriolis platform (CNRS/LEGI, Grenoble, France).

Composites from Hurricanes John (1–3 September 2006), Henriette (1–4 September 2007), Norbert (9–12 October 2008), and Jimena (1–4 September 2009). Plus signs are circulation center positions. Images indicate minimum temperatures (maximum cloud tops) from 30-min infrared imagery. The coldest (below –60°C, highest) clouds appear in black, red, and yellow tones. These images are derived from the GOES-11 satellite and indicate the location of deep convection and likelihood of heavy rainfall prior to and during the landfall of each hurricane.

A simple method to incorporate carbon nanotubes onto optical fibers is to immerse its tip in a solution of nanostructures dispersed in ethanol. Laser light guided by the fiber attracts the nanostructures thus forming deposits on the optical fiber tip. After deposition, micron-sized bubbles can be formed on the tips of the optical fibers owing to light absorption by the nanostructures.

Pressure drop inside a hydraulic installation was measured by piezoelectric transducers when cavitation begins. Bubbles appear in the vicinity of blades of the centrifugal pump and after they moves through the outlet pipe following, in some cases, a line. The three last figures (second row) show different cavitation regimes. On the other side bubbles reveal regions of vorticity concentration both near the blades and in the outlet pipe.

In the process to disperse a viscous oil in water in a stirred tank, filaments are produced before droplets appear. The impeller blades drive the oil and pushed it radially into the liquid bulk. The process is followed by an elongation of the filaments due to the fluid forces that make them thinner. This set of photographs was obtained with a high speed camera. Note that filaments are highly unstable and deformed, which causes the breakage to occur unexpectedly. The broken filaments recoil and finally droplets are produced.

Visualization by synthetic schlieren of the filling box process with fluid heated by a thermal source located on the floor. A constant power of 73 W is released in a 25 cm tall, closed, insulated box filled with water. The initial temperature of the fluid is uniform and equal to the environment.

A container with salt water is introduced into a larger container with distilled water. A quasi-periodic oscillation is induced when the small hole in the bottom of the small container is opened. The difference in the level of water is negligible. Initially, as expected, salt water starts flowing down. However, after a certain time the process is inverted and distilled water starts flowing up.