Formation of corner waves in the wake of a partially submerged bluff body

We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth Δh into a uniform stream of velocity U, in the presence of gravity, g. When the Froude number, Fr=U/√gΔh, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave's initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference Δh. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed

Cooperative cell motility during tandem locomotion of amoeboid cells.

Streams of migratory cells are initiated by the formation of tandem pairs of cells connected head to tail to which other cells subsequently adhere. The mechanisms regulating the transition from single to streaming cell migration remain elusive, although several molecules have been suggested to be involved. In this work, we investigate the mechanics of the locomotion ofDictyosteliumtandem pairs by analyzing the spatiotemporal evolution of their traction adhesions (TAs). We find that in migrating wild-type tandem pairs, each cell exerts traction forces on stationary sites (∼80% of the time), and the trailing cell reuses the location of the TAs of the leading cell. Both leading and trailing cells form contractile dipoles and synchronize the formation of new frontal TAs with ∼54-s time delay. Cells not expressing the lectin discoidin I or moving on discoidin I-coated substrata form fewer tandems, but the trailing cell still reuses the locations of the TAs of the leading cell, suggesting that discoidin I is not responsible for a possible chemically driven synchronization process. The migration dynamics of the tandems indicate that their TAs' reuse results from the mechanical synchronization of the leading and trailing cells' protrusions and retractions (motility cycles) aided by the cell-cell adhesions

Run-to-run control with Bayesian optimization for soft landing of short-stroke reluctance actuators

There is great interest in minimizing the impact forces of reluctance actuators during commutations, in order to reduce contact bouncing, acoustic noise and mechanical wear. In this regard, a run-to-run control algorithm is proposed to decrease the contact velocity, by exploiting the repetitive operations of these devices. The complete control is presented, with special focus on the optimization method and the input definition. The search method is based on Bayesian optimization, and several additions are introduced for its application in run-to-run control, e.g. the removal of stored points and the definition of a new acquisition function. Additionally, methods for the input parametrization and dimension reduction are presented. For analysis, Monte Carlo simulations are performed using a dynamic model of a commercial solenoid valve, comparing the proposed search method with two alternatives. Furthermore, the control strategy is validated through experimental testing, using several devices from the same ensemble of solenoid valves. IEE

Considerations on bubble fragmentation models

n this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22 f(D; D0) = D2 f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3 f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3 D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension

Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (\ie cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses

The dynamics and mixing of small spherical particles in a plane, free shear layer

The equation of motion of small rigid spheres settling under gravity in a two-dimensional inviscid flow given by the Stuart solution of the Euler equations is analyzed as a fourdimensional dynamical system. It is shown that depending on the values of the Stokes, Grashof, and a scaled Reynolds number, particles may either sediment or remain permanently suspended in the flow. When suspension occurs, the particle trajectories are shown to be attracted by a single period, quasiperiodic, or chaotic orbits. A consequence of the existence of a strange attractor (chaotic orbit) is that heavy particles can reach a stage ofjhdization by which they remain indefinitely suspended in a layer of finite height located above the center of the Stuart vortices.Secretaria de Estado de Universidades e Investigación de España FPU-2868794

Three-dimensional stability of periodic arrays of counter-rotating vortices

International audienceWe study the temporally developing three-dimensional stability of a row of counter-rotating vortices defined by the exact solution of Euler's equations proposed by Mallier and Maslowe [Phys. Fluids 5, 1074 (1993)]. On the basis of the symmetries of the base state, the instability modes are classified into two types, symmetric and anti-symmetric. We show that the row is unstable to two-dimensional symmetric perturbations leading to the formation of a staggered array of counter-rotating vortices. For long wavelengths, the anti-symmetric mode is shown to exhibit a maximum amplification rate at small wave numbers whose wavelengths scale mainly with the period of the row. This mode could be interpreted as due to the Crow-type of instability extended to the case of a periodic array of vortices. For short wavelengths, symmetric and anti-symmetric instability modes are shown to have comparable growth rates, and the shorter the wavelength, the more complex the structure of the eigenmode. We show that this short wavelength dynamic is due to the elliptic instability of the base flow vortices, and is well modeled by the asymptotic theory of Tsai and Widnall. The effect of varying the Reynolds number was also found to agree with theoretical predictions based on the elliptic instability. © 2002 American Institute of Physics

Real-time electromagnetic estimation for reluctance actuators

Several modeling, estimation, and control strategies have been recently presented for simple reluctance devices like solenoid valves and electromagnetic switches. In this paper, we present a new algorithm to online estimate the flux linkage and the electrical time-variant parameters of these devices, namely the resistance and the inductance, only by making use of discrete-time measurements of voltage and current. The algorithm, which is robust against measurement noise, is able to deal with temperature variations of the device and provides accurate estimations during the motion of the armature. Additionally, an integral estimator that uses the start of each operation of the actuator as reset condition has been also implemented for comparative purposes. The performances of both estimation methods are studied and compared by means of simulations and experimental tests, and the benefits of our proposal are emphasized. Possible uses of the estimates and further modeling developments are also described and discussed

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 2. Size PDF of the resulting daughter bubbles

Based on energy principles, we propose a statistical model to describe the bubble size probability density function of the daughter bubbles resulting from the shattering of a mother bubble of size D0 immersed in a fully developed turbulent water flow. The model shows that the bubble size p.d.f. depends not only on D0, but also on the value of the dissipation rate of turbulent kinetic energy of the underlying turbulence of the water, [epsilon]. The phenomenological model is simple, yet it predicts detailed experimental measurements of the transient bubble size p.d.f.s performed over a range of bubble sizes and dissipation rates [epsilon] in a very consistent manner. The agreement between the model and the experiments is particularly good for low and moderate bubble turbulent Weber numbers, Wet = [rho][Delta]u2(D0)D0/[sigma] where the assumption of the binary breakup is shown to be consistent with the experimental observations. At larger values of Wet, it was found that the most probable number of daughter bubbles increases and the assumption of tertiary breakup is shown to lead to a better fit of the experimental measurements

On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter Dc defined as Dc = 1.26 ([sigma]/[rho])3/5[epsilon][minus sign]2/5, where [epsilon] is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to Dc, the breakup frequency is shown to increase as ([sigma]/[rho])[minus sign]2/5[epsilon][minus sign]3/5 [surd radical]D/Dc[minus sign]1, while for large bubbles whose sizes are greater than 1.63Dc, it decreases with the bubble size as [epsilon]1/3D[minus sign]2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensitie