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

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

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

Bubble size distribution resulting from the breakup of an air cavity injected into a turbulent water jet

We investigated experimentally the shape of the final size PDF(D) resulting from the breakup of an air bubble injected into the fully developed region of a high Reynolds number turbulent water jet. It is shown that the PDF(Dcirc) of the normalized bubble size Dcirc=D/D32, where D32 is the Sauter mean diameter of the distribution, has a universal single shape independent of the value of the turbulent kinetic energy of the water jet at the bubble injection point and of the air void fraction, α. The shape of the exponential tails characterizing each PDF(D) is shown to be only a function of the initial bubble size D0 and the critical bubble size Dc, defined as Dc=(1.46σ/ρ)3/5ɛ-2/5, where ɛ is the value of the dissipation rate of turbulent kinetic energy per unit mass at the air injection point

Vorticity dynamics in three-dimensional pulsating co-flowing jet diffusion flames

The vorticity dynamics in the near field of laminar (Re = 103) co-flowing jets subjected to the single or combined effeets of axial and azimuthal forcing is analyzed. It is shown that the interaction of the three-dimensional vortex structure resulting from the growth of the two and three-dimensional instabilities may result in large changes in the entrainment and mixing characteristics of the jet. For each azimuthal forcing, and for a fixed velocity ratio between the inner and outer jet, we show the existence of several instability modes leading to a pattern of lateral ejections of closed vortex loops. These modes and their topological changes are analyzed in view of the three-dimensional inviscid induction of the two concentric array of vortex rings emanating from the j e t s exit nozzle. For the case of methane-air diffusion flames, fiow visualizations revealed the existence of qualitatively similar patterns of closed fíame cells and fingers

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