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Register a new userDean flow and vortex shedding in a three-dimensional 180$^circ$ sharp bend
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We present a detailed analysis of the flow in a 180 sharp bend of square cross-section. Besides numerous applications where this generic configuration is found, its main fundamental interest resides in the co-existence of a recirculation bubble in the outlet and a pair of Dean vortices driven from within the turning part of the bend, and how their interaction may drive the flow dynamics. A critical point analysis first shows that the complex flow topology that results from this particular configuration can be reduced to three pairs of critical points in the symmetry plane of the bend (with a focus and a half-saddle each). These pairs respectively generate the first recirculation bubble, the pair of Dean vortex tubes and a third pair of vortex tubes located in the upper corner of the bend, akin to the Dean vortices but of much lower intensity and impact on the rest of the flow. The Dean flow by contrast drives a strong vertical jet that splits the recirculation bubble into two symmetric lobes. Unsteadiness sets in at $Relesssim800$ through a supercritical bifurcation, as these lobes start oscillating antisymmetrically. These initially periodic oscillations grow in amplitude until the lobes break away from the main recirculation. The system then settles into a second periodic state where streamwise vortices driven by the Dean flow are alternatively formed and shed on the left and right part of the outlet. This novel mechanism of periodic vortex shedding results from the subtle interaction between the recirculation bubble in the outlet and the pair of Dean vortices generated in the turning part, and in this sense, they are expected to be a unique feature of the 180$^o$ bend with sufficiently close side walls.
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The present article represents part of the PhD. dissertation by C. Josserand. We discuss the nucleation of quantized vortices in the nonlinear Schr{o}dinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field $psi$ gives an Euler-Tricomi type equation for the stationary solutions below threshold. This equation is closely related to the one known in shock wave dynamics for gas. Then using solvability condition, we extract a time-dependent scenario for the evolution of the amplitude of the solution, which we, finally, relate to a known family solution of NLS which gives rise to a vortex nucleation. We also give a first order correction at the Landau velocity of nucleation, taking into account the geometry of the flow.
Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number.
In a recent paper, Liu, Zhu and Wu (2015, {it J. Fluid Mech.} {bf 784}: 304) present a force theory for a body in a two-dimensional, viscous, compressible and steady flow. In this companion paper we do the same for three-dimensional flow. Using the fundamental solution of the linearized Navier-Stokes equations, we improve the force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, which is further proved to be universally true from subsonic to supersonic flows. We call this result the textit{unified force theorem}, which states that the forces are always determined by the vector circulation $pGamma_phi$ of longitudinal velocity and the scalar inflow $Q_psi$ of transverse velocity. Since this theorem is not directly observable either experimentally or computationally, a testable version is also derived, which, however, holds only in the linear far field. We name this version the textit{testable unified force formula}. After that, a general principle to increase the lift-drag ratio is proposed.
Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincare section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.
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