Analytical and numerical study of the nonlinear interaction between a point vortex and a wall-bounded shear layer

1998 ◽  
Vol 373 ◽  
pp. 155-192 ◽  
Author(s):  
OLIVER V. ATASSI

The unsteady interaction between a vortex and a wall-bounded vorticity layer is studied as a model for transport and mixing between rotational and irrotational flows. The problem is formulated in terms of contour integrals and a kinematic condition along the interface which demarcates the vortical and potential regions. Asymptotic solutions are derived for linear, weakly nonlinear and nonlinear long-wave approximations. The solutions show that the initial process of ejection of vorticity into the irrotational flow occurs at a stationary point along the interface. A nonlinear model is derived and shows that such a stationary point is more likely to exist when the circulation of the vortex is counter to the vorticity in the layer. A Lagrangian numerical method based on contour dynamics is then developed for the general nonlinear problem. Two sets of results are presented where for every initial height of the vortex its magnitude and sign are varied. In both sets, it is observed that when the magnitude of the vortex is held constant a much stronger interaction occurs when the sign of the vortex circulation is opposite to that of the vorticity in the layer. Moreover, when the horizontal velocity of the vortex is close to the velocity of the interfacial waves a strong nonlinear interaction between the vortex and the layer ensues and results in the ejection of thin filaments of vorticity into the irrotational flow. In order to study the dynamical consequences of strong unsteady interaction, the wall pressure distribution is computed. The results indicate that a significant rise in the magnitude of the wall pressure is associated with ejection of vorticity from the wall. The present analysis confirms that coherent vortical structures in the outer layer of a turbulent boundary layer can cause ejection of concentrated wall-layer vorticity and explains how and when this process occurs.

2009 ◽  
Vol 618 ◽  
pp. 1-11 ◽  
Author(s):  
PAOLO BLONDEAUX ◽  
GIOVANNA VITTORI

The process which leads to the formation of three-dimensional sand waves is investigated by means of a stability analysis which considers the time development of a small-amplitude bottom perturbation of a shallow tidal sea. The weakly nonlinear interaction of a triad of resonant harmonic components of the bottom perturbation is considered. The results show that the investigated resonance mechanism can trigger the formation of a three-dimensional bottom pattern similar to that observed in the field.


2015 ◽  
Vol 282 ◽  
pp. 43-54 ◽  
Author(s):  
Yin Wang ◽  
Yong Lu ◽  
Jin Y. Ooi

Author(s):  
Takashi Sakajo

A two-dimensional potential flow in an unbounded domain with two parallel plates is considered. We examine whether two free point vortices can be trapped near the two plates in the presence of a uniform flow and observe whether these stationary point vortices enhance the force on the plates. The present study is an extension of previously published work in which a free point vortex over a single plate is investigated. The flow problem is motivated by an airfoil design problem for the double wings. Moreover, it also contributes to a design problem for an efficient wind turbine with vertical blades. In order to obtain the point-vortex equilibria numerically, we make use of a linear algebraic algorithm combined with a stochastic process, called the Brownian ratchet scheme. The ratchet scheme allows us to capture a family of stationary point vortices in multiply connected domains with ease. As a result, we find that stationary point vortices exist around the two plates and they enhance the downward force and the counter-clockwise rotational force acting on the two plates.


2010 ◽  
Vol 662 ◽  
pp. 260-268 ◽  
Author(s):  
A. SAURET ◽  
D. CÉBRON ◽  
C. MORIZE ◽  
M. LE BARS

We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (J. Fluid Mech., vol. 650, 2010, pp. 505–512), developed in the limit of small libration frequency–rotation rate ratio and large libration frequency–spin-up time product. Using particle image velocimetry measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid-body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.


2018 ◽  
Vol 849 ◽  
pp. 860-884 ◽  
Author(s):  
Petteri Sippola ◽  
Jari Kolehmainen ◽  
Ali Ozel ◽  
Xiaoyu Liu ◽  
Pentti Saarenrinne ◽  
...  

The effects of triboelectricity in a small-scale fluidized bed of polyethylene particles were investigated by imaging the particle layer in the vicinity of the column wall and by measuring the pressure drop across the bed. The average charge on the particles was altered by changing the relative humidity of the gas. A triboelectric charging model coupled with a computational fluid dynamics–discrete element method (CFD-DEM) model was utilized to simulate gas–particle flow in the bed. The electrostatic forces were evaluated based on a particle–particle particle–mesh method, accounting for the surface charge on the insulating walls. It was found that simulations with fixed and uniform charge distribution among the particles capture remarkably well both the agglomeration of the particles on the wall and the associated decrease in the pressure drop across the bed. With a dynamic tribocharging model, the charging rate had to be accelerated to render the computations affordable. Such simulations with an artificial acceleration significantly over-predict charge segregation and the wall becomes rapidly sheeted with a single layer of strongly charged particles.


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