A theoretical formulation of wave-vortex interactions

1989 ◽  
Author(s):  
J. WU ◽  
J. WU
Keyword(s):  
Theoretical Formulation ◽  
Vortex Interactions

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Unstructured Adaptive Meshes

AIAA Journal ◽  
2002 ◽  
Vol 40 (3) ◽  
pp. 474-480 ◽  
Author(s):  
Woo Seop Oh ◽  
Joo Sung Kim ◽  
Oh Joon Kwon
Keyword(s):  
Numerical Simulation ◽  
Two Dimensional ◽  
Adaptive Meshes ◽  
Vortex Interactions

Analytical redefinition of DOL and managerial investment decisions

2014 ◽  
Vol 40 (7) ◽  
pp. 734-754 ◽  
Author(s):  
Yoram Kroll ◽  
David Yechiam Aharon
Keyword(s):  
Large Scale ◽  
Investment Decision ◽  
Production Level ◽  
Fixed Cost ◽  
Theoretical Formulation ◽  
Optimal Production ◽  
Demand Shocks ◽  
Content Type ◽  
Operating Leverage ◽  
The Impact

Purpose – The purpose of this paper is to develop alternative analytical measures for the degree of operating leverage (DOL) that reflect the impact of uncertain demand shocks in the product's market on optimal production levels, sales and profits of the firm. Design/methodology/approach – The elasticity measures are constructed according to a theoretical formulation of optimal production level that corresponds to demand shocks for given predetermined levels of fixed cost. Findings – The paper suggests two main findings. First, the analytical marginal DOL is at least twice the traditional DOL depending on the structure of the shock, the production function and demand's elasticity. The traditional DOL is equal to the measure only when large-scale negative demand prompts the firm to abandon production. Second, the paper also provides an analytical measure of DOL in terms of elasticity of profit to sales rather than to production level. Both theoretically and empirically elasticity of profit to sales can be better measured and better reflects risk. Research limitations/implications – This paper should be extended to encompass multiple shocks on demand and supply while investigating the empirical multi variants distribution of the shocks. Practical implications – The model can be used by managers who are well informed about the fixed and variable costs of their firm. The model determines the mean profit- risk trade off which is an important factor in all investment decision problems. Originality/value – Surprisingly and according to the best knowledge, this paper is the first attempt in the literature for alternative analytical DOLs’ formulations that is coherent with basic economic theories of optimal production level under risk.

scholarly journals Vortex–Vortex Interactions for the Maintenance of Blocking. Part II: Numerical Experiments

2013 ◽  
Vol 70 (3) ◽  
pp. 743-766 ◽  
Author(s):  
Akira Yamazaki ◽  
Hisanori Itoh
Keyword(s):  
Numerical Experiments ◽  
Channel Model ◽  
Spherical Model ◽  
Zonal Flow ◽  
Selective Absorption ◽  
Absorption Mechanism ◽  
Vortex Interactions ◽  
Maintenance Mechanism ◽  
Uniform Background

Abstract The selective absorption mechanism (SAM), newly proposed in Part I of this study on the maintenance mechanism of blocking, is verified through numerical experiments. The experiments were based on the nonlinear equivalent-barotropic potential vorticity equation, with varying conditions with respect to the shape and amplitude of blocking, and characteristics of storm tracks (displacement and strength) and background zonal flow. The experiments indicate that the SAM effectively maintains blocking, irrespective of the above conditions. At first, by applying a channel model on a β plane, numerical experiments were conducted using a uniform background westerly with and without a jet. The results show that the presence of a jet promotes the effectiveness of the SAM. Then, two types of spherical model experiments were also performed. In idealized experiments, the SAM was as effective as the β-plane model in explaining the maintenance of blocking. Moreover, experiments performed under realistic meteorological conditions showed that the SAM maintained a real block, demonstrating that the SAM is effective. These results, and the case study in Part I, verify that the SAM is the effective general maintenance mechanism for blocking.

DYNAMIC BEHAVIOR OF TELESCOPIC CRANES BOOM

2013 ◽  
Vol 13 (01) ◽  
pp. 1350010 ◽  
Author(s):  
IOANNIS G. RAFTOYIANNIS ◽  
GEORGE T. MICHALTSOS
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Constant Velocity ◽  
Steel Beam ◽  
Continuum Approach ◽  
Theoretical Formulation ◽  
Modal Superposition ◽  
Superposition Technique

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.

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