A method solving equations of motion in incompressible vicous flow : Two dimensional motion

2004 ◽  
Vol 2004.41 (0) ◽  
pp. 111-112
Author(s):  
Isao TAKATAMA
Keyword(s):  
Equations Of Motion ◽  
Two Dimensional ◽  
Solving Equations

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

Investigation of Sinkage and Trim by Ships in Shallow Water Based on Overset Grid

2015 ◽  
Vol 713-715 ◽  
pp. 2126-2132
Author(s):  
Da Ming Sun ◽  
Ji Yong Liu ◽  
Qing Wen Kong
Keyword(s):  
Shallow Water ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Overset Grid ◽  
Ship Hulls ◽  
Surface Ship ◽  
Solving Equations ◽  
Sinkage And Trim ◽  
Volume Method ◽  
Good Agreement

A study on the navigation behavior for ships in shallow water had been carried out on CFD. The problem of surface ship hulls free of sinkage and trim in shallow water is analyzed numerically by simultaneously solving equations of the Reynolds averaged Navier-Stokes (RANS). The computations, based on the single-phase level set and overset grid, are discretized by finite volume method (FVM). An earth-based reference system is used for the solution to the fluid flow, while a ship-based reference is used to compute the rigid-body equations of motion. A S60 CB=0.6 ship model is taken as an example to the numerical simulation. Numerical results of the sinkage and trim of the seven Froude Numbers (Fn=0.5~0.8) are compared against experimental data, which have a good agreement.

The Asymptotic Stability of Weakly Perturbed Two Dimensional Hamiltonian Systems

2001 ◽  
Author(s):  
Ludwig Arnold ◽  
Peter Imkeller ◽  
N. Sri Namachchivaya
Keyword(s):  
Lyapunov Exponent ◽  
Equations Of Motion ◽  
Perturbation Approach ◽  
Two Dimensional ◽  
White Noise Process ◽  
System A ◽  
Additive White Noise ◽  
Small Dissipation ◽  
Small Intensity ◽  
Single Well

Abstract The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers Oscillator driven by either a multiplicative or an additive white noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ε and dissipation ε the exponent grows proportional to ε1/3.

scholarly journals Construction And Test Of Thermostats And Twirlers For Molecular Rotations

2003 ◽  
Vol 58 (7-8) ◽  
pp. 377-391 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Time Reversal ◽  
Rotational Diffusion ◽  
Equations Of Motion ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Polymer Molecules ◽  
Isotropic Harmonic Oscillator ◽  
Molecular Rotations ◽  
Basic Equations ◽  
Nonlinear Elastic

The equations of motion are coupled with a dynamical variable, referred to as twirler, which randomizes the angular momentum. The equations are time-reversal invariant, just as those for the standard Gaussian, Nosé-Hoover and configurational thermostats. The derivation of the basic equations is outlined. Test calculations are performed for the two-dimensional isotropic harmonic oscillator and for a nonlinear elastic dumbbell, used as a simple model to study properties of polymer molecules. Graphs of characteristic quantities and orbits, some of which are rather intriguing, are displayed. As applications, the rotational diffusion and the influence of a shear flow on the angular velocity and the deformation of the model polymer are analyzed.

scholarly journals THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS

1994 ◽  
Vol 09 (30) ◽  
pp. 2783-2801 ◽  
Author(s):  
H. ARATYN ◽  
L. A. FERREIRA ◽  
J. F. GOMES ◽  
A. H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Equations Of Motion ◽  
Curvature Form ◽  
Two Dimensional ◽  
Conserved Charges ◽  
Zero Curvature ◽  
Algebraic Properties ◽  
Toda Model ◽  
Infinite Sets ◽  
Poisson Commute

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

Open Physics ◽  
2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Equations Of Motion ◽  
Complex Variables ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional ◽  
Cyclotron Motion ◽  
Lissajous Figures ◽  
Long Time ◽  
Concentric Circles

AbstractThe classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.

Boundary-layer development at a two-dimensional rear stagnation point

1972 ◽  
Vol 56 (1) ◽  
pp. 161-171 ◽  
Author(s):  
A. J. Robins ◽  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Initial Value ◽  
Boundary Layer Development ◽  
Leading Term ◽  
Layer Development ◽  
Rear Stagnation Point ◽  
Good Agreement

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

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