The axisymmetric problem with initial conditions for the equations of motion of an ideal incompressible fluid

1967 ◽  
Vol 2 (3) ◽  
pp. 1-6 ◽  
Author(s):  
M. R. Ukhovskii
Keyword(s):  
Incompressible Fluid ◽  
Axisymmetric Problem ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Ideal Incompressible Fluid

Bound Coherent Structures Propagating on the Free Surface of Deep Water

2021 ◽  
Author(s):  
Sergey Dremov ◽  
Dmitry Kachulin ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Ideal Incompressible Fluid ◽  
System Of Nonlinear Equations ◽  
Computational Domain

<p><span>               The work presents the results of studying the bound coherent structures propagating on the free surface of ideal incompressible fluid of infinite depth. Examples of such structures are bi-solitons which are exact solutions of the known approximate model for deep water waves — the nonlinear Schrödinger equation (NLSE). Recently, when studying multiple breathers collisions, the occurrence of such objects was found in a more accurate model of the supercompact equation for unidirectional water waves [1]. The aim of this work is obtaining and further studying such structures with different parameters in the supercompact equation and in the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. </span><span>The algorithm used for finding the bound coherent objects was similar to the one described in [2]. As the initial conditions for obtaining such structures in the framework of the above models, the NLSE bi-soliton solutions were used, as well as two single breathers numerically found by the Petviashvili method and placed in a same point of the computational domain. During the evolution calculation the initial structures emitted incoherent waves which were filtered at the boundaries of the domain using the damping procedure. It is shown that after switching off the filtering of radiation, periodically oscillating coherent objects remain on the surface of the liquid, propagate stably during one hundred thousand characteristic wave periods and do not lose energy. The profiles of such structures at different parameters are compared.</span></p><p><span>This work was supported by RSF grant </span><span>19-72-30028</span><span> and </span><span>RFBR grant </span><span>20-31-90093</span><span>.</span></p><p><span>[1] Kachulin D., Dyachenko A., Dremov S. Multiple Soliton Interactions on the Surface of Deep Water //Fluids. – 2020. – Т. 5. – №. 2. – С. 65.</span></p><p><span>[2] Dyachenko A. I., Zakharov V. E. On the formation of freak waves on the surface of deep water //JETP letters. – 2008. – Т. 88. – №. 5. – С. 307.</span></p>

scholarly journals Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

1993 ◽  
Vol 134 ◽  
pp. 73-76
Author(s):  
A. S. Baranov
Keyword(s):  
Incompressible Fluid ◽  
Equatorial Plane ◽  
Equations Of Motion ◽  
Critical Evaluation ◽  
Oscillation Theory ◽  
Ideal Incompressible Fluid ◽  
Equilibrium Figure ◽  
Theory Analysis ◽  
Oscillation Modes ◽  
Non Linear

Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

2021 ◽  
Author(s):  
Renan F. Corrêa ◽  
Flávio D. Marques
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Nonlinear Behavior ◽  
Limit Cycle Oscillation ◽  
Restoring Force ◽  
Aeroelastic System ◽  
Technical Literature ◽  
Practical Applications

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.

Sign in / Sign up

Export Citation Format

Share Document