Constant angular velocity

About: Constant angular velocity is a research topic. Over the lifetime, 1113 publications have been published within this topic receiving 15884 citations.

The flow due to a rotating disc

Abstract: 1. The steady motion of an incompressible viscous fluid, due to an infinite rotating plane lamina, has been considered by Karman. If r, θ, z are cylindrical polar coordinates, the plane lamina is taken to be z = 0; it is rotating with constant angular velocity ω about the axis r = 0. We consider the motion of the fluid on the side of the plane for which z is positive; the fluid is infinite in extent and z = 0 is the only boundary. If u, v, w are the components of the velocity of the fluid in the directions of r, θ and z increasing, respectively, and p is the pressure, then Karman shows that the equations of motion and continuity are satisfied by taking

A remarkable periodic solution of the three-body problem in the case of equal masses

Abstract: Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a flxed eight-shaped curve. Setting aside collinear motions, the only other known motion along a flxed curve in the inertial plane is the \Lagrange relative equilibrium" in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle. Our orbit visits in turns every \Euler conflguration" in which one of the bodies sits at the midpoint of the segment deflned by the other two (Figure 1). Numerical computations

On almost rigid rotations

Abstract: In order to answer some of Proudman's questions (1956) concerning shear layers in rotating fluids, a study is made of the flow between two coaxial rotating discs, each having an arbitrary small angular velocity superposed on a finite constant angular velocity. It is found that, if the perturbation velocity is a smooth function of r, the distance from the axis, then the angular velocity of the main body of fluid is determined by balancing the outflow from the boundary layer on one disc with the inflow to the boundary layer on the other at the same value of r. At a discontinuity in the angular velocity of either disc a shear layer parallel to the axis occurs. If the angular velocity of the main body of the fluid is continuous, according to the theory given below the purpose of this shear layer is solely to transfer fluid from the boundary layer on one disc to the boundary layer of the other. It has a thickness O(v1/3), where v is the kinematic viscosity, and in it the induced angular velocity is O(v1/6) of the perturbation angular velocity of the discs. On the other hand, if the angular velocity of the main body of fluid is discontinuous, according to the theory given below the thickness of the shear layer is O(v1/4). A secondary circulation is also set up in which fluid drifts parallel to the axis in this shear layer and is returned in an inner shear layer of thickness O(v1/3).The theory is also applied to the motion of fluid inside a closed circular cylinder of finite length rotating about its axis almost as if solid.

A remarkable periodic solution of the three-body problem in the case of equal masses

Abstract: Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ``Lagrange relative equilibrium" in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle. Our orbit visits in turns every ``Euler configuration" in which one of the bodies sits at the midpoint of the segment defined by the other two (Figure 1). Numerical computations by Carles Simo, to be published elsewhere, indicate that the orbit is ``stable" (i.e. completely elliptic with torsion). Moreover, they show that the moment of inertia I(t) with respect to the center of mass and the potential U(t) as functions of time are almost constant.

Laminar boundary layer on an impulsively started rotating sphere

Abstract: The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time The calculations have been carried out on the assumption that the Reynolds number is very large The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers