Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, the initial value problem of the equation of motion which has been linearized in the deviations from this similarity solution is solved by an expansion of the solution in terms of eigenfunctions of the linearized equation.
Abstract: The equation which describes the motion of an ice sheet under its own weight has a cylindrically symmetric similarity solution. The initial value problem of the equation of motion which has been linearized in the deviations from this similarity solution is solved by an expansion of the solution in terms of eigenfunctions of the linearized equation. The linearized equation determines, for all ice sheets of the same volume, an asymptotically stable motion. These results are compared with the corresponding results of the two-dimensional case (Halfar, 1981).
40 citations
TL;DR: In this paper, the uniqueness of the solution of the title problem has been examined through a simple mathematical procedure, and the solution has been shown to be unique in a number of applications.
Abstract: The uniqueness of the solution of the title problem has been examined through a simple mathematical procedure.
39 citations
TL;DR: In this article, a similarity solution of the Navier-Stokes equations that describes the two-dimensional flow of a viscous incompressible fluid through a channel with one porous wall is analyzed.
Abstract: A similarity solution of the Navier-Stokes equations that describes the two-dimensional flow of a viscous incompressible fluid through a channel with one porous wall is analysed. The analysis, which determines the number and character of solutions in various cases according to the higher-order boundary conditions at the impermeable wall of the channel, agrees with asymptotic results in the limits of small and large Reynolds numbers. Flow in a channel with one or two accelerating walls is similarly analysed.
39 citations
TL;DR: In this paper, a semi-analytical solution for the redistribution of two fluid phases in a horizontal one-dimensional and homogeneous porous medium is presented, based on a similarity transformation.
39 citations
TL;DR: In this article, the hydrodynamic impact due to a two-dimensional (2D) liquid column or a 2D liquid droplet hitting on a solid wedge is analyzed using the complex velocity potential together with the boundary element method.
Abstract: The hydrodynamic impact due to a two-dimensional (2D) liquid column or a 2D liquid droplet hitting on a solid wedge is analysed. The problem is solved using the complex velocity potential together with the boundary element method. A stretched coordinate system is used, which is defined through the ratio of the normal Cartesian coordinate system to an appropriately chosen time-varying length scale. Numerical simulations are first made for impact by a liquid wedge. The results from the time-domain method are found to be in a good agreement with the similarity solution. Simulations are also made for impact by an elliptic droplet. A condition for bisection of the droplet is introduced, which is found to provide stable and converged results.
39 citations