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: Similarity reductions of the two-space-dimensional versions of the Korteweg-de-Vries, modified versions of it, and nonlinear Schroedinger equations are discussed in this paper.
Abstract: Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.
27 citations
TL;DR: In this paper, the authors investigated mixed free and forced convection of non-Newtonian fluids from a vertical isothermal plate embedded in a homogenous porous medium and developed a mathematical model based on the modified Darcy's law and boundary layer approximations, and the exact similarity solution is obtained as well as an integral solution.
Abstract: This paper investigates mixed free and forced convection of non-Newtonian fluids from a vertical isothermal plate embedded in a homogenous porous medium. A mathematical model is developed based on the modified Darcy's law and boundary-layer approximations, and the exact similarity solution is obtained as well as an integral solution. These two solutions agree within 3% for aiding flows and 10% for opposing flows. It is found that, non-Newtonian characteristics of fluids have appreciable influences on velocity profiles, temperature distributions and flow regimes.
27 citations
TL;DR: The wave field resulting from a surface pressure or bottom topography in a horizontally unbounded domain is studied in this article, where upstream advancing waves successively generated by various forcing disturbances moving with near-resonant speeds are found by numerically solving a forced Kadomtsev-Petviashvili (fKP) equation, which shows in its simplest form the interplay of a basic linear wave operator, longitudinal and transverse dispersion, nonlinearity, and forcing.
Abstract: The wave field resulting from a surface pressure or a bottom topography in a horizontally unbounded domain is studied. Upstream‐advancing waves successively generated by various forcing disturbances moving with near‐resonant speeds are found by numerically solving a forced Kadomtsev–Petviashvili (fKP) equation, which shows in its simplest form the interplay of a basic linear wave operator, longitudinal and transverse dispersion, nonlinearity, and forcing. Curved solitary waves are found as a slowly varying similarity solution of the Kadomtsev–Petviashvili (KP) equation, and are favorably compared with the upstream‐advancing waves numerically obtained.
27 citations
TL;DR: In this paper, a local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. But their projections on planes normal to the line of intersection of the boundaries are precisely the Taylor streamlines of the well-known ‘paint-scraper’ problem.
Abstract: The three-dimensional flow in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the ‘Taylor’ streamlines of the well-known ‘paint-scraper’ problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honed by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows.
27 citations
TL;DR: In this paper, the natural-convection boundary-layer flow over a semi-infinite heated plate of arbitrary inclination is studied by first identifying a set of combined boundary layer variables and then casting the governing equations into a universal form.
Abstract: The natural-convection boundary-layer flow over a semi-infinite heated plate of arbitrary inclination is studied by first identifying a set of combined boundary-layer variables and then casting the governing equations into a universal form. The generalized problem yields the existing similarity solutions for the limiting cases of horizontal and vertical plates, and describes the gradual transition of the flow pattern between these two limits at distances from the leading edge which depend on the inclination angle. Near the leading edge the buoyancy force acting normal to the plate causes an ‘impulsive’ driving force to the fluid motion along the plate, while the ‘regular’ driving force exerted by the tangential buoyancy force becomes dominating downstream. Both the exact and the locally-similar solutions are obtained and are found to agree well with each other.
27 citations