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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 authors derived a modified version of the Orr-Sommerfeld equation governing the disturbances of a two-dimensional vertical plume and derived the base flow profile using boundary layer approximation and similarity hypothesis, in the spirit of Blasius boundary layer solution.
Abstract: The meandering instability of a two-dimensional vertical plume is considered in this paper. The base flow profile is derived using boundary layer approximation and similarity hypothesis, in the spirit of Blasius boundary layer solution. Using linear stability analysis, we derive a modified version of the Orr-Sommerfeld equation governing the disturbances. The resulting eigenvalue problem is solved by the Galerkin method. It is found that a vertical plume is unstable to meandering, and in particular, three different wavelengths of meanders exist. A meandering instability of long wavelength ensues at the lowest portion of a vertically rising plume, where R<94 . Beyond R=94 and R=192 , the most unstable wavelength shifts to an intermediate and to a short wavelength meandering during the course of rising motion.
01 Jan 2018
TL;DR: In this paper, the authors presented results for a towed a sphere through water at a Reynolds number, based on sphere diameter, of 13000, and showed that the wake transition from the high local Reynolds number solution to the low local Reynolds solution via high-speed time-resolved PIV.
Abstract: The classic turbulent axisymmetric wake derivation for the spreading of wake half-width, δ, and maximum mean velocity, ūmax decay comes from arguments of a high local Reynolds number, Re, and thus negligible viscosity. If instead one assumes the local Reynolds number is small, then at some distance sufficiently far downstream the turbulent production term in the Reynolds shear stress equation will decay and a new similarity solution will arise: as shown by [2, 4]. This solution features the scaling of δ ∼ (x/d)1/2 and ūmax ∼ (x/d)−1. In other words, the turbulent wake is scaling itself at rates that match the theoretical laminar wake, yet with a local Reynolds number high enough for the turbulent fluctuations to be non-negligible. Whilst the derivation of a low Reynolds number solution is a mathematical exercise, obtaining data to confirm or deny its existence has proved difficult. No experiment has been conducted at a combination of high enough initial Reynolds number and far enough downstream to capture this transition behaviour. Furthermore, only the DNS study of Gourlay [3] has been able to achieve this behaviour; leading some researchers to question whether this decay state would occur or if the wake instead would relaminarise [7]. This paper presents results for a towed a sphere through water at a Reynolds number, based on sphere diameter, of 13000. Our experiments have been able to capture the wake transitioning from the high local Reynolds number solution to the low local Reynolds number solution via high-speed time-resolved PIV. The value of local Reynolds number that exhibits itself in the extreme far wake during the low local Reynolds number solution suggests the wake is still turbulent, supporting the claim of [2, 4].
Journal ArticleDOI
TL;DR: In this paper, Lie's infinitesimal transformation groups, which leave the basic equations of axially symmetric problems of classical elasticity invariant, are constructed for the case of the Boussinesque's problem of an elastic semi-space subjected to a point force applied normal to its surface.
Abstract: Lie's infinitesimal transformation groups, which leave the basic equations of axially symmetric problems of classical elasticity invariant, are constructed. For the case of the axisymmetric Boussinesque's problem of an elastic semi-space subjected to a point force applied normal to its surface, the invariance of boundary and boundary conditions leads to the explicit form of similarity transformations which are used to solve the problem. Expressions for the displacements and stresses derived by this approach, which is believed to be new, are found to agree with the known results.
Journal ArticleDOI
TL;DR: In this article, a model describing a non-Newtonian compressible and isotropic fluid was considered in the framework of extended thermodynamics and the governing equations in the particular case of cylindrical symmetry and the propagation of weak discontinuities.
Abstract: In the framework of extended thermodynamics, we consider a model describing a compressible and isotropic non-Newtonian fluid, neglecting heat effects For simplicity we consider the governing equations in the particular case of cylindrical symmetry and look for the propagation of weak discontinuities, comparing the results with those for classical fluids Moreover, under suitable conditions, the system under investigation proves to be invariant with respect to the dilatation group of transformations so that it is possible to characterize similarity solutions Some constitutive relations are characterized for the phenomenological parameters
Book ChapterDOI
04 Oct 2018
TL;DR: In this paper, a study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted, which shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones.
Abstract: A study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850