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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 presented a similarity solution for the wave boundary layer and the Ekman layers of the two fluids, which showed that under steady-state neutral conditions the pure drift current lies along the direction of the geostrophic wind, and has a magnitude 0.034 that of the wind speed, and also showed that the frictional properties of the coupled air-sea system are easily evaluated functions of the 10m wind speed and the peak wave period.
Abstract: The ocean drift current consists of a (local) pure drift current generated by the interaction of wind and waves at the sea surface, to which the surface geostrophic current is added vectorially. We present (a) a similarity solution for the wave boundary layer (which has been validated through the prediction of the 10-m drag law), from which the component of pure drift current along the direction of the wind (and hence the speed factor) can be evaluated from the 10-m wind speed and the peak wave period, and (b) a similarity solution for the Ekman layers of the two fluids, which shows that under steady-state neutral conditions the pure drift current lies along the direction of the geostrophic wind, and has a magnitude 0.034 that of the geostrophic wind speed. The co-existence of these two similarity solutions indicates that the frictional properties of the coupled air-sea system are easily evaluated functions of the 10-m wind speed and the peak wave period, and also leads to a simple expression for the angle of deflection of the pure drift current to the 10 m wind. The analysis provides a dynamical model for global ocean drift on monthly and annual time scales for which the steady-state neutral model is a good approximation. In particular, the theoretical results appear to be able to successfully predict the mean surface drift measured by HF Radar, which at present is the best technique for studying the near surface velocity profile.

3 citations

Journal ArticleDOI
TL;DR: In this article, a numerical simulation of the laminar buoyant plume created by a heated sphere situated in an otherwise quiescent environment is presented, where the authors obtain a numerically exact solution of the equations representing mass, momentum, and energy conservation.
Abstract: This article is concerned with the numerical simulation of the laminar buoyant plume created by a heated sphere situated in an otherwise quiescent environment. The limit of vanishing sphere diameter corresponds to the point source of heat, for which extensive results have been obtained in the literature. The dual objectives of this work are the attainment of an exact characterization of the buoyant plume, and the diagnosis of an existing similarity solution for the limiting problem of the point source. These objectives were fulfilled by means of a numerically exact solution of the equations representing mass, momentum, and energy conservation. The solutions were carried out over a range of the radius-based Grashof number extending from 50 to 5 × 106 for a Prandtl number of 0.7, which corresponds to air. The velocities in the plume were found to increase with elevation above the sphere but approach a fully developed state characterized by congruent (similar) velocity profiles at sufficiently high elevation...

3 citations

Journal ArticleDOI
TL;DR: In this paper, a vortex-sheet representation for a start-up separated flow at the trailing edge is developed whose time-wise evolution is described by a Birkhoff-Rott equation coupled to an appropriate Kutta condition.
Abstract: We consider the trailing-edge vortex produced in an inviscid fluid by the start-up motion of a two-dimensional flat plate. A general starting motion is studied that includes the initial angle-of-attack of the plate (which may be zero), individual time power laws for plate translational and rotational speeds and the pivot position for plate rotation. A vortex-sheet representation for a start-up separated flow at the trailing edge is developed whose time-wise evolution is described by a Birkhoff–Rott equation coupled to an appropriate Kutta condition. This description includes convection by the outer flow, rotation and vortex-image self-induction. It admits a power-law similarity solution for the (small-time) primitive vortex, leading to an equation set where each term carries its own time-wise power-law factor. A set of four general plate motions is defined. Dominant-balance analysis of this set leads to discovery of three distinct start-up vortex-structure types that form the basis for all vortex motion. The properties of each type are developed in detail for some special cases. Numerical and analytical solutions are described and transition between solution types is discussed. Singular and degenerate vortex behaviour is discovered which may be due to the absence of fluid viscosity. An interesting case is start-up motion with zero initial angle of attack coupled to power-law plate rotation for which time-series examples are given that can be compared to high Reynolds number viscous flows.

3 citations

Journal ArticleDOI
TL;DR: In this article, the upper boundary layer of the seafloor is estimated from the balance of the viscous force with the horizontal pressure gradient at the sea floor and the importance of the frictional heating.
Abstract: The equations of conservations of momentum and energy scaled with the characteristic values of the mantle indicate the presence of the upper boundary layer to produce the estimated rate of the ocean floor spreading by convection and the importance of the frictional heating. The depth of the upper boundary layer can be estimated from the balance of the viscous force with the horizontal pressure gradient at the sea floor. It is of the orders of 100 km and becomes deeper for the Pacific than for the Atlantic Ocean and also with frictional heating than without it. The frictional heating increases the surface heat flow of the heat conduction by ten to twenty percent for the Pacific Ocean but only by a few percent for the Atlantic Ocean. The similarity solutions are determined for the temperature and horizontal velocity in the upper boundary layer. These solutions are expressed in power series of the variabley x−n, wherex, y, andn are horizontal and vertical coordinates and numerical constant, respectively. Both temperature and horizontal velocity within the boundary layer are higher for the Pacific than for the Atlantic Ocean. When a larger viscosity is applied, it causes the increase of horizontal velocity below the surface because of the surface boundary conditions of the finite velocity and of vanishment of the velocity shear. The higher horizontal velocity generates higher temperature because it advects hotter material from the mid-ocean ridge site. The direct effect of frictional heating on the temperature distribution of the similarity solution is almost negligible, since the shear zone is deep and near the lower boundary of the upper boundary layer. In the similarity solution, the surface heat flow which is increased by the frictional heating is given as the boundary value. The effect of the frictional heating is important below the mid-ocean ridge.

3 citations

Journal ArticleDOI
TL;DR: In this paper, a simple turbulent diffusion model is described for predicting late term mixing due to Rayleigh-Taylor instability at an interface that initially separates two semi-infinite regions of fluid of different densities.

3 citations


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