The small time behaviour for the impulsively started flow past a semi- infinite flat plate
type: Item
instance of: scholarly article
title: The small time behaviour for the impulsively started flow past a semi- infinite flat plate
zbMATH Open document ID: 0757.76010
DOI: 10.1016/0022-247X(92)90248-C
author: S. Singh
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-01-16T00:00:00Z
review text: Let \((x,y)\) be the system of Cartesian coordinates in which the half plate is represented by \(y=0\), \(x>0\). The flow is started impulsively with a uniform velocity \(V\) in the direction of the positive \(x\)-axis. Neglecting the inertia terms the equations to be solved are \(\omega_ t=\nu\nabla^ 2\omega\), \(\omega=\nabla^ 2\Psi\) (\(\omega\)= vorticity, \(\Psi\)= stream function), with the conditions \(\Psi=\Psi_ y=0\) for \(y=0\), \(x>0\), \(t>0\), \(\Psi=\Psi_{yy}=0\) for \(y=0\), \(x<0\), \(t>0\), \(\Psi=U_ y\) for \(t=0\), \(y\neq 0\). The initial condition reduces to be homogeneous by taking the transformation \(\Psi=U_ y+\Psi\), \(\Omega=\nabla^ 2\Psi\). The condition for \(\Psi_ y\) on \(y=0\), \(x>0\) is modified to \(\Psi_ y=- Ue^{-\delta x}\) in order to eliminate singularities in the subsequent treatment, letting \(\delta\) tend to zero at the end of the calculation. The equations for \(\Omega\), \(\Psi\) are solved by taking Laplace and Fourier transforms (in this order) and finally the inverse transforms in the reverse order, thus obtaining approximated expressions of \(\Psi\), \(\Omega\). An accurate discussion of the results follows, estimating the time for which each order of approximation provides a satisfactory description of the phenomenon. Finally a similar analysis is developed for the case in which the initial flow has a non-zero inclination with respect to the plate.
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 91583
zbMATH Keywords: boundary layers
zbMATH Keywords: Laplace and Fourier transforms
reviewed by: Antonio Fasano
MaRDI profile type: Publication
cites work: On the nature of the boundary layer near the leading edge of a flat plate
cites work: On the flow near the trailing edge of a flat plate II
cites work: Boundary-Layer Flow Near the Trailing Edge of a Flat Plate
cites work: ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID
cites work: ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID. II
cites work: Unsteady Stokes' flow in two dimensions
cites work: Q3244933
cites work: On the diffraction of sound waves in a viscous medium
description: scientific article; zbMATH DE number 91583