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Showing papers on "Similarity solution published in 1972"


Journal ArticleDOI
TL;DR: In this article, a similarity solution is presented which describes the internal waves generated by a simpleharmonic localized disturbance in a stably stratified viscous fluid and some experimental results support the theoretical predictions for the waves in a linearly stratified salt solution.
Abstract: A similarity solution is presented which describes the internal waves generated by a simple-harmonic localized disturbance in a stably stratified viscous fluid. Some experimental results support the theoretical predictions for the waves in a linearly stratified salt solution.

114 citations


Journal ArticleDOI
TL;DR: For the uniform flow past a semi-infinite flat plate subject to a blowing velocity profile equal to C(Uv/x), the conventional boundary-layer approximations break down as C approaches 0middot;6192 as discussed by the authors.
Abstract: For the uniform flow past a semi-infinite flat plate subject to a blowing velocity profile equal to C(Uv/x),½ the conventional boundary-layer approximations break down as C approaches 0middot;6192. Here, we consider the structure of the flow for large Reynolds numbers R when C exceeds this critical value. It is shown that, for C > 0·6192, a region containing injected fluid O(R-1/3)) in thickness forms directly above the plate. To a first approximation the flow in this region is inviscid and the pressure a function of x only. This blowing region is separated from the free stream by a free shear boundary layer of thickness O(R-½). Thus the flow domain consists of three distinct regions which interact to yield a similarity solution valid for large values of Rx. This solution is then extended to higher order by expanding the stream function in each region in powers of (Rx)-1/3 and evaluating the first four terms in the resulting series using standard matching techniques. Finally, more general blowing profiles which also lead to boundary-layer ‘blow off’ are considered and an expression, valid far downstream of boundary-layer detachment, is derived for the position of the streamline separating the injected fluid from that of the free stream. For the case of uniform blowing the blowing region takes on the shape of a wedge, indicating that no solution can exist for the corresponding external flow if the plate is truly semi-infinite.

24 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived the governing perturbation potential equations for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonic regime.
Abstract: A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

20 citations


Journal ArticleDOI
TL;DR: In this paper, a circular cylinder is positioned horizontally in an incompressible stably stratified fluid which has a constant Brunt-Vaisala frequency and a vertical two-dimensional internal wave is produced when the cylinder is oscillated at this natural frequency.
Abstract: A circular cylinder is positioned horizontally in an incompressible stably stratified fluid which has a constant Brunt-Vaisala frequency. A vertical two-dimensional internal wave is produced when the cylinder is oscillated at this natural frequency. A small amplitude viscous similarity solution which explains the main features of the internal wave is presented.

18 citations


01 Nov 1972
TL;DR: In this article, a two dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, with solutions found in the form of perturbations from a uniform, sonic, isentropic flow.
Abstract: : A two dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, with solutions found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are included so that shock waves can be considered. The case where the characteristic time of a temporal flow disturbance is large compared to the time taken by a sonic disturbance to cross the transonic regime is considered. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady channel flows with shock waves, for the case where the walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves in unsteady flows, both for decelerating and accelerating channel flows. For the thin shock case, both numerical and asymptotic solutions are given. (Author)

14 citations



Journal ArticleDOI
TL;DR: In this article, the freezing or melting processes, using substances with variable thermal properties, taking place in a body with variable cross-sectional area, are considered, and the method of obtaining the similarity s...
Abstract: Freezing or melting processes, using substances with variable thermal properties, taking place in a body with variable cross-sectional area, are considered. The method of obtaining the similarity s...

1 citations


Journal ArticleDOI
S. Ghoshal1
TL;DR: In this paper, a unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow inside a boundary layer along a flat plate, taking account of the viscous dissipation term.
Abstract: A unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow, inside a boundary layer along a flat plate. Though previously, attempts were made to obtain similarity solutions of a steady boundary layer flow neglecting viscous dissipation term in the energy conservation equation but the treatments were not complete. Here we have taken account of the viscous dissipation term. In the steady case it has been shown that for a similarity solution of both velocity and temperature, there should be a relation between the undisturbed flow outside the boundary layer and the temperature of the plate. It has been shown that the similarity solution exists in the unsteady case if we neglet the viscous dissipation term in the energy equation.