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Showing 1 to 12 of 12 for “"Orr-Sommerfeld"”.
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Uniformly valid asymptotic solutions of the Orr-Sommerfeld equation and their application to plane Poiseuille flow
Thesis: M.S., Massachusetts Institute of Technology, Department of Mathematics, 1961
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A numerical investigation of the linear hydrodynamic stability of Newtonian and weakly non-Newtonian channel flows as described by the Orr-Sommerfeld equation
The Orr-Sommerfeld equation describes the growth of infinitesimal disturbances to laminar solutions of the Newtonaian Navier-Stokes equations. In this dissertation we consides in part idealised flows between two parallel planes of infinite extent and a finite distance apart. They are referred to as …
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The Effects of Variable Parameters on the Behavior of Initial Wind Waves
… by integrating a transformed version of the Orr-Sommerfeld equation, subject to the boundary conditions at a two-fluid interface. Unbounded growth problems usually encountered in a direct numerical integration of the Orr-Sommerfeld equation were avoided by the use of the compound matrix …
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Nichtlineare Stabilitätsanalyse der3D-Couette-Strömung unter Berücksichtigung derEnergietransfererhaltung
… einer 108-dimensionalen Galerkindarstellung in Orr-Sommerfeld- und Squire-Moden untersucht. Im Reynoldzahlbereich 325<= R <= 350 wird ein deutliches Übergangsverhalten gefunden; des weiteren wird auch die sensitive Abhängigkeit von den Anfangsbedingungen im Intermittenzbereich bestätigt, die …
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Hydrodynamic Stability of the boundary layer beneath a Stokes wave
… and Chebyshev collocation methods to solve the Orr-Sommerfeld eigenvalue problem, we examine the stability of the flow across a broader parameter space. Our findings suggest that, while the laminar boundary layer remains stable for the momentary stability criterion against infinitesimal …
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Stability of flows in channels
… differential equations have at lowest-order the Orr--Sommerfeld equation on which much of the subsequent work in laminar stabi1ity depends. The second order correction to the growth rates was the highest order in the works reviewed.The criteria of stability that was adopted was such that if a …
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Generation of discrete frequency tones by the flow around an aerofoil
… rates of the waves were obtained by solving the Orr–Sommerfeld problem at several stations on the aerofoil. The Falkner–Skan boundary layers were found to be a suitable form of velocity profiles to incorporate the adverse pressure gradients experienced by the flow over an aerofoil. The …
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Hydrodynamic stability of liquid films adjacent to incompressible gas streams including effects of interface mass transfer
… to linear profiles. This makes the governing Orr-Sommerfeld, temperature and concentration perturbation equations amenable to closed form analytical solutions and therefore enables one to isolate the effects of mass transfer. The present analysis considers instabilities in both gas and liquid …
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Stability analysis of a bilayer contained within a cylindrical tube
… for arbitrary bilayer thickness. A system of two Orr-Sommerfeld equations is obtained using this more general approach, and together with the boundary conditions yields an eigenvalue problem for the growth rate. Validations and comparisons with lubrication theory models (both extended and …
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Unsteady flow physics of airfoil dynamic stall
… 0.14. Finally, a numerical implementation of the Orr-Sommerfeld equation was used to extract the spatially-unstable modes associated with the phase-averaged velocity measurements near the airfoil leading edge. The most unstable frequencies from linear stability analysis were found to be consistent …
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Hydrodynamic linear stability of the two-dimensional bluff-body wake through modal analysis and initial-value problem formulation
… dynamics of the base flow. The first order corrections find absolute instability pockets in the first part of the intermediate wake (and not in the near wake, where the recirculating eddies are, as usually seen in literature in contrast with the near-parallelism hypothesis). These regions are …
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Statistical Stability and Fast Transient Growth in Wall-Bounded Turbulence
… the second order flow statistics. The extended Orr-Sommerfeld stability analysis is developed by mapping the statistical stability problem back to the physical space. The model is then tested on statistically stable turbulent states in two-dimensional channel generated in chapter 2, showing at …