Three-dimensional marginal separation

The three dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudo-spectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively, the results are similar to previously reported two dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three dimensional results are much different

Unsteady three-dimensional marginal separation, including breakdown

A situation involving a three-dimensional marginal separation is considered, where a (steady) boundary layer flow is on the verge of separating at a point (located along a line of symmetry/centerline). At this point, a triple-deck is included, thereby permitting a small amount of interaction to occur. Unsteadiness is included within this interaction region through some external means. It is shown that the problem reduces to the solution of a nonlinear, unsteady, partial-integro system, which is solved numerically by means of time-marching together with a pseudo-spectral method spatially. A number of solutions to this system are presented which strongly suggest a breakdown of this system may occur, at a finite spatial position, at a finite time. The structure and details of this breakdown are then described

The response of a laminar boundary layer in supersonic flow to small amplitude progressive waves

The effect of a small amplitude progressive wave on the laminar boundary layer on a semi-infinite flat plate, due to a uniform supersonic freestream flow, is considered. The perturbation to the flow divides into two streamwise zones. In the first, relatively close to the leading edge of the plate, on a transverse scale comparable to the boundary layer thickness, the perturbation flow is described by a form of the unsteady linearized compressible boundary layer equations. In the freestream, this component of flow is governed by the wave equation, the solution of which provides the outer velocity conditions for the boundary layer. This system is solved numerically, and also the asymptotic structure in the far downstream limit is studied. This reveals a breakdown and a subsequent second streamwise zone, where the flow disturbance is predominantly inviscid. The two zones are shown to match in a proper asymptotic sense

On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up

Informational Accuracy and the Optimal Monetary Regime

King (1997) develops a framework for assessing four monetary regimes: an optimal state-contingent rule; a non-contingent rule; pure discretion; and a Rogoffian conservative central banker. Using this framework we show (a) that King is wrong to claim that it implies that an optimally-conservative central banker always dominates a fixed-rule monetary regime; (b) that if the private sector has a signal of the shock to which monetary policy responds - the accuracy of which is exogenously fixed - then either the optimal state-contingent rule or the optimally-conservative central bank can dominate; and (c) that if the private sector optimally chooses the accuracy of its signal then any regime can dominate.Monetary policy, expectations, Rogoffian central banker.

Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows

In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes

Relative Prices as Aggregate Supply Shocks with Trend Inflation

This paper modifies the menu-cost model that Ball and Mankiw (1995) put forward to explain the correlation between the first- and higher-moments of the distribution of US price changes by allowing for non-zero trend inflation. Simulations suggest that even if trend inflation is only mildly positive - such as the 3 percent per annum experienced by the US in the last 50 years - the predictions of the Ball and Mankiw model are greatly altered. We then show that some of these predictions are rejected by annual post-WW2 US data.Inflation, menu-cost, relative price variance, relative price skewness, skew-normal.

Estimating Betas and Stock-Return Correlations From Monthly Data: A Warning Note.

The empirical finance literature makes extensive use of 'monthly' stock returns, where a monthly return is the change in stock price between one particular day of the calendar month - which we term the reference day - and the corresponding day of the following month. We show that estimates of betas and stock-market correlations are highly sensitive to the choice of reference day and we suggest that studies based on such estimates can be unreliable. We support this claim by carrying out two small-scale empirical studies showing in each case that the results of critical tests are dependent upon the choice of reference day.betas, international correlations, estimation risk

On the effects of viscosity on the stability of a trailing-line vortex

The linear stability of the Batchelor (1964) vortex is investigated. Particular emphasis is placed on modes found recently in a numerical study by Khorrami (1991). These modes have a number of features very distinct from those found previously for this vortex, including exhibiting small growth rates at large Reynolds numbers and susceptibility to destabilization by viscosity. These modes are described using asymptotic techniques, producing results which compare favorably with fully numerical results at large Reynolds numbers

The inviscid stability of supersonic flow past a sharp cone

The laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem is considered. This flow is then analyzed from the point of view of linear, temporal, inviscid stability. The basic, non-axisymmetric disturbance equations are derived for general flows of this class, and a so called triply generalized inflexion condition is found for the existence of subsonic neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and aximuthal wavenumbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving curvature. Additionally, asymptotic analyses valid close to the tip of the cone, far downstream of the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability