S. N. Brown

Trailing-edge stall

A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is

On the viscous flow about the trailing edge of a rapidly oscillating plate

\alpha^{*} = O(R^{\frac{1}{16}})

The inviscid instability of a Blasius boundary layer at large values of the Mach number

, where R is a representative Reynolds number, for incompressible flow, and α* = O ( R −¼ ) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of order R −⅜ , and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

Near-neutral centre-modes as inviscid perturbations to a trailing line vortex

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of high frequency and low amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. The aerofoil is replaced by a flat plate on the assumption that leadingedge stall does not take place. It is shown that, for oscillations of non-dimensional frequency

Collision phenomena in free-convective flow over a sphere

O(R^{\frac{1}{4}})

On finite amplitude Bénard convection in a cylindrical container

and amplitude

The evolution of a small inviscid disturbance to a marginally unstable stratified shear flow; stage two

O(R^{\frac{9}{16}})

On hypersonic boundary-layer interactions and transition

, a rational description of the flow at the trailing edge is based on a subdivision of the boundary layer above the plate into five distinct regions. Asymptotic analytic solutions are found in four of these, whilst in the fifth a linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

An asymptotic expansion for the eigenvalues arising in perturbations about the blasius solution

The unstable and neutral modes of a compressible boundary-layer flow past an insulated flat plate are discussed in the limit of infinite Mach number. These modes have been documented by Mack and many of the asymptotic results derived here are becoming evident in his computations at finite values of the Mach number. Of particular interest is the existence of a vorticity mode for which the wavenumber is a discontinuous function of Mach number at finite Mach number but is continuous in the limit M ∞ → ∞. At large Mach number this is the most unstable mode, and is expected to have relevance also in the hypersonic limit when the flow field is no longer shock-free.

Viscous Centre Modes in the Stability of Swirling Poiseuille Flow

Inviscid linear perturbations to a columnar trailing line vortex are found in the form of centre-modes. These near-neutral modes, occurring at moderate values of the azimuthal wavenumber n , are the analogue of the ring modes for large n discussed by Stewartson & Capell (1985). The appearance and disappearance of these modes as the swirl parameter varies may partly explain the difficulties encountered by numerical analysts in the computation of such modes. In addition, instabilities are found at higher values of the swirl parameter than have previously been reported.