This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier–Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document th...

The distribution of the wall shear stress on the bed and sidewalls of an open channel receiving lateral inflow was obtained from experimental measurements of the distribution of the velocity in the viscous sublayer using a laser doppler velocimeter. The experiments were conducted in a 0.4 m wide by 7.5 m long flume. Lateral inflow was provided into the channel from above via sets of nozzles pos...

The Kidder problem is uxx + 2x(1 − αu)−1/2ux = 0 with u(0) = 1 and u(∞) = 0 where α ∈ [0, 1]. This looks challenging because of the square root singularity. We prove, however, that |u(x ;α) − erfc(x)| ≤ 0.046 for all x, α. Other very simple but very accurate curve fits and bounds are given in the text; |u(x ;α) − erfc(x + 0.15076x/(1 + 1.55607x2))| ≤ 0.0019. Maple code for a rational Chebyshev ...

When investigating sediment transport in laboratory open-channel flows, it is often necessary to remove sidewall effects for computing effective bed shear stress. Previous sidewall correction methods include some assumptions that have not been completely verified, and therefore different values of the bed shear stress may be obtained, depending on the approach used in making sidewall correction...

The development of wall shear stress in Görtler vortex flow was investigated by hot-wire measurements. The wavelengths of the vortices were pre-set by thin vertical perturbation wires so to produce the most amplified wavelengths. Three different vortex wavelengths of 12 mm, 15 mm, and 20 mm were considered, and near-wall velocity measurements were carried out to obtain the “linear” layers of ve...

A physically-based computational technique was investigated which is intended to estimate an initial guess for complex values of the wavenumber of a disturbance leading to the solution of the fourth-order Orr-Sommerfeld (O-S) equation. The complex wavenumbers, or eigenvalues, were associated with the stability characteristics of a semi-infinite shear flow represented by a hyperbolic-tangent fun...