ICE - Institution of Civil Engineers - Virtual Library

The counter-rotating pair of vortices formed from aircraft wingtips in flight presents a potential hazard to other aircraft in the form of a sustained rolling moment. Such a trailing vortex pair travels downwards with a self-induced velocity, and may interact with the ground plane at airports. The ground affects both the trajectories of the original vortex pair as well as the development of three-dimensional instabilities in the pair. As the vortex pair approaches the ground plane, it generates a boundary layer on the ground that separates to form opposite-sign, secondary vortices. These secondary vortices impact the trajectories and development of the original vortex pair. The focus of the current paper is not simply the 2D behaviour of the vorticity, but also the development of 3D instabilities. A novel technique has been developed using laser-induced fluorescence to visualise this secondary vorticity in unprecedented detail, revealing new flow phenomena.

A Stokes-style analytical theory for standing waves is developed and explored. The theory is numerically confirmed as correct to fifth order, and details of the solution are archived in a manner that anticipates the confirmation demands of application code. The uniquely non-linear aspects of the predicted kinematics are demonstrated in parallel with the equivalent linear theory prediction. Finally, the limits of validity of the analytical solution are examined, and lead to a preliminary but pragmatic estimate of limit standing waves.

Based on the mild-slope equation derived by Smith and Sprinks and the extended refraction–diffraction equation developed by Massel, a two-layer mild-slope equation is constructed for interfacial waves propagating on the interface of a two-layer ocean model. First, Smith and Sprinks's approach is followed to derive the mild-slope equation for the propagation of interfacial waves, with the higher-order terms proportional to the bottom slope and bottom curvature all being neglected. The extended version of the mild-slope equation is then derived with the higher-order terms included. While it is possible to solve the first equation analytically, a numerical solution is presented for the second equation. As part of a verification process, both solutions are compared with each other and also with the single-layer mild-slope equation when the density of the upper layer tends to zero. The new solution is then used to study the effect of the hump dimensions on the refraction of the interfacial waves over a circular hump.

Rayleigh damping is widely used for dynamic analysis of structures. Although it is based on a simple formula, the use of Rayleigh damping for seismic analysis involves a hidden complication, which is commonly overlooked both in theory and in practice. The complication arises because mass-proportional damping introduces an extra term into the equations of motion when these are written as total displacements. If this term is not included, the validity of the results obtained from finite element analysis may be doubtful. This paper presents the correct equations of motions for problems involving foundation motion and Rayleigh damping. The paper provides evidence suggesting that at least two of the most widely used commercial finite element codes do not contain a consistent implementation of Rayleigh damping. This evidence is presented in the form of two verification problems. Finally, an estimate of the likely error in seismic analysis carried out to date is offered.

A damage–plasticity constitutive model for the description of fracture in plain concrete is presented. Two approaches – the local model comprising the adjustment of the softening modulus and the non-local model based on spatial averaging of history variables – are applied to the analysis of a concrete bar subjected to uniaxial tension and to a three-point bending test. The influence of mesh size and the decomposition into damage and plasticity components are discussed. It is shown that for the two examples studied, both approaches give mesh-independent results. However, the non-local model, which relies on spatial averaging of history variables, exhibits sensitivity with respect to boundary conditions which requires further studies.