A wake model is pursued for potential flow past a submerged, finite-length plate that is perpendicular to a uniform, horizontal stream bounded above by a free surface. The effects of gravity are included along the free surface. The approach is to adopt an open-wake model such that the wake boundaries become parallel to the undisturbed stream at some (unknown) point downstream. Boundary integral equations are formed and then discretised along the wake boundaries and free surface in order to obtain a solution numerically. In terms of the dependency of the solution on various parameters, the problem will be formulated in two ways. First, for a given Froude number and ratio of the length of the vertical plate to the draft (the depth of the bottom of the vertical plate relative to the undisturbed free surface), the effect of the wake underpressure coefficient on the size of the wake will be considered. Then, the problem will be discussed where we instead (more naturally) fix the Froude number, draft and length of the vertical, submerged plate. The dependencies of the solution on these parameters will be analysed regarding the effects on several factors, including the size of the wake, the relative lengths of the upper and lower wake boundaries, and the resulting wake underpressure coefficient.

Most simple ailerons produce adverse yaw. However, with proper aileron placement and wing twist, an aileron can produce proverse or neutral yaw, eliminating the need for aileron-rudder mixing, differential aileron deflection or Frise ailerons. The relationship between wing planform, aileron placement and lift distribution is studied here for a special class of optimal lift distributions that minimise induced drag for a variety of design constraints. It is shown that a wing employing the elliptic lift distribution will always produce adverse yaw, independent of aileron design or operating condition. However, for wings employing other optimal lift distributions, the ailerons can be placed to produce proverse or neutral yaw. A numerical lifting-line algorithm is used to explore the impact of aileron design on a wide range of wing planforms and lift distributions. Results can be used in the early stages of design to correctly place ailerons with respect to desired roll-yaw coupling.

Steady-state diffusion in long axisymmetric structures is considered. The goal is to assess one-dimensional approximations by comparing them with axisymmetric eigenfunction expansions. Two problems are considered in detail: a finite tube with one end that is partly absorbing and partly reflecting; and two finite coaxial tubes with different cross-sectional radii joined together abruptly. Both problems may be modelled using effective boundary conditions, containing a parameter known as the trapping rate. We show that trapping rates depend on the lengths of the finite tubes (and that they decay slowly as these lengths increase) and we show how trapping rates are related to blockage coefficients, which are well known in the context of potential flow along tubes of infinite length.

In this paper, the prediction of the unsteady flow field over typical high aspect ratio (AR) wings in the transonic flow regime but below the sonic Mach number is of interest. The methodology adopted is a computational approach based on the transonic small disturbance unsteady potential equation. It is shown that the higher AR wings generally have a higher lift coefficient as well as a higher lift-to-drag ratio. With NASA’s common research model (CRM) wing, there is an increase in maximum lift with increasing AR while the induced drag is almost the same. There is also an optimum sweep angle, which is different for each angle-of-attack so that variable sweep lifting surfaces may be designed to provide optimum solutions. The computed flutter speeds indicate an expected reduction with increasing AR.

Control laws for implementing active flutter suppression are generally derived from linear aeroelastic models. In this paper, families of control laws for implementing an active flutter suppression system were initially designed using linearised aeroelastic models based on the doublet lattice method after ignoring the aerodynamic loads associated with relatively faster time scales. Using these preliminary sets of control laws and the nonlinear transonic small disturbance theory, near-optimum control laws were chosen in the transonic domain to maximally increase the flutter speed of a typical aircraft wing by at least 16% or more. Thus it is shown that it is feasible to systematically design near-optimal control laws for active flutter suppression using computational models in transonic flow. The doublet lattice method coupled with the zeroth-order matrix Padé approximant provided the fastest method for synthesising a large number of preliminary control laws. The methodology was successfully demonstrated by applying it to two benchmarking examples.

Most modern aircraft employ discrete ailerons for roll control. The induced drag, rolling moment, and yawing moment for an aircraft depend in part on the location and size of the ailerons. In the present study, lifting-line theory is used to formulate theoretical relationships between aileron design and the resulting forces and moments. The theory predicts that the optimum aileron geometry is independent of prescribed lift and rolling moment. A numerical potential flow algorithm is used to evaluate the optimum size and location of ailerons for a wide range of planforms with varying aspect ratio and taper ratio. Results show that the optimum aileron design to minimise induced drag always extends to the wing tip. Impacts to induced drag and yawing moment are also considered, and results can be used to inform initial design and placement of ailerons on future aircraft. Results of this optimisation study are also compared to theoretical optimum results that could be obtained from morphing-wing technology. Results of this comparison can be used to evaluate the potential benefits of using morphing-wing technology rather than traditional discrete ailerons.

The dynamic ground effect enhances the swimming of fish. The dynamic ground effect affects the kinematic conditions of fish, causing them to swim more efficiently. However, predicting the degree to which the dynamic ground effect can improve the swimming performance of fish is difficult. The dynamic ground effect can potentially save energy for biomimetic underwater vehicles. Therefore, a theoretical model was developed to investigate the effect of a planar boundary on the swimming performance of a two-dimensional undulating plate. General expressions for the thrust, power input, efficiency, and energy loss of the plate were obtained. As examples, cases in which an undulating plate with linearly varying amplitude swam far from and close to a wall under a range of different kinematic conditions were studied. The dynamic ground effect improved the swimming performance of the plate by reducing the power input while maintaining an almost constant thrust; the degree of improvement depended on the kinematic conditions of the plate. Furthermore, the swimming performance of the plate was improved over a range of distances from the wall; this range of distances also depended on the kinematic conditions of the plate.

This paper re-examines the problem of the flow of a fluid of finite depth over two Gaussian-shaped obstructions on the stream bed. A weakly nonlinear analysis in the form of the Korteweg–de Vries equation is used to compare with the results of the fully nonlinear problem. The main focus is to find waveless subcritical solutions, and contours showing the obstruction height and separation values that result in waveless solutions are found for different Froude numbers and different obstruction widths.

The subcritical flow of a stream over a bottom obstruction or depression is considered with particular interest in obtaining solutions with no downstream waves. In the linearised problem this can always be achieved by superposition of multiple obstructions, but it is not clear whether this is possible in a full nonlinear problem. Solutions computed here indicate that there is an effective nonlinear superposition principle at work as no special shape modifications were required to obtain wave-cancelling solutions. Waveless solutions corresponding to one or more trapped waves are computed at a range of different Froude numbers and are shown to provide a rather elaborate mosaic of solution curves in parameter space when both negative and positive obstruction heights are included.

This is a review of thin-body and slender-body theories, with indications of some new applications. Topics discussed include bodies with near-constant surface pressure, subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in Stokes flow, slender footings in elastic media, and slender moonpools. Mathematical features of the thin- and slender-body approximations are also discussed, especially nonlocal convolution terms modelling three-dimensionality in the otherwise two-dimensional near field, end effects, and the role of the logarithm of the slenderness ratio. This review was presented by the first author as the IMA Lighthill Memorial Lecture at the British Applied Mathematics Colloquium (BAMC) 2004.

This work integrates the Taylor theorem and the method of fundamental solutions to develop a numerical tool for estimating the added mass coefficient tensor for a solid object of any convex shape moving in potential flow. In potential flow theory, the Taylor theorem calculates the added mass coefficient tensor for a Rankine body with algebraic manipulations of the properties of the internal singularities employed to generate the corresponding flow. To apply this theorem for objects in other shapes, the singularity strength and locations are required information which is facilitated numerically in this work by the method of fundamental solutions (MFS). The developed scheme is tested on a circle, an ellipse, a square, and a rhombus and the numerical results are in good agreement with the corresponding analytical values. A final example of a Cassini oval is also considered to show the potential applications on bio-engineering problems.