What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Analysis of ship roll gyrostabiliser control

The use of dedicated spinning wheels that generate gyroscopic forces for reducing the roll motion of ships was considered and tested over 100 years ago. These devices, known as gyrostabilisers, presented a remarkable performance, but they fell into disuse due to their relatively large size and, primarily, due to the inability of the control systems to maintain performance over an extended envelope of sea states and sailing conditions (speed and heading relative to the waves). To date, advances in materials, mechanical design, electrical drives, and computer control systems have resulted in a revitalized interest in gyro-stabilisers for ships. This paper revisits the modelling of the coupled vessel-gyrostabiliser and delves into the associated gyrostabiliser control design problem. It also describes design trade-offs and potential performance limitations. A simulation study based on a navy patrol vessel is presented.

MIMO and SISO identification of radiation force terms for models of marine structures in waves

This paper presents a discussion on the use of MIMO and SISO techniques for identification of the radiation force terms in models for surface vessels. We compare and discuss two techniques recently proposed in literature for this application: time domain identification and frequency domain identification. We compare the methods in terms of estimates model order, accuracy of the fit, use of the available information, and ease of use and implementation.

Ship Seakeeping Operability, Motion Control, and Autonomy - A Bayesian Perspective

Ship seakeeping operability refers to the quantification of motion performance in waves relative to mission requirements. This is used to make decisions about preferred vessel designs, but it can also be used as comprehensive assessment of the benefits of ship-motion-control systems. Traditionally, operability computation aggregates statistics of motion computed over over the envelope of likely environmental conditions in order to determine a coefficient in the range from 0 to 1 called operability. When used for assessment of motion-control systems, the increase of operability is taken as the key performance indicator. The operability coefficient is often given the interpretation of the percentage of time operable. This paper considers an alternative probabilistic approach to this traditional computation of operability. It characterises operability not as a number to which a frequency interpretation is attached, but as a hypothesis that a vessel will attain the desired performance in one mission considering the envelope of likely operational conditions. This enables the use of Bayesian theory to compute the probability of that this hypothesis is true conditional on data from simulations. Thus, the metric considered is the probability of operability. This formulation not only adheres to recent developments in reliability and risk analysis, but also allows incorporating into the analysis more accurate descriptions of ship-motion-control systems since the analysis is not limited to linear ship responses in the frequency domain. The paper also discusses an extension of the approach to the case of assessment of increased levels of autonomy for unmanned marine craft.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

A study of vibration and vibration control of ship structures

This paper examines the vibration characteristics and vibration control of complex ship structures. It is shown that input mobilities of a ship structure at engine supports, due to out-of-plane force or bending moment excitations, are governed by the flexural stiffness of the engine supports. The frequency averaged input mobilities of the ship structure, due to such excitations, can be represented by those of the corresponding infinite beam. The torsional moment input mobility at the engine support can be estimated from the torsional response of the engine bed section under direct excitation. It is found that the inclusion of ship hull and deck plates in the ship structure model has little effect on the frequency-averaged response of the ship structure. This study also shows that vibration propagation in complex ship structures at low frequencies can be attenuated by imposing irregularities to the ring frame locations in ships. Vibration responses of ship structures due to machinery excitations at higher frequencies can be controlled by structural modifications of the local supporting structures such as engine beds in ships.

Source location of acoustic emission waves for structural health monitoring of bridges

The process of structural health monitoring (SHM) involves monitoring a structure over a period of time using appropriate sensors, extracting damage sensitive features from the measurements made by the sensors and analysing these features to determine the current state of the structure. Various techniques are available for structural health monitoring of structures and acoustic emission (AE) is one technique that is finding an increasing use. Acoustic emission waves are the stress waves generated by the mechanical deformation of materials. AE waves produced inside a structure can be recorded by means of sensors attached on the surface. Analysis of these recorded signals can locate and assess the extent of damage. This paper describes preliminary studies on the application of AE technique for health monitoring of bridge structures. Crack initiation or structural damage will result in wave propagation in solid and this can take place in various forms. Propagation of these waves is likely to be affected by the dimensions, surface properties and shape of the specimen. This, in turn, will affect source localization. Various laboratory test results will be presented on source localization, using pencil lead break tests. The results from the tests can be expected to aid in enhancement of knowledge of acoustic emission process and development of effective bridge structure diagnostics system.

Vibration of ship structures and its control

Noise and vibration in complex ship structures are becoming a prominent issue for ship building industry and ship companies due to the constant demand of building faster ships of lighter weight, and the stringent noise and libration regulation of the industry. In order to retain the full benefit of building faster ships without compromising too much on ride comfort and safety, noise and vibration control needs to be implemented. Due to the complexity of ship structures, the coupling of different wave types and multiple wave propagation paths, active control of global hull modes is difficult to implement and very expensive. Traditional passive control such as adding damping materials is only effective in the high frequency range. However, most severe damage to ship structures is caused by large structural deformation of hull structures and high dynamic stress concentration at low frequencies. The most discomfort and fatigue of passengers and the crew onboard ships is also due to the low frequency noise and vibration. Innovative approaches are therefore, required to attenuate the noise and vibration at low frequencies. This book was developed from several specialized research topics on vibration and vibration control of ship structures, mostly from the author's own PhD work at the University of Western Australia. The book aims to provide a better understanding of vibration characteristics of ribbed plate structures, plate/plate coupled structures and the mechanism governing wave propagation and attenuation in periodic and irregular ribbed structures as well as in complex ship structures. The book is designed to be a reference book for ship builders, vibro-acoustic engineers and researchers. The author also hopes that the book can stimulate more exciting future work in this area of research. It is the author's humble desire that the book can be some use for those who purchase it. This book is divided into eight chapters. Each chapter focuses on providing solution to address a particular issue on vibration problems of ship structures. A brief summary of each chapter is given in the general introduction. All chapters are inter-dependent to each other to form an integration volume on the subject of vibration and vibration control of ship structures and alike. I am in debt to many people in completing this work. In particular, I would like to thank Professor J. Pan, Dr N.H. Farag, Dr K. Sum and many others from the University of Western Australia for useful advices and helps during my times at the University and beyond. I would also like to thank my wife, Miaoling Wang, my children, Anita, Sophia and Angela Lin, for their sacrifice and continuing supports to make this work possible. Financial supports from Australian Research Council, Australian Defense Science and Technology Organization and Strategic Marine Pty Ltd at Western Australia for this work is gratefully acknowledged.