The majority of existing single-unit devices for extracting power from sea-waves relies on resona... more The majority of existing single-unit devices for extracting power from sea-waves relies on resonance at the peak frequency of the incident wave spectrum. Such designs usually call for structural dimensions not too small compared to a typical wavelength and yield high efficiency only within a limited frequency band. A recent innovation in Norway departs from this norm by gathering many small buoys in a compact array. Each buoy is too small to be resonated in typical sea conditions. In this article a theoretical study is performed to evaluate this new design. Within the framework of linearisation, we consider a periodic array of small buoys with similarly small separation compared to the typical wave length. The method of homogenization (multiple scales) is used to derive the equations governing the macro-scale behaviour of the entire array. These equations are then applied to energy extraction by an infinite strip of buoys, and by a circular array. In the latter case advantages are found when compared to a single buoy of equal volume.
We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wi... more We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wide channel. Focusing attention on slow flows appropriate for gentle slopes, low discharge rates or the final stage of deposition, we ignore inertia and apply the long-wave approximation. For steady flows, the velocity distribution, total discharge, and section-averaged flux are obtained analytically in terms of the fluid property and the geometry of the channel cross-section. Nonlinear stationary waves, which connect a uniform depth upstream to another uniform depth downstream, are then investigated, for both wet and dry beds. A numerical scheme is applied to calculate the transient flow evolution. The final development of the stationary wave due to steady discharge upstream is obtained numerically and the relation between the tongue-like shape of the wave front and the fluid property is discussed. The phase speed of the stationary wave is also derived analytically. Finally, the transient spreading of a finite fluid mass released from a reservoir after a dam break is simulated numerically. The transient development of the front and the final extent of deposition are examined.
The fundamental solution of the gravity waves due to a two-dimensional point singularity submerge... more The fundamental solution of the gravity waves due to a two-dimensional point singularity submerged in a steady free-surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Love's equations. The effect of density stratification po(y) and the gravity effect are characterized by two flow parameters u = -(dpo/dy)/po and A = gL/U', where A-! may be regarded as the internal Froude number if L assumes a characteristic value of u-1 • Two special cases of u and A are treated in this paper. In the first case of constant u (and arbitrary A) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as A> or < Yz, in analogy to the corresponding states of channel flows. In addition to a potential surface wave which exists only for A> Yz, there arises an internal wave which is attenuated at large distances for AS,. .}4 and decays exponentially for A< )4:. In the second example an asymptotic theory for large A is developed while u(y) may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium.
Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This ph... more Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake tsunamis in the open ocean in that (i) the affected areas are usually within the near-field of the source, (ii) the highest runup occurs within the time period of the geophysical event, and (iii) the enclosed geometry of a lake does not let the tsunami energy escape. To address the problem of transient landslide tsunami runup and to predict the resulting inundation, we utilize a nonlinear model equation in the Lagrangian frame of reference. The motivation for using such a scheme lies in the fact that the runup on an inclined boundary is directly and readily computed in the Lagrangian framework without the need to resort to approximations. In this work, we investigate the inundation patterns due to landslide tsunamis in a lake. We show by numerical computations that Airy's approximation of an irrotational theory using Lagrangian coordinates can legitimately predict runup of large amplitude. We also demonstrate that in a lake of finite size the highest runup may be magnified by constructive interference between edge-waves that are trapped along the shore and multiple reflections of outgoing waves from opposite shores, and may occur somewhat later after the first inundation.
We examine the effects of viscous damping in the boundary layers on the Bragg resonance of surfac... more We examine the effects of viscous damping in the boundary layers on the Bragg resonance of surface water waves by a two-dimensional array of vertical cylinders. For cylinders of small radius relative to the wavelength, we first derive an effective boundary condition for the radial derivative of the velocity potential to account for the viscous forces. Coupled-mode equations are then rederived by an asymptotic method for the envelopes of multiply resonated waves inside the array. Effects of viscosity on band gaps and scattering coefficients due to a plane incident wave are examined analytically for an infinitely long array of finite width surrounded by open water. For normal incidence the envelope physics is one dimensional. The transmission and reflection properties are studied first. Oblique incidence can in principle excite several wave trains in different directions. Explicit solutions are given and discussed when there are only two wave trains inside the array. Results are compared with recent theories where viscosity is not taken into account. The asymptotic theory can be modified for two-dimensional sound scattering by a cylinder array.
Massachusetts Institute of Technology eBooks, 1976
TABLE OF CONTENTS 1. 85 3.4 ~Elli tic Island with a Circular Base ~Pa e 4. ERROR ESTIMATES AND CO... more TABLE OF CONTENTS 1. 85 3.4 ~Elli tic Island with a Circular Base ~Pa e 4. ERROR ESTIMATES AND CONVERGENCE TESTS 4.1 Th 4.2 ~Conver ence of the. Finite Element A roximation 4.3 Conv~er ence of Series Terse in tahe Ansi t~ic Pe resentstion 5. COMP1.TATXONAL ASPECTS AN1! THE PROGRAM USAGE 5.1 Fr~pram ~lm lementati~on ~Esca and Time Re nirements 5.2 ~The H hrid Finite E1ement P~ro ram 5.2.1 ~Pro ra~mLo ic 52.30t tF 129
We analyse theoretically the interaction between water waves and a thin layer of fluid mud on a s... more We analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.
We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to c... more We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out.
The publisher does not give any warranty express or implied or make any representation that the c... more The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
We investigate the slow spreading of fluid mud over a gently sloped conical surface which may sim... more We investigate the slow spreading of fluid mud over a gently sloped conical surface which may simulate a shallow basin or a hill. The mud is assumed to behave as a Bingham plastic possessing a finite yield stress and the lubrication approximation is used. Because of the finite yield stress, a variety of non-trivial equilibrium profiles can exist, corresponding to the state of deposit at the end of upward or downward motion. Analytical solutions are derived for axially symmetric deposits. It is shown that the front of the final profile in axisymmetric spreading is of a common form in dimensionless variables, independent of the total mud volume. Transient evolutions are then studied numerically by employing a finite-volume scheme for both axially symmetric and asymmetric spreading from a localized source. The characteristic features of the mud pile at different stages of spreading are examined. The final shape in asymmetric spreading is strongly affected by the total volume released and by the rate of discharge.
All content in PEARL is protected by copyright law. Author manuscripts are made available in acco... more All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. Under consideration for publication in J. Fluid Mech.
An instability theory is presented for the initiation of longitudinal vortices due to waves inter... more An instability theory is presented for the initiation of longitudinal vortices due to waves interacting with a turbulent current in an open channel of finite depth. With a simple model of eddy viscosity the dimensionless shearing rate of the basic current is much weaker than the dimensionless velocity almost everywhere except near the bed. We shall show that in addition to the internal vortex force, a mean shear stress exists on the mean sea level, owing to nonlinear wave-current interactions, despite the absence of wind. This stress adds vertical vorticity to the interior and augments the vortex force mechanism of instability significantly. Effects of current strength and wave conditions on the unstable growth are studied by numerical examples.
Medical & Biological Engineering & Computing, Jan 8, 2018
We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-st... more We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-structure interactions. The phenomenon has its origin in an old-fashioned fire-fighting equipment where an air chamber serves to transform the intermittent influx from a pump to a more steady stream out of the hose. A similar mechanism exists in the cardiovascular system where blood injected intermittantly from the heart becomes rather smooth after passing through an elastic aorta. In existing haeodynamics literature this mechanism is explained on the basis of electric circuit analogy with empirical impedances. We present a mechanistic theory based on the principles of fluid/structure interactions. Using a simple one-dimensional model, wave motion in the elastic aorta is coupled to the viscous flow in the rigid peripheral artery. Explicit formulas are derived that exhibit the role of material properties such as the blood density, viscosity, wall elasticity, radii and lengths of the vessels. The current two-element model in haemodynamics is shown to be the limit of short aorta and low injection frequency and the impedance coefficients are derived theoretically. Numerical results for different aorta lengths and radii are discussed to demonstrate their effects on the time variations of blood pressure, wall shear stress and discharge.
The available experimental results have shown that in time-periodic motion the rheology of fluid ... more The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.
In this thesis investigations are made on the theory of a train of slowly modulated gravity waves... more In this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length. The solution of the wave train is expressed in expansions of the WKB type with a small parameter which is proportional to the wave steepness and the rate of modulation. A systematic perturbation scheme that may be carried out for all orders is presented. It is found that new terms directly representing modulation rate must be included to extend the scope of the Whitham's theory based on an averaged variational principle. Several specific examples are discussed and the following main conclusions are reached: 1. The Stokes waves of constant amplitude are unstable for all depths under three dimensional disturbances. 2. For quasi-steady waves normally incident on a mild beach, the local rate of depth variation is found to affect the wave phase which in turn gives additional dispersion effect as compared to Stokes waves of constant amplitude. 3. In deep water, there exist solutions of permanent wave envelopes which represent exact balance between amplitude dispersion and frequency dispersion. 4. Numerical computation on the transient development of the wave envelopes reveals that any wave group deviated from permanent form will eventually disintegrate into a sequence of peaks separated by nodal points (where amplitude is zero) and locally the wave group tends to approach the dynamically stable permanent form. It is believed that basic studies of this kind may ultimately be of importance to ocean engineering and oceanography as they permit a closer look at the significance of the classical Stokes waves which have led to an oversimplified picture of reality.
The linearized theory of water waves is reviewed in the context of Jave-energy absorbers . A glob... more The linearized theory of water waves is reviewed in the context of Jave-energy absorbers . A global analysis is outlined , leading to relatively simple expressions for the maximum energy absorption . Calculations are presented for the performance of a Salter cam in two dimensions , and of a Cockerell raft in both two and three dimensions. Similar rates of optimum energy absorption are anticipated for other devices including the ~aimei sh ip and French air bag.
Bulletin of the American Physical Society, Nov 24, 2014
settlements and infrastructures are exposed and vulnerable to long waves because such waves can c... more settlements and infrastructures are exposed and vulnerable to long waves because such waves can climb up sloping beaches without breaking. Thus accurate long-wave runup predictions are of significant importance for effective mitigation and evacuation. Although numerical models are now routinely used for long-wave propagation, calculating the runup remains an arduous task. Operational and research models usually rely on the Eulerian description of the fluid. Yet, runup processes at sloping shores can involve large horizontal stretches of the fluid domain, thereby requiring a varying number of computational nodes based on ad-hoc criteria. Here we argue that a convenient alternative is the less used Lagrangian coordinates system in which the fluid flow is described by following the trajectory of each fluid particle as an unknown function of the initial position. An immediate advantage of the Lagrangian formulation is that the free-surface and the moving shoreline become explicitly part of the solution and defined by their initial positions. As a case study we consider 3D landslide tsunamis in lakes, and present numerical results that highlight the significance of nonlinearity and wave superposition.
The majority of existing single-unit devices for extracting power from sea-waves relies on resona... more The majority of existing single-unit devices for extracting power from sea-waves relies on resonance at the peak frequency of the incident wave spectrum. Such designs usually call for structural dimensions not too small compared to a typical wavelength and yield high efficiency only within a limited frequency band. A recent innovation in Norway departs from this norm by gathering many small buoys in a compact array. Each buoy is too small to be resonated in typical sea conditions. In this article a theoretical study is performed to evaluate this new design. Within the framework of linearisation, we consider a periodic array of small buoys with similarly small separation compared to the typical wave length. The method of homogenization (multiple scales) is used to derive the equations governing the macro-scale behaviour of the entire array. These equations are then applied to energy extraction by an infinite strip of buoys, and by a circular array. In the latter case advantages are found when compared to a single buoy of equal volume.
We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wi... more We present a theory for the three-dimensional flow of a Bingham-plastic fluid in a shallow and wide channel. Focusing attention on slow flows appropriate for gentle slopes, low discharge rates or the final stage of deposition, we ignore inertia and apply the long-wave approximation. For steady flows, the velocity distribution, total discharge, and section-averaged flux are obtained analytically in terms of the fluid property and the geometry of the channel cross-section. Nonlinear stationary waves, which connect a uniform depth upstream to another uniform depth downstream, are then investigated, for both wet and dry beds. A numerical scheme is applied to calculate the transient flow evolution. The final development of the stationary wave due to steady discharge upstream is obtained numerically and the relation between the tongue-like shape of the wave front and the fluid property is discussed. The phase speed of the stationary wave is also derived analytically. Finally, the transient spreading of a finite fluid mass released from a reservoir after a dam break is simulated numerically. The transient development of the front and the final extent of deposition are examined.
The fundamental solution of the gravity waves due to a two-dimensional point singularity submerge... more The fundamental solution of the gravity waves due to a two-dimensional point singularity submerged in a steady free-surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Love's equations. The effect of density stratification po(y) and the gravity effect are characterized by two flow parameters u = -(dpo/dy)/po and A = gL/U', where A-! may be regarded as the internal Froude number if L assumes a characteristic value of u-1 • Two special cases of u and A are treated in this paper. In the first case of constant u (and arbitrary A) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as A> or < Yz, in analogy to the corresponding states of channel flows. In addition to a potential surface wave which exists only for A> Yz, there arises an internal wave which is attenuated at large distances for AS,. .}4 and decays exponentially for A< )4:. In the second example an asymptotic theory for large A is developed while u(y) may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium.
Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This ph... more Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake tsunamis in the open ocean in that (i) the affected areas are usually within the near-field of the source, (ii) the highest runup occurs within the time period of the geophysical event, and (iii) the enclosed geometry of a lake does not let the tsunami energy escape. To address the problem of transient landslide tsunami runup and to predict the resulting inundation, we utilize a nonlinear model equation in the Lagrangian frame of reference. The motivation for using such a scheme lies in the fact that the runup on an inclined boundary is directly and readily computed in the Lagrangian framework without the need to resort to approximations. In this work, we investigate the inundation patterns due to landslide tsunamis in a lake. We show by numerical computations that Airy's approximation of an irrotational theory using Lagrangian coordinates can legitimately predict runup of large amplitude. We also demonstrate that in a lake of finite size the highest runup may be magnified by constructive interference between edge-waves that are trapped along the shore and multiple reflections of outgoing waves from opposite shores, and may occur somewhat later after the first inundation.
We examine the effects of viscous damping in the boundary layers on the Bragg resonance of surfac... more We examine the effects of viscous damping in the boundary layers on the Bragg resonance of surface water waves by a two-dimensional array of vertical cylinders. For cylinders of small radius relative to the wavelength, we first derive an effective boundary condition for the radial derivative of the velocity potential to account for the viscous forces. Coupled-mode equations are then rederived by an asymptotic method for the envelopes of multiply resonated waves inside the array. Effects of viscosity on band gaps and scattering coefficients due to a plane incident wave are examined analytically for an infinitely long array of finite width surrounded by open water. For normal incidence the envelope physics is one dimensional. The transmission and reflection properties are studied first. Oblique incidence can in principle excite several wave trains in different directions. Explicit solutions are given and discussed when there are only two wave trains inside the array. Results are compared with recent theories where viscosity is not taken into account. The asymptotic theory can be modified for two-dimensional sound scattering by a cylinder array.
Massachusetts Institute of Technology eBooks, 1976
TABLE OF CONTENTS 1. 85 3.4 ~Elli tic Island with a Circular Base ~Pa e 4. ERROR ESTIMATES AND CO... more TABLE OF CONTENTS 1. 85 3.4 ~Elli tic Island with a Circular Base ~Pa e 4. ERROR ESTIMATES AND CONVERGENCE TESTS 4.1 Th 4.2 ~Conver ence of the. Finite Element A roximation 4.3 Conv~er ence of Series Terse in tahe Ansi t~ic Pe resentstion 5. COMP1.TATXONAL ASPECTS AN1! THE PROGRAM USAGE 5.1 Fr~pram ~lm lementati~on ~Esca and Time Re nirements 5.2 ~The H hrid Finite E1ement P~ro ram 5.2.1 ~Pro ra~mLo ic 52.30t tF 129
We analyse theoretically the interaction between water waves and a thin layer of fluid mud on a s... more We analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.
We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to c... more We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out.
The publisher does not give any warranty express or implied or make any representation that the c... more The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
We investigate the slow spreading of fluid mud over a gently sloped conical surface which may sim... more We investigate the slow spreading of fluid mud over a gently sloped conical surface which may simulate a shallow basin or a hill. The mud is assumed to behave as a Bingham plastic possessing a finite yield stress and the lubrication approximation is used. Because of the finite yield stress, a variety of non-trivial equilibrium profiles can exist, corresponding to the state of deposit at the end of upward or downward motion. Analytical solutions are derived for axially symmetric deposits. It is shown that the front of the final profile in axisymmetric spreading is of a common form in dimensionless variables, independent of the total mud volume. Transient evolutions are then studied numerically by employing a finite-volume scheme for both axially symmetric and asymmetric spreading from a localized source. The characteristic features of the mud pile at different stages of spreading are examined. The final shape in asymmetric spreading is strongly affected by the total volume released and by the rate of discharge.
All content in PEARL is protected by copyright law. Author manuscripts are made available in acco... more All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. Under consideration for publication in J. Fluid Mech.
An instability theory is presented for the initiation of longitudinal vortices due to waves inter... more An instability theory is presented for the initiation of longitudinal vortices due to waves interacting with a turbulent current in an open channel of finite depth. With a simple model of eddy viscosity the dimensionless shearing rate of the basic current is much weaker than the dimensionless velocity almost everywhere except near the bed. We shall show that in addition to the internal vortex force, a mean shear stress exists on the mean sea level, owing to nonlinear wave-current interactions, despite the absence of wind. This stress adds vertical vorticity to the interior and augments the vortex force mechanism of instability significantly. Effects of current strength and wave conditions on the unstable growth are studied by numerical examples.
Medical & Biological Engineering & Computing, Jan 8, 2018
We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-st... more We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-structure interactions. The phenomenon has its origin in an old-fashioned fire-fighting equipment where an air chamber serves to transform the intermittent influx from a pump to a more steady stream out of the hose. A similar mechanism exists in the cardiovascular system where blood injected intermittantly from the heart becomes rather smooth after passing through an elastic aorta. In existing haeodynamics literature this mechanism is explained on the basis of electric circuit analogy with empirical impedances. We present a mechanistic theory based on the principles of fluid/structure interactions. Using a simple one-dimensional model, wave motion in the elastic aorta is coupled to the viscous flow in the rigid peripheral artery. Explicit formulas are derived that exhibit the role of material properties such as the blood density, viscosity, wall elasticity, radii and lengths of the vessels. The current two-element model in haemodynamics is shown to be the limit of short aorta and low injection frequency and the impedance coefficients are derived theoretically. Numerical results for different aorta lengths and radii are discussed to demonstrate their effects on the time variations of blood pressure, wall shear stress and discharge.
The available experimental results have shown that in time-periodic motion the rheology of fluid ... more The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.
In this thesis investigations are made on the theory of a train of slowly modulated gravity waves... more In this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length. The solution of the wave train is expressed in expansions of the WKB type with a small parameter which is proportional to the wave steepness and the rate of modulation. A systematic perturbation scheme that may be carried out for all orders is presented. It is found that new terms directly representing modulation rate must be included to extend the scope of the Whitham's theory based on an averaged variational principle. Several specific examples are discussed and the following main conclusions are reached: 1. The Stokes waves of constant amplitude are unstable for all depths under three dimensional disturbances. 2. For quasi-steady waves normally incident on a mild beach, the local rate of depth variation is found to affect the wave phase which in turn gives additional dispersion effect as compared to Stokes waves of constant amplitude. 3. In deep water, there exist solutions of permanent wave envelopes which represent exact balance between amplitude dispersion and frequency dispersion. 4. Numerical computation on the transient development of the wave envelopes reveals that any wave group deviated from permanent form will eventually disintegrate into a sequence of peaks separated by nodal points (where amplitude is zero) and locally the wave group tends to approach the dynamically stable permanent form. It is believed that basic studies of this kind may ultimately be of importance to ocean engineering and oceanography as they permit a closer look at the significance of the classical Stokes waves which have led to an oversimplified picture of reality.
The linearized theory of water waves is reviewed in the context of Jave-energy absorbers . A glob... more The linearized theory of water waves is reviewed in the context of Jave-energy absorbers . A global analysis is outlined , leading to relatively simple expressions for the maximum energy absorption . Calculations are presented for the performance of a Salter cam in two dimensions , and of a Cockerell raft in both two and three dimensions. Similar rates of optimum energy absorption are anticipated for other devices including the ~aimei sh ip and French air bag.
Bulletin of the American Physical Society, Nov 24, 2014
settlements and infrastructures are exposed and vulnerable to long waves because such waves can c... more settlements and infrastructures are exposed and vulnerable to long waves because such waves can climb up sloping beaches without breaking. Thus accurate long-wave runup predictions are of significant importance for effective mitigation and evacuation. Although numerical models are now routinely used for long-wave propagation, calculating the runup remains an arduous task. Operational and research models usually rely on the Eulerian description of the fluid. Yet, runup processes at sloping shores can involve large horizontal stretches of the fluid domain, thereby requiring a varying number of computational nodes based on ad-hoc criteria. Here we argue that a convenient alternative is the less used Lagrangian coordinates system in which the fluid flow is described by following the trajectory of each fluid particle as an unknown function of the initial position. An immediate advantage of the Lagrangian formulation is that the free-surface and the moving shoreline become explicitly part of the solution and defined by their initial positions. As a case study we consider 3D landslide tsunamis in lakes, and present numerical results that highlight the significance of nonlinearity and wave superposition.
Uploads
Papers by Chiang Mei