Air parcels and air particles: Hamiltonian dynamics

We present a simple Hamiltonian formulation of the Euler equations for fluid flow in the Lagrangian framework. In contrast to the conventional formulation, which involves coupled partial differential equations, our "innovative'' mathematical formulation involves only ordinary differential equations coupled by integral equations. We illustrate the utility of the new formulation by applying it to a simple stability problem for the atmosphere

Friction dependence of shallow granular flows from discrete particle simulations

A shallow-layer model for granular flows is completed with a closure relation for the macroscopic bed friction or basal roughness obtained from micro-scale discrete particle simulations of steady flows. We systematically vary the bed friction by changing the contact friction coefficient between basal and flowing particles, while the base remains geometrically rough. By simulating steady uniform flow over a wide parameter range, we obtain a friction law that is a function of both flow and bed variables. Surprisingly, we find that the macroscopic bed friction is only weakly dependent on the contact friction of bed particles and predominantly determined by the properties of the flowing particles

Modelling of nonlinear wave-buoy dynamics using constrained variational methods

We consider a comprehensive mathematical and numerical strategy to couple water-wave motion with rigid ship dynamics using variational principles. We present a methodology that applies to three-dimensional potential flow water waves and ship dynamics. For simplicity, in this paper we demonstrate the method for shallow-water waves coupled to buoy motion in two dimensions, the latter being the symmetric motion of a crosssection of a ship. The novelty in the presented model is that it employs a Lagrange multiplier to impose a physical restriction on the water height under the buoy in the form of an inequality constraint. A system of evolution equations can be obtained from the model and consists of the classical shallow-water equations for shallow, incompressible and irrotational waves, and relevant equations for the dynamics of the wave-energy buoy. One of the advantages of the variational approach followed is that, when combined with symplectic integrators, it eliminates any numerical damping and preserves the discrete energy; this is confirmed in our numerical results

Discrete element study of liquid-solid slurry flows through constricted channels

Discrete element model is used to simulate the flow of liquid-granule mixtures in an inclined channel containing a linear contraction. All the relevant particle/particle and particle/fluid interactions are included in the numerical model. The presence of the contraction induces different steady morphologies of the solid phase or the mixture depending on whether closed or open channels are used. These flows behave quite differently depending on the upstream Froude number and the contraction size ratio. The model is first validated by comparing with the existing results for dry granular (glass particles) chute flows (Vreman et al., 2007). Then simulations of a chute of glass particles in water flowing in a closed channel are compared to the dry granular case. With the same solid flux at the inlet, the hydrodynamic forces in the liquid-solid mixture induce higher particle solid volume fractions in the part of the flow containing the solid phase. The streamwise particle velocity (resp. depth of the solid phase) has the same evolution along the channel with smaller (larger) values than in the dry granular flow case

A Hamiltonian Boussinesq model with horizontally sheared currents

We are interested in the numerical modeling of wave-current interactions around beaches’ surf zones. Any model to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have formulated the Hamiltonian dynamics of a new water wave model. This model incorporates both the shallow water model and the potential flow model as limiting systems. The variational model derived by Cotter and Bokhove (2010) is such a model, but the variables used have been difficult to work with. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential field plus horizontal velocity components, such that the vertical component of vorticity is nonzero. Our aims are to augment the new model locally with bores and to derive a numerical finite element discretization of the new model including the capturing of bores. As a preliminary step, the variational finite element discretization of Miles’ variational principle coupled to an elliptic mesh generator is shown

Fluid Fascinations

De Art & Science show “Fluid Fascinations��? omvat een presentatie over de wetenschappelijke context, inclusief een live experiment (ontworpen samen met kunstenaar/designer Wout Zweers); en, gemengde media en olieverfschilderijen, en digitale fotowerken van kunstenares Valerie Zwart. De show is gebaseerd op de collectie van dia’s en foto’s van Professor Howell Peregrine (1938-2007). Howell was een Brits toegepast wiskundige inzonderheid voor stromingsleer en watergolven, een redacteur van het fameuze tijdschrift Journal of Fluid Mechanics gedurende 28 jaar, en een begaafd amateurfotograaf. Het boeiende van Peregrine’s dia’s en foto’s zit hem in hun iconische wetenschappelijke waarde. Hij gebruikte zijn eigen beelden dikwijls om ideeën over brekende golven en uiteenspattend water te introduceren en uit te werken in zijn onderzoeksartikelen. Wij hebben ons er door laten inspireren. De introductie (pdf-bestand) in de eprints is tweetalig. Beelden van de kunstwerken zijn te vinden op: http://www.zw-artprojects.nl/fluidgallery.html The Art & Science show “Fluid Fascinations��? consists of a presentation on the scientific context, including a live experiment (made together with artist/designer Wout Zweers); and, mixed media and oil paintings, and digital photoworks of artist Valerie Zwart. The show draws from the photographic images of the late Professor Howell Peregrine (1938-2007). Howell was a British applied mathematician on fluid mechanics and water waves, an editor of the famous Journal of Fluid Mechanics for 28 years, and a gifted amateur photographer. The quality of Peregrine’s slides and photographs lies in their iconic scientific value. He was known for using his images to convey and introduce key ideas on breaking waves and splashing fluids in his research articles. We are inspired by his work. The introduction (pdf-file) in these eprints is bilingual. Images of the art works are found at: http://www.zw-artprojects.nl/fluidgallery.htm

Closure Relations for Shallow Granular Flows from Particle Simulations

The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed where the flow is either highly energetic and strongly layered in depth for small inclinations, or non-uniform and oscillating for larger inclinations. For steady uniform flows, depth profiles of density, velocity and stress have been obtained using an improved coarse-graining method, which allows accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We thus obtain relations for the effective basal friction, shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness. For collisional flows, the functional dependencies are well determined and have been obtained.Comment: Will be presented at PARTICLES 2011 - CIMN

Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves

A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for the linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions, which poses numerical challenges. These challenges concern: (i) discretisation of a divergence-free velocity field; (ii) discretisation of geostrophic boundary conditions combined with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved, for example: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible flows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal flow at solid walls in a weak form and geostrophic tangential flow along the wall; and, (iii) by applying a symplectic time discretisation. We compared our simulations with exact solutions of three-dimensional incompressible flows, in (non) rotating periodic and partly periodic cuboids (Poincaré waves). Additional verifications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls. Finally, a simulation in a tilted rotating tank, yielding more complicated wave dynamics, demonstrates the potential of our new method

A novel wave-energy device with enhanced wave amplification and induction actuator

© 2020, European Wave and Tidal Energy Conference. All rights reserved. A novel wave-energy device is presented. Both a preliminary proof-of-principle of a working, scaled laboratory version of the energy device is shown as well as the derivation and analysis of a comprehensive mathematical and numerical model of the new device. The wave-energy device includes a convergence in which the waves are amplified, a constrained wave buoy with a (curved) mast and direct energy conversion of the buoy motion into electrical power via an electro-magnetic generator. The device is designed for use in breakwaters and it is possible to be taken out of action during severe weather. The new design is a deconstruction of elements of existing waveenergy devices, such as the TapChan, IP wave-buoy and the Berkeley Wedge, put together in a different manner to enhance energy conversion and, hence, efficiency. The idea of wave-focusing in a contraction emerged from our work on creating and simulating rogue waves in crossing seas, including a “bore-soliton-splash”. Such crossing seas have been recreated and modelled in the laboratory and in simulations by using a geometric channel convergence. The mathematical and numerical modelling is also novel. One monolithic variational principle governs the dynamics including the combined (potential-flow) hydrodynamics, the buoy motion and the power generation, to which the dissipative elements such as the electrical resistance of the circuits, coils and loads have been added a posteriori. The numerical model is a direct and consistent discretisation of this comprehensive variational principle. Preliminary numerical calculations are shown for the case of linearised dynamics; optimisation of efficiency is a target of future work