Irrotational Fluid Research Articles

Hydrodynamic modelling of a direct drive wave energy converter

In this article we present numerical studies of waves interacting with a cylindrical point absorber that is directly driving a seabed based linear generator. For waves useful for power conversion, the wave/point absorber interaction can be modelled, using potential theory assuming an inviscid irrotational incompressible fluid. The generator is modelled as a viscous damper. This paper pays special attention to the case when the converter is in resonance with the wave. The power capture capability of the system has been studied both for a harmonic wave and for real ocean waves.

Second-order perturbations of a zero-pressure cosmological medium: Proofs of the relativistic-Newtonian correspondence

The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure, the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that, except for the gravitational wave contribution, even to the second-order perturbations, equations for the relativistic irrotational zero-pressure fluid in a flat Friedmann background coincide exactly with the previously known Newtonian equations. Thus, to the second order, we correctly identify the relativistic density and velocity perturbation variables, and we expand the range of applicability of the Newtonian medium without pressure to all cosmological scales including the superhorizon scale. In the relativistic analyses, however, we do not have a relativistic variable which corresponds to the Newtonian potential to the second order. Mixed usage of different gauge conditions is useful to make such proofs and to examine the result with perspective. We also present the gravitational wave equation to the second order. Since our correspondence includes the cosmological constant, our results are relevant to currently favored cosmology. Our result has an important practical implication that one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near horizon.

On the Free Boundary to the Incompressible Euler Equations

In this paper, we consider an inviscid, incompressible, irrotational fluid in a region of R 3 with free boundary. Motivated by [1], we find that in this particular case, we do not need the complicated energy functional in [1], instead we can use a simpler replacement and get the a priori energy estimate for a positive time, which depends only on the initial data.

Relativistic-Newtonian correspondence of the zero pressure but weakly nonlinear cosmology

It is well known that couplings occur among the scalar-, vector- and tensor-type perturbations of the Friedmann world model in the second perturbational order. Here, we prove that, except for the gravitational wave contribution, the relativistic zero-pressure irrotational fluid perturbed to second order in a flat Friedmann background coincides exactly with the Newtonian result. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to the second order, our result has an important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches and even goes beyond the horizon. That is, our discovery shows that, in the zero-pressure case, except for the gravitational wave contribution, there are no relativistic correction terms even near and beyond the horizon to the second-order perturbation.

The inertia-gravity waves caused by the impact of shoemaker-levy 9 with jupiter

After the collision of Comet Shoemaker-Levy 9 (SL9) with Jupiter, some ring structures were observed propagating outwards at a constant speed (∼450 m/s) on the Jovian surface. These are thought to be linear waves caused by the collision. A linear model of the collision is presented, in which the Jovian atmosphere is considered as an irrotational, inviscid, stratified and incompressible fluid layer moving at a speed of U = b + az. We take an initial impulsive pressure p(r; 0) as the initial condition and solve the fluid dynamics equations for inertia-gravity waves. It is found that most part of the perturbation energy is used to produce internal waves when Jovian atmosphere moves at a constant speed (U = Uo (∼170 m/s)). A relation between the impact depth H and the horizontal phase speed vp is deduced. Finally, the inertia-gravity waves are discussed for the case U = b + az and it is found that the perturbation energy is then not divided equally between kinetic energy and potential energy because of the effect of a shear.

Solitons and antisolitons on bounded surfaces

We generalize the one-dimensional KdV equation for an inviscid incompressible irrotational fluid layer with free surface, finite depth, and finite boundary conditions. We study the nonlinear dynamics of a fluid of arbitrary depth in a bounded domain. By introducing a special relation between the asymptotic limit of the potential of velocities at the bottom and the surface equation we obtain an infinite order PDE. The dispersion relation of the linearized equation is the well known capillarity-gravity dispersion relation for arbitrary depth. This generalized equation can be written as a differential-difference expression, and a class of traveling waves solutions in terms of power series expansion with coefficients satisfying a nonlinear recursion relation is obtained. In the limit of infinite long shallow water we recover the KdV equation together with its one-soliton solution. This generalized equation provides higher order (nonlinear) dispersion terms that do not cancel in the limit B 0 = 1 / 3 . Consequently this equation can be used for investigation of soliton-antisoliton transition when the depth of the layer is closed to the critical one.

Unified treatment of cosmological perturbations from superhorizon to small scales

We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for leading-order source terms of gravitational waves, while including also the first and second-order perturbative approximations. Our equations, which are derived in the Poisson gauge, provide a unified description of matter inhomogeneities in a Universe filled with a pressureless and irrotational fluid and a cosmological constant, ranging from the linear to the highly non-linear regime. The derived expressions for scalar, vector and tensor modes can have a wide range of cosmological applications, ranging from secondary CMB anisotropy and polarization effects, cosmographic relations in a inhomogeneous Universe, gravitational lensing effects and the stochastic gravitational-wave backgrounds generated by non-linear cosmic structures.

Initial value problem for second order scalar fluctuations in the Einstein static universe

We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe must be present if the second order constraint equations are to be integrable. I.e., the ``linearization stability'' constraint forces the presence of these homogeneous modes. Since these linear homogeneous scalar modes are well known to be exponentially unstable, the tactic of neglecting these modes to create a long-lived, almost Einstein universe does not work, even if all higher order $(\mathrm{L}>1)$ modes are dynamically stable.

배플을 갖는 원통형 유체저장 탱크의 연성진동해석

The coupled vibration characteristics for the fluid-structure interaction systems are investigated through the finite element method. The present paper is focused on vibration characteristics of the cylindrical fluid-storage tank with a baffle. The tank is partially filled with an inviscid and irrotational fluid having a free surface. A baffle is assumed here to have the shape of a thin annular plate and a conical shell, attached to the cylindrical tank and positioned below the fluid surface. The liquid domain is limited by a rigid flat bottom. As the effect of free surface waves is taken into account in the analysis, the bulging and sloshing modes are studied. To demonstrate the validity of present results, they are compared with the published ones. The effect of positions and inner-to-outer radius ratio of annular baffle and setting angles of conical baffle on coupled vibration characteristics is investigated.

Relaxed formulation and existence result of the degenerated elliptic small disturbance model

We consider an elliptic–parabolic PDE, governing the flow of a steady state two-dimensional irrotational compressible fluid in a channel or around a thin profile. The model is formulated in term of a noncoercive variational problem with an integral functional, in a truncated domain. We propose a relaxed formulation in the bounded variation functions space and we prove the existence and the uniqueness of the relaxed optimal solution. We consider also the asymptotic behavior of the solution when the domain grows to infinity.

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.

Numerical simulation of two-dimensional nonlinear standing acoustic waves

In this paper the behavior of strongly nonlinear waves in two-dimensional resonators filled with thermoviscous fluid is studied. For this purpose a set of differential equations, written in Lagrangian coordinates, is proposed and a time-domain numerical scheme is developed for solving them. Full nonlinear equations are derived from the conservation laws and state equation by assuming an irrotational fluid. Auxiliary conditions are written by considering a rigid-walled cavity, excitation at some points of the boundary, and rest at the outset. Finite differences are applied in the space and time domains, and lead to an implicit scheme. The numerical model solves the problem in terms of displacement vector field. The pressure field is then obtained from the displacement values. The algorithm allows us to analyze the evolution of the behavior of complex standing waves. The nonlinear characteristics of standing waves, well known in one-dimensional chambers, are now apparent in two-dimensional resonators by means of this new computational model. Some numerical experiments are carried out, a validation of the model is achieved, and results are given at a complex mode for which plane wave approximation is not appropriate. Several aspects of the nonlinear pressure field inside two-dimensional resonators are presented, such as harmonic distortion and nonlinear attenuation effects. In particular the quasi-standing character of such waves is detected and described. The effect of redistribution of rms pressure inside a two-dimensional cavity is commented.

Reduced models for fluid–structure interaction problems

AbstractSeveral so‐called reduced order formulations are reviewed for linear vibration analysis of bounded fluid–structure systems for low modal density situations. Compressibility effects in the fluid for interior structural–acoustic problems, and free surface gravity effects, for hydroelastic–sloshing interaction problems in the case of incompressible liquids, are examined. Reduced order models leading to symmetric matrix systems are then described using the static well‐posed behaviour of the irrotational fluid. In this respect, the fluid–structure boundary value local equations, expressed in terms of fluid scalar field variables for the fluid (and displacement variables for the structure) are regularized for zero‐frequency limit. Copyright 2004 John Wiley & Sons, Ltd.

Embedding commutative and noncommutative theories in the symplectic framework

This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative self-dual model. In the process of this new path of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and puts some light on the so called ''arbitrariness problem".

Hydrodynamic forces on two moving discs

We give a detailed presentation of a flexible method for constructing explicit expressions of irrotational and incompressible fluid flows around two rigid circular moving discs. We also discuss how such expressions can be used to compute the fluid-induced forces and torques on the discs in terms of Killing drives. Conformal mapping techniques are used to identify a meromorphic function on an annular region in C with a flow around two circular discs by a Mobius transformation. First order poles in the annular region correspond to vortices outside of the two discs. Inflows are incorporated by putting a second order pole at the point in the annulus that corresponds to infinity.

Stabilization of a 1-D tank containing a fluid modeled by the shallow water equations

Consider a rectangular tank containing an inviscid incompressible and irrotational fluid. The tank is subject to a one-dimensional horizontal move (the control) and the motion of the fluid is described by the shallow water equations. By means of a Lyapunov approach, control laws that stabilize the state of the fluid–tank system are derived. Two classes of control are considered: full-state feedback and output feedback where the output is given by the trajectory of the tank, the level of the fluid at the boundary of the tank and the time. Although global asymptotic stability is yet to be proved, stabilization is observed through numerical simulations.

Rotating Bose-Einstein condensate with attractive interaction in one dimension: Single-Lstates and mesoscopics

We present the results of an exact numeric simulation of N one-dimensional bosons with attractive \ensuremath{\delta}-functional interaction in a rotating ring. We prove that even at intermediate values of N, the system can be described by conventional methods of weakly interacting gas, the dimensionless parameter of weak interaction being just $1/N.$ When the strength of interaction is less than a certain threshold value, the dependence of angular momentum on the rotation frequency features plateaus characteristic of the irrotational fluid.

Coupled vibration of partially fluid-filled cylindrical shells with ring stiffeners

A theoretical method is developed to investigate the coupled vibration characteristics of the ring-stiffened cylindrical shells partially filled with an inviscid, incompressible and irrotational fluid having a free surface. As the effect of free surface waves is taken into account in the analysis, the bulging and sloshing modes are studied. The Rayleigh–Ritz method is used to derive the frequency equation of the ring-stiffened and partially fluid-filled shells based on Love's thin shell theory. The solution for the velocity potential of fluid movement is assumed as a sum of two sets of linear combinations of suitable harmonic functions that satisfy Laplace equation and the relevant boundary conditions. The effect of fluid level, stiffener's number and position on the coupled vibration characteristics is investigated. To demonstrate the validity of present theoretical method, the published results are compared for simply supported shell and the finite element analysis is performed for unstiffened/stiffened, partially fluid-filled shells with clamped–free boundary condition.

Statistical analysis of multimode weakly nonlinear Rayleigh-Taylor instability in the presence of surface tension.

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of surface tension. The dynamics of a multimode perturbation of the interface between two incompressible, inviscid, irrotational, and immiscible fluids is analyzed. The quadratic and cubic nonlinear effects are taken into account. They include the nonlinear corrections to the exponential growths of the fundamental modulations. The role of the initial modulation spectrum is discussed. A saturation criterion in terms of the product of a local rms and a particular wave number is exhibited. It gives theoretical foundations for numerical conjectures and allows one to analyze the effects of fundamental parameters of the problem such as the dimension or the Atwood number.

The fluid flow due to two submerged sinks in a two layer stratified fluid

A boundary integral technique is developed to study the free surface flow of a steady, two‐dimensional, incompressible, irrotational and inviscid fluid flow which is produced by two submerged sinks (or sources) which are of equal strength, placed along a solid horizontal boundary with a stagnation point on the free surface in a two layer stratified fluid in the presence of gravity. A special form of the Riemann‐Hilbert problem, namely the Dirichlet boundary problem, is applied in the derivation of the governing non‐linear boundary integral‐differential equations which are solved for the fluid velocity on the free surface and this involves the use of an interpolative technique and an iterative process. Results have been obtained for the free surface flow for various values of the Froude number and sink locations on the solid horizontal boundary and we have also studied the largest value of the Froude number for which no convergent solutions are possible, namely the critical Froude number. We have found that the free surface profile is dependent on two parameters, namely the Froude number on the free surface and the non‐dimensional distance between the two sinks.