Showing papers on "Bernoulli's principle published in 2003"

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

Abstract: This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations. Copyright © 2003 John Wiley & Sons, Ltd.

Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

Abstract: We are concerned with the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as the following second-order nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential φ : Ω ⊂ R → R: (1.1) div (ρ(|Dφ|)Dφ) = 0, where the density function ρ(q) is

A mixed finite element method for beam and frame problems

Abstract: In this work we consider solutions for the Euler- Bernoulli and Timoshenko theories of beams in which material behavior may be elastic or inelastic. The formu- lation relies on the integration of the local constitutive equation over the beam cross section to develop the relations for beam resultants. For this case we include axial, bending and shear effects. This permits consider- ation in a direct manner of elastic and inelastic behavior with or without shear deformation. A finite element solution method is presented from a three-field variational form based on an extension of the Hu-Washizu principle to permit inelastic material be- havior. The approximation for beams uses equilibrium satisfying axial force and bending moments in each ele- ment combined with discontinuous strain approximations. Shear forces are computed as derivative of bending mo- ment and, thus, also satisfy equilibrium. For quasi-static applications no interpolation is needed for the displace- ment fields, these are merely expressed in terms of nodal values. The development results in a straight forward, variationally consistent formulation which shares all the properties of so-called flexibility methods. Moreover, the approach leads to a shear deformable formulation which is free of locking effects - identical to the behavior of flexibility based elements. The advantages of the approach are illustrated with a few numerical examples.

Capillary pinch-off in inviscid fluids

Abstract: The axisymmetric pinch-off of an inviscid drop of density ρ1 immersed in an ambient inviscid fluid of density ρ2 is examined over a range of the density ratio D=ρ2/ρ1. For moderate values of D, time-dependent simulations based on a boundary-integral representation show that inviscid pinch-off is asymptotically self-similar with both radial and axial length scales decreasing like τ2/3 and velocities increasing like τ−1/3, where τ is the time to pinch-off. The similarity form is independent of initial conditions for a given value of D. The similarity equations are solved directly using a modified Newton’s method and continuation on D to obtain a branch of similarity solutions for 0⩽D⩽11.8. All solutions have a double-cone interfacial shape with one of the cones folding back over the other in such a way that its internal angle is greater than 90°. Bernoulli suction due to a rapid internal jet from the narrow cone into the folded-back cone plays a significant role near pinching. The similarity solutions are l...

Influence of collision on the flow through in-vitro rigid models of the vocal folds.

Abstract: Measurements of pressure in oscillating rigid replicas of vocal folds are presented. The pressure upstream of the replica is used as input to various theoretical approximations to predict the pressure within the glottis. As the vocal folds collide the classical quasisteady boundary layer theory fails. It appears however that for physiologically reasonable shapes of the replicas, viscous effects are more important than the influence of the flow unsteadiness due to the wall movement. A simple model based on a quasisteady Bernoulli equation corrected for viscous effect, combined with a simple boundary layer separation model does globally predict the observed pressure behavior.

Steady finite-Reynolds-number flows in three-dimensional collapsible tubes

Abstract: A fully coupled finite-element method is used to investigate the steady flow of a viscous fluid through a thin-walled elastic tube mounted between two rigid tubes. The steady three-dimensional Navier–Stokes equations are solved simultaneously with the equations of geometrically nonlinear Kirchhoff–Love shell theory. If the transmural (internal minus external) pressure acting on the tube is sufficiently negative then the tube buckles non-axisymmetrically and the subsequent large deformations lead to a strong interaction between the fluid and solid mechanics. The main effect of fluid inertia on the macroscopic behaviour of the system is due to the Bernoulli effect, which induces an additional local pressure drop when the tube buckles and its cross-sectional area is reduced. Thus, the tube collapses more strongly than it would in the absence of fluid inertia. Typical tube shapes and flow fields are presented. In strongly collapsed tubes, at finite values of the Reynolds number, two ’jets‘ develop downstream of the region of strongest collapse and persist for considerable axial distances. For sufficiently high values of the Reynolds number, these jets impact upon the sidewalls and spread azimuthally. The consequent azimuthal transport of momentum dramatically changes the axial velocity profiles, which become approximately $\uTheta$-shaped when the flow enters the rigid downstream pipe. Further convection of momentum causes the development of a ring-shaped velocity profile before the ultimate return to a parabolic profile far downstream.

Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type

Abstract: This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers.

On a Nonsymmetric Version of the Khinchine-Kahane Inequality

Abstract: We prove a new version of the Khinchine—Kahane inequality in which Bernoulli random variables no longer need to be symmetric. The constant in the inequality is optimal up to some universal factor. The proof uses hypercontractive methods and the optimal hypercontractivity constant for a mean-zero Bernoulli random variable is found. A simple observation generalizing Pisier’s Rademacher projection norm estimate is added.

Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules

Abstract: In this paper we study the role of uniform Bernoulli measure in the dynamics of cellular automata of algebraic origin. First we show a representation result for classes of permutative cellular automata: those with associative type local rule are the product of a group cellular automaton with a translation map, and if they satisfy a scaling condition, they are the product of an affine cellular automaton (the alphabet is an Abelian group) with a translation map. For cellular automata of this type with an Abelian factor group, and starting from a translation invariant probability measure with complete connections and summable decay, it is shown that the Cesaro mean of the iteration of this measure by the cellular automaton converges to the product of the uniform Bernoulli measure with a shift invariant measure. Finally, the following characterization is shown for affine cellular automaton whose alphabet is a group of prime order: the uniform Bernoulli measure is the unique invariant probability measure which has positive entropy for the automaton, and is either ergodic for the shift or ergodic for the $\mathbb Z^2$-action induced by the shift and the automaton, together with a condition on the rational eigenvalues of the automaton.

The Medium-Frequency Range in Computational Acoustics: Practical and Numerical Aspects

Abstract: The upper frequency limit of vibroacoustic calculations with finite element methods is usually concluded from resolution rules for the minimal wavelength encountered in the problem. Here, we derive general resolution rules that account for the pollution effect in finite element solutions of time-harmonic equations. These rules are given for the Helmholtz equation and the Bernoulli beam equation. The latter are based on an analysis of numerical dispersion for finite difference solutions. The theoretical results are given in the broader context of industrial vibroacoustic computations in the medium-frequency range. The governing equations of deterministic vibroacoustic computations and statistical energy analysis are reviewed with the goal to indicate, respectively, upper and lower frequency bounds for the applicability of either model. From the discussion of priorities in industrial application, open questions for theoretical investigations are deduced.

Sir epidemics on a Bernoulli random graph

Abstract: We consider a generalized stochastic epidemic on a Bernoulli random graph. By constructing the epidemic and graph in unison, the epidemic is shown to be a randomized Reed-Frost epidemic. Hence, the exact final-size distribution and extensive asymptotic results can be derived.

Modeling vocal fold motion with a hydrodynamic semicontinuum model

Abstract: Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. The traditional modeling approach makes use of quasisteady flow approximation or Bernoulli’s law which ignores air compressibility, and is known to be invalid during VF opening. A hydrodynamic semicontinuum system for VF motion is presented. The airflow is modeled by a modified quasi-one-dimensional Euler system with coupling to VF velocity. The VF is modeled by a lumped two mass system with a built-in geometric condition on flow separation. The modified Euler system contains the Bernoulli’s law as a special case, and is derivable from the two-dimensional compressible Navier–Stokes equations in the inviscid limit. The computational domain contains also solid walls next to VFs (flexible walls). It is shown numerically that several salient features of VFs are captured, especially transients such as the double peaks of the driving subglottal pressures at the opening and the closing stages of VF motion consistent with fully resolved two-dimensional direct simulations, and experimental data. The system is much simpler to compute than a VF model based on two-dimensional Navier–Stokes system.

Vibration of beams with general boundary conditions due to a moving random load

Abstract: The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail.

Ergodic-theoretic properties of certain Bernoulli convolutions

Abstract: In [20] the author and A. Vershik have shown that for β=1/2(1 + √5) and the alphabet {0,1} the infinite Bernoulli convolution (= the Erdős measure) has a property similar to the Lebesgue measure. Namely, it is quasi-invariant of type II1 under the β-shift, and the natural extension of the β-shift provided with the measure equivalent to the Erdős measure, is Bernoulli. In this note we extend this result to all Pisot parameters β (modulo some general arithmetic conjecture) and an arbitrary “sufficient” alphabet.

Calculation of the Pitot tube correction factor for Newtonian and non-Newtonian fluids.

Abstract: This paper presents the numerical investigation performed to calculate the correction factor for Pitot tubes. The purely viscous non-Newtonian fluids with the power-law model constitutive equation were considered. It was shown that the power-law index, the Reynolds number, and the distance between the impact and static tubes have a major influence on the Pitot tube correction factor. The problem was solved for a wide range of these parameters. It was shown that employing Bernoulli's equation could lead to large errors, which depend on the magnitude of the kinetic energy and energy friction loss terms. A neural network model was used to correlate the correction factor of a Pitot tube as a function of these three parameters. This correlation is valid for most Newtonian, pseudoplastic, and dilatant fluids at low Reynolds number.

The scenery factor of the [T,T^-^1] transformation is not loosely Bernoulli

Abstract: Kalikow (1982) proved that the [T,T -1 ] transformation is not isomorphic to a Bernoulli shift. We show that the scenery factor of the [T, T -1 ] transformation is not isomorphic to a Bernoulli shift. Moreover, we show that it is not Kakutani equivalent to a Bernoulli shift.

Illustrations of the Dynamical Theory of Gases

Abstract: In view of the current interest in the theory of gases proposed by Bernoulli (Selection 3), Joule, Kronig, Clausius (Selections 8 and 9) and others, a mathematical investigation of the laws of motion of a large number of small, hard, and perfectly elastic spheres acting on one another only during impact seems desirable.

Microseism and infrasound generation by cyclones.

Abstract: A two-dimensional cylindrical shear-flow wave theory for the generation of microseisms and infrasound by hurricanes and cyclones is developed as a linearized theory paralleling the seminal work by Longuet-Higgins which was limited to one-dimensional plane waves. Both theories are based on Bernoulli's principle. A little appreciated consequence of the Bernoulli principle is that surface gravity waves induce a time dependent pressure on the sea floor through a vertical column of water. A significant difference exists between microseisms detected at the bottom of each column and seismic signals radiated into the crust through coherence over a region of the sea floor. The dominant measured frequency of radiated microseisms is matched by this new theory for seismic data gathered at the Fordham Seismic Station both for a hurricane and a mid-latitude cyclone in 1998. Implications for Bernoulli's principle and this cylindrical stress flow theory on observations in the literature are also discussed.

Bernoulli convolutions associated with certain non—Pisot numbers

Abstract: The Bernoulli convolution νλ measure is shown to be absolutely continuous with L2 density for almost all 1/2<λ<1, and singular if λ- is a Pisot number. Itis an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convolutions νλ such that their density functions, if they exist, are not L2. We also construct other Bernolulli convolutions whose density functions, if they exist, behave rather badly.

Effect of coriolis force on accretion flows around rotating compact object

Abstract: Using the generalised set of fluid equations that include the "Coriolis force" along with the centrifugal and pressure gradient forces, we have reanalysed the class of self-similar solutions, with the pseudo-Newtonian potential. We find that the class of solutions is well behaved for almost the entire parameter space except for a few selected combinations of γ and α for the co-rotating flow. The analysis of the Bernoulli number shows that whereas it remains positive for co-rotating flow for f > 1/3, for the counter-rotating flow it does admit both positive and negative values, indicating the possibility of energy transfer in either direction.