Presence Of Rigid Boundary Research Articles

“They're coming up!”: Disciplining the Urban Landscape in F. Scott Fitzgerald's “May Day”

Abstract In “May Day,” F. Scott Fitzgerald represents New York City as a highly contested landscape, marked by the alternating absence and presence of rigid boundaries, and fundamentally segregated by class privilege. Warning against an inadequately disciplined cityscape, Fitzgerald engages central modern-era concerns regarding the identity of the increasingly diversifying city, especially as they were expressed in emerging landscape debates and regulation. Situating “May Day” in this context provides a potent historical grounding for examining the comparative freedoms the story's diverse characters have to traverse the urban landscape, and, more broadly, illuminates how Fitzgerald's developing political and historical understanding both produces his representation of the urban landscape and advocates for the spatial practices (and the embedded social meanings) it expresses.

An approach to aerodynamic sound prediction based on incompressible-flow pressure

Abstract Curle's analogy provides a solution to Lighthill's equation to predict flow-generated sound in the presence of rigid boundaries. Nevertheless, Curle's solution requires the flow pressure, including its acoustic component, to be known in the source region. If the pressure corresponds to an incompressible-flow description instead and the surface is not acoustically compact, significant errors can arise in the acoustic prediction. In this work, it is argued that flow wall pressure can be used to define appropriate boundary conditions of an equivalent acoustic boundary value problem for an arbitrary geometry, and a formulation of a boundary condition based on incompressible-flow pressure is proposed. The theoretical analysis suggests that if the flow is incompressible, the error has the leading order of a dipole plus a quadrupole for Curle's analogy and of just a quadrupole for the proposed alternative approach, thus making the latter more accurate when dipole sources are dominant. A numerical test case is presented as a proof of concept, consisting of a trailing edge noise problem due to the flow past a slender body.

A new approximate analytical solution for arbitrary Stokes flow past rigid bodies

A method of computing general Stokes flows in the presence of rigid boundaries of arbitrary shape is proposed. The solution satisfies the governing field equations exactly and the boundary conditions approximately. The method has been illustrated with three examples. The advantage of the method lies in the ease of implementation for rigid bodies of arbitrary shape, providing an approximate but analytical solution throughout the domain.

A multi-domain Fourier pseudospectral time-domain method for the linearized Euler equations

The Fourier pseudospectral time-domain (F-PSTD) method is computationally one of the most cost-efficient methods for solving the linearized Euler equations for wave propagation through a medium with smoothly varying spatial inhomogeneities in the presence of rigid boundaries. As the method utilizes an equidistant discretization, local fine scale effects of geometry or medium inhomogeneities require a refinement of the whole grid which significantly reduces the computational efficiency. For this reason, a multi-domain F-PSTD methodology is presented with a coarse grid covering the complete domain and fine grids acting as a subgrid resolution of the coarse grid near local fine scale effects. Data transfer between coarse and fine grids takes place utilizing spectral interpolation with super-Gaussian window functions to impose spatial periodicity. Local time stepping is employed without intermediate interpolation. The errors introduced by the window functions and the multi-domain implementation are quantified and compared to errors related to the initial conditions and from the time iteration scheme. It is concluded that the multi-domain methodology does not introduce significant errors compared to the single-domain method. Examples of scattering from small scale density scatters, sound reflecting from a slitted rigid object and sound propagation through a jet are accurately modelled by the proposed methodology. For problems that can be solved by F-PSTD, the presented methodology can lead to a significant gain in computational efficiency.

A two-dimensional model of low-Reynolds number swimming beneath a free surface

Biological organisms swimming at low-Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper, we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.

Vortices, Complex Flows and Inertial Particles

The properties of vortical structures at high Reynolds number in uniform flows and near rigid boundaries are reviewed. New properties are derived by analysing the dynamics of the main flow features and the related integral constraints, including the relations between mean swirl and bulk speed, the relative level of internal fluctuations to bulk properties, and connections between the steadiness and topology of the structures. A crucial property that determines energy dissipation and the transport of inertial particles (with finite fall speed) is the variation across the structure of the ratio of the mean strain rate (Σ) to the mean vorticity (Ω). It is shown how, once such particles are entrained into the vortical regions of a coherent structure, they can be transported over significant distances even as the vortices grow and their internal structure is distorted by internal turbulence, swirling motions and the presence of rigid boundaries. However if the vortex is strongly distorted by a straining motion so that Σ is greater than Ω, the entrained particles are ejected quite rapidly. These mechanisms are consistent with previous studies of entrained and sedimenting particles in disperse two phase flows over flat surfaces, and over bluff obstacles and dunes. They are also tested in more detail here through laboratory observations and measurements of 50–200-μm particles entrained into circular and non-circular vortices moving first into still air and then onto rigid surfaces placed parallel and perpendicular to the direction of motion of the vortices.

Investigation of Resonant Frequency and Amplitude of Vibrating Footing Resting on a Layered Soil System

Abstract Influence of layering and presence of rigid boundary in the soil mass on natural frequency and resonant amplitude are studied experimentally by conducting model block vibration tests in vertical mode. Tests are conducted on different layered beds prepared in a tank using a model footing. A Lazan type mechanical oscillator is used for inducing vibration and two different materials (sand and sawdust) are used to form a layered system. In total, 180 tests are conducted in different layering combinations and different static and dynamic loading combinations, and several important observations are reported. Damping factors are found to be within 6.5% for the entire test series, which indicates that radiation damping is insignificant in the test system. It is also found that layering including layer position and thickness has significant effect on natural frequency. Observed natural frequencies are also compared with the predicted one based on static equivalent stiffness; encouraging agreement between observed and predicted values are found.

A theoretical study of natural frequencies of bubbles in sediments

Bubbles that are highly efficient scatterers have dramatic effects on the acoustic characteristics of sediments. The incorporation of such effects in continuum models requires the knowledge of individual bubble frequency and response to acoustic waves. For bubbles that are smaller than the acoustic wavelength but large enough that the liquid viscosity is insignificant, the potential flow approximation is reasonable. The natural frequency of bubbles surrounded by sediment grains of comparable size are computed by a boundary integral formulation allowing in detail for bubble deformation and the presence of rigid boundaries. Even though the geometry is restricted to axisymmetric cases, main features of this process are adequately captured by simulating a number of cases. Several configurations are tested and, in many instances, substantial differences between the current calculations and the commonly used formula have been found. [Work supported by the Office of Naval Research.]

Wave form of short shock wave reflected from bubble layers in water

Experimental and theoretical investigation of an influence of the local layer parameters, presence of rigid boundary on the bubble dynamics under the action of strong pressure pulse as well as the formation of reflected signal are reported. It is shown that duration of reflected pulse, its amplitude and presence of an oscillations behing it depend not only on the amplitude and duration of incident pulse, but on the spatial gradient of void fraction and distribution of the bubble radii within the layer. This phenomenon is described within the framework of the model, taking into account a specific variation of void fraction inside the layer as well as the specific bubble dynamics in it.

On the convected linear stability of a viscoelastic Oldroyd B fluid heated from below

We investigate the linear stability problem of convection by the general Oldroyd B fluid and its Maxwell limit in the presence of rigid or free boundaries and fixed temperature or fixed flux. Comparison with recent results by Rosenblat [9] for the analytically accessible case of free boundary conditions shows a qualitative similarity in the shape of the neutral stability curves. But while Newtonian and Jeffreys (general Oldroyd B) fluids are sharply stabilized by the presence of rigid boundaries, the Maxwell fluid is largely unaffected at even moderately large Prandtl number. The reasons for this are discussed. Also, a discrepancy between the earlier works by Vest and Arpaci [3], and Sokolov and Tanner [4], which treat the case of a Maxwell fluid, is found to be due to algebraic error, and not multivaluedness of the stress-strain rate relation as earlier suggested by Eltayeb [6].

Lateral Pressures on Retaining Walls Due to Loads on Surface of Granular Backfill

ABSTRACT The lateral pressure transmittal through different types of backfill material; characterized through a material parameter E/G; subjected to different types of contact pressure on its surface is evaluated theoretically by the use of the concept, in which it is considered that E/G > 2(l + v). The backfill material extending upto infinity depth as well as limited by the presence of rigid boundaries having different frictional characteristics have been considered. The physical and mechanical characteristics of the granular materials affecting the development of lateral pressures on retaining wall are investigated. The model used in the analysis is found to be applicable to a wide range of materials ranging from solid like at one end to liquid like at the other end. Qualitative numerical results over a wide range of the values of the material parameter (E/G) have been presented in a non-dimensional form to elucidate its influence on this problem. The results are also compared with that of Boussinesq’s approach. It is observed that the softer/looser the backfill, the poorer is pressure transmission in horizontal direction resulting in a overall decrease of the lateral pressure on the retaining structure. The proposed model gives a partial explanation of the divergences between the results of the existing theories and reality.

Overstability of a viscoelastic fluid layer heated from below

The stability of a horizontal layer of Maxwellian fluid heated from below is considered. Critical Rayleigh numbers, wave-numbers, and frequencies for overstability are determined for both free and rigid boundaries. Elasticity is found to destabilize the fluid, and the presence of rigid boundaries is found to be slightly stabilizing.

The motion of rigid particles in a shear flow at low Reynolds number

According to Jeffery (1923) the axis of an isolated rigid neutrally buoyant ellipsoid of revolution in a uniform simple shear at low Reynolds number moves in one of a family of closed periodic orbits, the centre of the particle moving with the velocity of the undisturbed fluid at that point. The present work is a theoretical investigation of how far the orbit of a particle of more general shape in a non-uniform shear in the presence of rigid boundaries may be expected to be qualitatively similar. Inertial and non-Newtonian effects are entirely neglected.The orientation of the axis of almost any body of revolution is a periodic function of time in any unidirectional flow, and also in a Couette viscometer. This is also true if there is a gravitational force on the particle in the direction of the streamlines. There is no lateral drift. On the other hand, certain extreme shapes, including some bodies of revolution, will assume one of two orientations and migrate to the bounding surfaces or to the centre of the flow. In any constant slightly three-dimensional uniform shear any body of revolution will ultimately assume a preferred orientation.