Effect of Schmidt number on the structure and propagation of density currents

The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number 1 ≤ Sc ≤ ∞ and Reynolds number 10² ≤ Re ≤ 10⁴. The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of O(10⁴) or more. On the contrary low- to moderate-Re density currents are dependant on Sc as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as (ScRe)^−1/2. Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of Sc. In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-Sc, (2) the formation of vortex structures generated by Kelvin–Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data.      

Numerical modeling of gravity currents in inclined channels

The mixing and wave formation processes in gravity currents induced by the rupture of a vertical dam initially separating a heavy and a light liquid are studied for different channel inclination angles. The calculations are performed using the LES and RANS models. It is shown that when the heavy liquid moves down the channel slope, the longitudinal and transverse internal waves break and form turbulent mixing zones. When the heavy liquid ascends the slope, the wavy motion mode predominates.     

Numerical study on wave propagation in a low-rigidity elastic medium considering the effects of gravity

We discuss the effects of vertical gravity force on wave propagation when a material is intermediate between solid and fluid, especially we focus on what kinds of phase are generated and how it propagates on the surface. We introduce gravity terms into the 2D linear finite element method in order to account for the contribution from the gravity. Numerical simulations are conducted for a half-space model and a two-layered, single horizontal layer overlain on a half-space, model. Both models are compared between the results including and excluding the viscosity. The fastest phase propagating from a surface point source, a leaking Rayleigh wave for usual elastic material, is transformed into an interesting phase including some common features to the gravity wave when the gravity effect becomes significant. The viscosity does not affect the fastest phases, whereas it affects other latter phases appearing only for the two-layered model.     

Direct numerical simulation of particle transport by hairpin vortices in a laminar boundary layer

The transport of solid particles by coherent wall structures is studied here. This phenomenon is present in numerous environmental and engineering flows. The flow above a wall-mounted hemisphere is used for generating hairpin vortices in a laminar boundary layer in a controlled way. By means of direct numerical simulation (DNS) of the fluid flow and simultaneous Lagrangian tracking of particles, the influence of hairpin vortices on solid particles released in the wake of the obstacle is analyzed.     

Effect of gravity on the vibration of vertical cantilevers

The free vibration of a vertically-oriented, thin, prismatic cantilever is influenced by weight. That is, the natural frequencies (and to a lesser extent, mode shapes) are affected by the application of a linearly varying axial load. A beam with an “upward” orientation, i.e., with the free end above the clamped end, will experience a de-stiffening effect, up to the point of self-weight buckling (at zero effective stiffness). A beam in a “downward” orientation will be stiffened by the weight of the beam. This technical note describes some simple experiments on very slender strips and their (vertical) orientation and shows a close correlation with theory.     

A dynamical study of the evolution of pressure waves propagating through a semi-infinite region of homogeneous gas combustion subject to a time-harmonic signal at the boundary

In this paper, we study the evolution of pressure waves propagating in a region of gas combustion subject to a time-harmonic signal at the boundary. The problem is modeled by a non-linear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for transient effects to have dissipated. The zeroth-order and first two approximations are obtained. Furthermore, the behavior of the following quantities is investigated, with particular attention paid to the low and high-frequency limits: the location of the peak of the first-order approximation, dispersion relations and phase speeds. Additionally, a maximum value of the perturbation parameter is determined ensuring boundedness of the solution. Next, approximate solutions are obtained in the low and high frequency limits and a comparison is made with the corresponding perturbation solution. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by a non-standard finite-difference scheme.     

A bi-modal structure imposed on gravity driven boundary currents in rotating systems by effects of the bottom topography

 An experimental observation related to the influence of the bottom topography on the development of gravity driven surface boundary currents in rotating systems is described and discussed. The results presented concern the local flow geometry in the vicinity of the head of the current. It is observed that, depending on the values of the independent experimental variables and the inclination angle of the bottom topography, the current propagates along the boundary with its head being either attached to or detached from the coastline. An appropriate scaling of the experimental data reveals that the attached and detached head mode occur in two distinct parameter regimes which are separated from each other by a well defined border. The discussion of the results suggests that this border identifies the division between two flow regimes in which the local flow structure in the vicinity of the head of the gravity current is and where it is not significantly influenced by the bottom topography. Received: 15 September 1997/Accepted: 23 January 1998     

A study of influence of gravity on bulk behavior of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method (DEM). Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions.The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

A DNS study on the effects of convex streamwise curvature on coherent structures in a temporally-developing turbulent boundary layer with supercritical water

Direct numerical simulation (DNS) results are used to establish the effect of convex streamwise curvature on the development of turbulent boundary layers, and the effect of such curvature on the forced-convection heat transfer variations observed at certain supercritical thermodynamic states. The results illustrate the stabilizing effects of this flow geometry through modification of the structure and distribution of hairpin-like vortical flow structures in the boundary layer. Furthermore, enhancement of convective heat transfer realized at a particular heat flux-to-mass flux ratio with the working fluid at a supercritical state is observed to be reduced by the stabilizing effect of convex surface curvature.     

A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method （DEM）. Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

对管内湍流边界层结构与流动阻力特性的数值研究

在研究紊流边界层的过程中,本文考虑了分子粘性对紊流产生的作用、雷诺数以及壁面附近脉动动能的耗散不是各向同性对紊流产生的影响,采用Jones-Launder模型对管内紊流流动边界层厚度、边界层内的脉动动能K,动能耗散ε,管壁切应力τ0以及由此可得的管内流动摩擦阻力系数λ进行了数值计算,计算结果与实验值、理论计算值得具有较好的一致性。     

Numerical simulation of cooling-induced convective currents on a littoral slope

The transient development of cooling-induced flow in a triangular domain filled with water is studied by means of numerical simulation as a model for flow developing in the littoral region of lakes or coasts. The domain is fitted in polar co-ordinates; solutions are obtained for different values of the independent parameters of the model, which are the Rayleigh number (Ra), the Prandtl number (Pr) and the slope of the domain (S). Within the ranges examined, as Ra is increased, different regimes of the developing flow are observed; these are found qualitatively to be insignificantly influenced by changes in S, whereas the flow is found to be quantitatively insensitive to Pr for high enough values of Pr. Several interesting features of the flow are depicted and integral values useful in the analysis of flow in lakes are extracted.     

To the boundary and back—a numerical study

This study identifies the key parameters upon which energy absorption at artificial boundaries depends. A thorough numerical study is presented, of typical reflections from open computational boundaries, for problems governed by hyperbolic systems of equations. The emphasis is on systems, where it is often the combination of all boundary procedures that determine the quality of boundary treatment. We study dissipative numerical models which have so far not been analysed to the same extent as non-dissipative models and employ a Law-Wendroff-type scheme as a prototype. While it is widely accepted that dissipative models tend to give fewer problems than non-dissipative ones, we show a variety of cases where substantial reflections do occur even in ID and quasi-ID set-ups, where theory predicts best results. This can partly be explained by the vanishing of dissipation in the far field. Group velocity analysis, justifiable on the grounds of weak dissipation, predicts a pathological behaviour which is confirmed by numerical experiments. We demonstrate strong focusing of asymptotic errors generated at the artificial boundary. Internal reflections due to slowly expanding grids are shown for non-linear systems. The need for high-frequency boundary conditions naturally arises and combined low-high-frequency boundary recipes following Higdon, Vichnevetsky and Pariser are adapted to systems and tested. Partial cures are also discussed, mainly in terms of pointing out their theoretically limited potential.     

A numerical study for small amplitude T-S waves in a supersonic boundary layer

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A numerical study of a rectangular jet along a shear free boundary: Surface jet

A numerical simulation of a rectangular surface jet is performed at a Reynolds number of ${\mathit{Re}}_j=4400$. The global parameters of the jet e.g. maximum velocity decay, jet surface normal and lateral spread rates, entrainment, jet momentum flux and turbulent momentum flux are in agreement with several other studies reported in the literature. It is shown that the mean velocity and Reynolds stress profiles scale with the maximum local streamwise velocity and jet half width in the surface normal and lateral directions. The current simulation provides balance, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal and shear stresses. The surface jet develops a thin layer of fast moving fluid in the lateral direction near the surface. This layer is called the ‘surface current’. It has been suggested that the surface current arises due to the Reynolds stress anisotropy in the near surface region. The current study shows that this explanation is incomplete. The turbulence production for the Reynolds stress in the lateral direction is negative, which can drive the mean flow in the lateral direction. The higher level of negative production in the near surface region is responsible for the development of the surface current.     

磁场和Hall电流对狭窄动脉中血液流动的影响

A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis （stenosis throat）, have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hail parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.     

Mesh effects on the computation of non-linear gravity waves of arbitrary discharge

Numerical computations of non-linear gravity waves are presented and the effects of mesh variations on the results are discussed. Waves are regarded as two-parameter families (λ,A)_Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.     

Direct numerical simulation of the near field dynamics of a rectangular reactive plume

Spatial direct numerical simulation (DNS) is used to study the near field dynamics of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field, which interact with the flame and temporally create localized holes within the reaction zone in which no chemical reactions take place. The interaction between density gradients and gravity plays a major role in the vorticity generation of the buoyant plume. At the downstream of the reactive plume, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional (3D) vortex interactions. Analysis of energy spectra shows that the spatially developing reactive plume has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. The buoyancy effects are found to be very important to the formation, development, interaction, and breakdown of vortices in reactive plumes. In contrast with the relaminarization effects of chemical exothermicity via viscous damping and volumetric expansion on non-buoyant jet diffusion flames, the tendency towards transition to turbulence in reactive plumes is greatly enhanced by the buoyancy effects.     

Dispersion of linear gravity waves on a viscoelastic fluid in an horizontal canal

A characteristic equation is derived that describes the spatial decay of linear surface gravity waves on Maxwell fluids. Except at small frequencies, the derived dispersion relation is different from the temporal decay dispersion relation which is normally studied within fluid mechanics. The implications for waves on viscous Newtonian fluids using the two different dispersion relations is briefly discussed. The wave number is measured experimentally as function of the frequency in a horizontal canal. Seven Newtonian fluids and four viscoelastic liquids with constant viscosity have been used in the experiments. The spatial decay theory for Newtonian fluids fits well to the experimental data. The model and experiments are used to determine limits for the Maxwell fluid time numbers for the four viscoelastic liquids. As a result of low viscosity it was not possible within this study to obtain these time numbers from oscillatory experiments. Therefore, a comparison of surface gravity wave experiments with theory is applicable as a method to evaluate memory times of low viscosity viscoelastic fluids.