Regions Of Strong Gradients Research Articles

Geographic correlation between hot spots and deep mantle lateral shear-wave velocity gradients

Hot spot volcanism may originate from the deep mantle in regions exhibiting the Earth’s most pronounced lateral S-wave velocity gradients. These strong gradient regions display an improved geographic correlation over S-wave velocities to surface hot spot locations. For the lowest velocities or strongest gradients occupying 10% of the surface area of the core–mantle boundary (CMB), hot spots are nearly twice as likely to overlie the anomalous gradients. If plumes arise in an isochemical lower mantle, plume initiation should occur in the hottest (thus lowest velocity) regions, or in the regions of strongest temperature gradients. However, if plume initiation occurs in the lowest velocity regions of the CMB lateral deflection of plumes or plume roots are required. The average lateral deflections of hot spot root locations from the vertical of the presumed current hot spot location ranges from ∼300 to 900 km at the CMB for the 10–30% of the CMB covered by the most anomalous low S-wave velocities. The deep mantle may, however, contain strong temperature gradients or be compositionally heterogeneous, with plume initiation in regions of strong lateral S-wave velocity gradients as well as low S-wave velocity regions. If mantle plumes arise from strong gradient regions, only half of the lateral deflection from plume root to hot spot surface location is required for the 10–30% of the CMB covered by the most anomalous strong lateral S-wave velocities. We find that strong gradient regions typically surround the large lower velocity regions in the base of the mantle, which may indicate a possible chemical, in addition to thermal, component to these regions.

Résolution des équations de dispersion–diffusion en présence de forts gradients

In order to resolve the convection terms in the simulation of coastal flows, we propose a numerical method based on the Total Variation Diminishing scheme completed with the Artificial Compression Method to reduce the artificial diffusion and to sharpen the tracer profile in strong gradient regions. This method was applied successfully at discontinuous regions, but out of these regions a limitation of its application is necessary. An application is made to estimate the width of the fresh water band in the Eastern English Channel. To cite this article: C. Sart et al., C. R. Mecanique 330 (2002) 159–165.

An Effective Particle Tracing Scheme on Structured/Unstructured Grids in Hybrid Finite Volume/PDF Monte Carlo Methods

To date, PDF/Monte Carlo simulations, either in stand-alone codes or in hybrid finite volume/PDF Monte Carlo programs, appear to have been mostly carried out with cells of similar size. In many situations, such as capturing sharp gradients in a flow field, fine grids or unstructured solution-adaptive grids must be used in the finite volume code, resulting in a cell system with large variations in cell size. Such grids present a challenge for a combined PDF/Monte Carlo code. In this paper, a new particle tracing scheme is proposed, in which we introduce the concept of variable time steps. Using locally adaptive time steps in the integration of particle equations, the particles' parameters are updated more frequently in regions of strong gradients than in those of flat gradients, which greatly improves the time efficiency of particle tracing. To reduce statistical errors, a particle splitting and combination procedure is also used. The new scheme allows the hybrid finite volume/PDF Monte Carlo code to use any grid that is constructed in the finite volume code. This relaxation of restrictions on the grid makes it possible to couple PDF/Monte Carlo methods to all popular commercial CFD codes and, consequently, extend existing CFD codes' capability to simulate turbulent reactive flow in a more accurate way. The numerical performance of the new particle tracing scheme and the solution procedure are illustrated by considering a turbulent heat transfer problem in a parallel channel and a turbulent diffusion combustion problem in a cylindrical combustor.

Coherent Vortex Simulation (CVS), A Semi- Deterministic Turbulence Model Using Wavelets

In the spirit of Ha Minh's semi-deterministic model, we propose a new method for com- puting fully-developed turbulent flows, called Coherent Vortex Simulation (CVS). It is based on the observation that turbulent flows contain both an organized part, the coherent vortices, and a random part, the incoherent background flow. The separation into coherent and incoherent contributions is done using the wavelet coefficients of the vorticity field and the Biot-Savart kernel to reconstruct the coherent and incoherent velocity fields. The evolution of the coherent part is computed using a wavelet basis, adapted at each time step to resolve the regions of strong gradients, while the incoherent part is discarded during the flow evolution, which models turbulent dissipation. The CVS method is similar to LES, but it uses nonlinear multiscale band-pass filters, which depend on the instantaneous flow realization, while LES uses linear low-pass filters, which do not adapt to the flow evolution. As example, we apply the CVS method to compute a time developing two- dimensional mixing layer and a wavelet forced two-dimensional homogeneous isotropic flow. We also demonstrate how walls or obstacles can be taken into account using penalization and compute a two-dimensional flow past an array of cylinders. Finally, we perform the same segmentation into coherent and incoherent components in a three-dimensional homogeneous isotropic turbulent flow. We show that the coherent components correspond to vortex tubes, which exhibit non-Gaussian statistics and long-range correlation, with the same k −5/3 power-law energy spectrum as the total flow. In contrast, the incoherent components correspond to an homogeneous random background flow which does not contain organized structures and presents an energy equipartition together with a Gaussian PDF of velocity. This justifies their elimination during the CVS computation to model turbulent dissipation.

Current sheet formation due to nonlinear kink modes in periodic and line-tied configurations

The full magnetohydrodynamic evolution of kink instabilities in cylindrical geometry is computed. The equilibria investigated serve as generic models of coronal loops. The effects of both periodic and line-tying boundary conditions at the axial ends of the cylinder are compared and contrasted. The net axial current, which is distributed internally to the loop, can be varied from case to case. It is found that one effect of the line-tying boundary condition is that the minimum length for the onset of a kink instability is increased. For line-tied loops, resonant surfaces do not exist, though linear analysis shows that there may or may not occur quasi-resonant regions, i.e., regions of strong gradients, which, however, are confined to the loop apex, far from the line-tied boundaries. When such a region is present for the linear mode, the formation and nonlinear development of current layers is confined to the central region of the loop. In a case where no such regions exist for the linear mode (corresponding to k⋅B≠0 in the periodic cylinder), current concentrations appear two thirds of the way from the center of the loop. This effect disappears in the axially periodic case. The consequences of these results for solar physics are discussed.

Adaptive mesh generation using a normal offsetting technique

A fully automatic adaptive remeshing approach is presented for two-dimensional applications. The approach uses a normal offsetting technique to deploy nodes followed by Delaunay triangulation with a mesh resolution function based on the physics and problem geometry. The method can handle multi-connected boundaries and multiple material regions. The mesh density function, based on a given problem, provides the mechanism for automatic refinement in regions of strong gradients and coarsens elements where gradients are mild to give appropriate mesh densities throughout the domain. As a consequence, one can reach a desired level of accuracy with reduced computational efforts.

Adaptive finite element analysis of hypersonic laminar flows for aerothermal load predictions

The use of an adaptive mesh refinement procedure for analyzing hypersonic laminar flows with application to aerothermal load predictions is described. The adaptation procedure, which uses both quadrilateral and triangular elements, is implemented with the multistep Galerkin-Runge-Kutta scheme. Elements that lie in regions of strong gradients are refined based on indicators to obtain better definition of flow features. The effectiveness of the adaptive procedure is demonstrated by modeling Mach 11.7 flow over a 15-deg ramp. Numerical results are compared with predictions of strong interaction theories and experimental data. Surface quantities such as heating rates and pressure loads, critical for the effective design of high-speed vehicles, are found to be in good agreement with experimental values.

A numerical study of the convergence properties of ENO schemes

We report numerical results obtained with finite difference ENO schemes for the model problem of the linear convection equation with periodic boundary conditions. For the test function sin(x), the spatial and temporal errors decrease at the rate expected from the order of local truncation errors as the discretization is refined. If we take sin4(x) as our test function, however, we find that the numerical solution does not converge uniformly and that an improved discretization can result in larger errors. This difficulty is traced back to the linear stability characteristics of the individual stencils employed by the ENO algorithm. If we modify the algorithm to prevent the use of linearly unstable stencils, the proper rate of convergence is reestablished. The way toward recovering the correct order of accuracy of ENO schemes appears to involve a combination of fixed stencils in smooth regions and ENO stencils in regions of strong gradients —a concept that is developed in detail in a companion paper by Shu (this issue, 1990).

Performance results of preliminary operation of Kuwait solar pond

SYNOPSIS A run-down trial operation of Kuwait's 1700m2 solar pond located at a windy and dry climate area indicated the major problem was mixing between the upper convective zone (UCZ) and the non-convective zone (NCZ). No mixing between the NCZ and the lower convective zone (LCZ) was observed. The wind effect was severe in causing mixing even when the UCZ was 0.90m deep. However, the strong-gradient region persisted all the way through, but the weak gradient could not tolerate the prevailing conditions.

The vertical thermohaline structure in the Argentine basin

The vertical thermohaline structure in the central Argentine basin is investigated on the basis of high‐resolution hydrographic data. Emphasis is placed on fronts, their horizontal gradients, vertical stability and associated fine structure. Horizontal thermohaline gradients vary strongly with depth, regions of strong gradients alternating with those of weak gradients. The strongest gradients occur often at depths below the upper mixed layer. The salinity gradient maximum occurs above the temperature gradient maximum. Enhanced gradients are found where warm, salty water moves over cooler, fresher water such as between the subtropical water (STW) and antarctic intermediate water (AAIW) and between the North Atlantic deep water (NADW) and the antarctic bottom water (AABW). Temperature, salinity, and density fronts do not always coexist. Density‐compensating temperature and salinity fronts occur in the surface layer of the subantarctic and at abyssal depth below 3500 m. Vertical profiles of the Väisälä frequency indicate much reduced hydrostatic stabilities in the Brazil current and subantarctic frontal zones. Potential vorticity minima indicate the formation of subantarctic mode water just north of the subantarctic front and its subsequent northward and upward spread across isopycnals. The thermohaline fine structure is vertically intermittent. The amplitude variances between the enhanced and quiet regions vary by almost 2 orders of magnitude. Enhanced fine structure amplitudes are found near the STW‐AAIW and NADW‐AABW interfaces, where large horizontal thermohaline gradients occur and the hydrostatic stability is low. The temperature and salinity fine structures are largely density compensating. The coherence between the temperature and salinity fine structure is strongly depth dependent and is highest in regions where warm, salty water moves over cooler, fresher water.

Vertical Microstructure Measurements in the Central Worth Pacific

Abstract Temperature profiles were made, during a period of calm weather in early autumn, in the center of the subtropical gyre in the North Pacific with free-fall microstructure instruments as well as with commerical salinity-temperature-depth recorders. In the depth range of 0.2–2 km the data records show irregularly spaced regions of strong gradients separated by sections with weak gradients, but otherwise lack conspicuous features. The general impression is one of strong stratification and only very weak levels of turbulence. Spectra of the gradient records from the upper kilometer exhibit distinct changes in slope at about 10−2 cycle per meter (cpm) and at 10 cpm. These changes in slope are interpreted as the scales at which different types of features dominate the vertical temperature profile: the nearly exponential mean profile is the principal feature for K<10−2 cpm, while for 10−2<K<2 cpm the irregularly spaced structures in the stratification are the principal contributors to the spectra. Wavenu...