Linear Fluctuation Growth during Frontogenesis

2009 ◽  
Vol 39 (12) ◽  
pp. 3111-3129 ◽  
Author(s):  
James C. McWilliams ◽  
M. J. Molemaker ◽  
E. I. Olafsdottir
Keyword(s):  
Growth Rate ◽  
Kinetic Energy ◽  
Energy Conversion ◽  
Deformation Rate ◽  
Three Dimensional ◽  
Mesoscale Eddies ◽  
Two Dimensional ◽  
Near Surface ◽  
Secondary Circulations ◽  
Frontal Instability

Abstract Near-surface, two-dimensional (2D) baroclinic frontogenesis induced by a barotropic deformation flow enhances the growth of three-dimensional (3D) fluctuations that occur on an ever smaller scale as the front progressively sharpens. The 3D fluctuation growth rate further increases with a larger deformation rate. The fluctuations grow by a combination of baroclinic and barotropic energy conversions from the 2D frontal flow, with the former dominating for most of the situations examined, ranging from small to 𝒪(1) values of the Rossby and Froude numbers and nondimensional deformation rate. Averaged 3D fluctuation buoyancy fluxes resist the 2D frontogenesis by a frontolytic tendency. They also augment the buoyancy restratification and potential-to-kinetic energy conversion tendencies of the 2D frontogenesis itself, and the 2D frontogenetic and 3D eddy-induced secondary circulations are mostly reinforcing (unlike in turbulent baroclinic jets). This shows that frontal instability coexists with, and potentially may even overcome, active frontogenesis; this conclusion is contrary to some previous studies. Frontal instability thus can augment frontogenesis in accomplishing a forward cascade of energy from oceanic mesoscale eddies into the submesoscale regime en route to finescale dissipation.

A RHEED Study of MBE Growth of ZnSe on GaAs (111) A-(2 × 2)

2003 ◽  
Vol 10 (04) ◽  
pp. 669-675
Author(s):  
F. S. Gard ◽  
J. D. Riley ◽  
R. Leckey ◽  
B. F. Usher
Keyword(s):  
Growth Rate ◽  
Electron Diffraction ◽  
Substrate Temperature ◽  
Three Dimensional ◽  
High Energy ◽  
Growth Mode ◽  
Two Dimensional ◽  
High Energy Electron ◽  
Mbe Growth ◽  
Atomic Flux

ZnSe epilayers have been grown under various Se/Zn atomic flux ratios in the range of 0.22–2.45 at a substrate temperature of 350°C on Zn pre-exposed GaAs (111) A surfaces. Real time reflection high energy electron diffraction (RHEED) observations have shown a transition from a two-dimensional (2D) to a three-dimensional (3D) growth mode. The transition time depends directly upon the growth rate. A detailed discussion is presented to explore the cause of this change in the growth mode.

Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations

2002 ◽  
Vol 451 ◽  
pp. 261-282 ◽  
Author(s):  
F. GRAF ◽  
E. MEIBURG ◽  
C. HÄRTEL
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Linear Stability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interface Thickness ◽  
Gap Width ◽  
Stability Results ◽  
Hele Shaw Cell

We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller wavelengths. Similar observations have been made for immiscible flows as well (Maxworthy 1989).In order to resolve the above discrepancy, we perform a linear stability analysis based on the full three-dimensional Stokes equations. A generalized eigenvalue problem is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion relations confirm that the optimally amplified wavelength is about five times the gap width, with the exact value depending on the interface thickness. The corresponding growth rate is in very good agreement with the experimental data as well. The eigenfunctions indicate that the predominant fluid motion occurs within the plane of the Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified, for which there is no motion in the spanwise direction. Scaling laws are provided for the dependence of the maximum growth rate, the corresponding wavenumber, and the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present results are compared both with experimental data, as well as with linear stability results obtained from the Hele-Shaw equations and a modified Brinkman equation.

Void growth in shear

1986 ◽  
Vol 407 (1833) ◽  
pp. 435-458 ◽  
Keyword(s):  
Growth Rate ◽  
Strain Rate ◽  
Void Growth ◽  
Three Dimensional ◽  
Shape Evolution ◽  
Two Dimensional ◽  
Simple Shearing ◽  
Hydrostatic Tension ◽  
Dilatation Rate ◽  
Approximate Formulas

The growth of an isolated void is analysed for a void contained in a block of material undergoing simple shearing combined with superimposed hydrostatic tension. The evolution of the size, shape and orientation of two- and three-dimensional voids in an incompressible, linearly viscous solid is first discussed. The main problem addressed is the behaviour of a two-dimensional cylindrical void in an incompressible, nonlinearly viscous solid for which the strain rate varies as the stress to a power. The growth rate of the void and its shape evolution are strong functions of the degree of material nonlinearity. Relatively simple approximate formulas are obtained for the dilatation rate of a circular void as well as for the void potential. The constitutive relation of a block of material containing a dilute distribution of circular cylindrical voids is obtained directly using the isolated void potential. The paper concludes with a summary of available results for the dilatation rates of voids and cracks under combinations of shear and hydrostatic tension.

scholarly journals Geostatistical FDEM inversion: a three-dimensional real case application

2021 ◽  
Author(s):  
Leonardo Azevedo ◽  
João Narciso ◽  
Ellen Van De Vijver
Keyword(s):  
Spatial Distribution ◽  
Physical Properties ◽  
Three Dimensional ◽  
Real Case ◽  
Small Scale ◽  
Inversion Method ◽  
Two Dimensional ◽  
Data Set ◽  
Near Surface ◽  
Direct Observations

<p>The near surface is a complex and often highly heterogeneous system as its current status results from interacting processes of both natural and anthropogenic origin. Effective sustainable management and land use planning, especially in urban environments, demands high-resolution subsurface property models enabling to capture small-scale processes of interest. The modelling methods based only on discrete direct observations from conventional invasive sampling techniques have limitations with respect to capturing the spatial variability of these systems. Near-surface geophysical surveys are emerging as powerful techniques to provide indirect measurements of subsurface properties. Their integration with direct observations has the potential for better predicting the spatial distribution of the subsurface physical properties of interest and capture the heterogeneities of the near-surface systems.</p><p>Within the most common geophysical techniques, frequency-domain electromagnetic (FDEM) induction methods have demonstrated their potential and efficiency to characterize heterogeneous deposits due to their simultaneous sensitivity to electrical conductivity (EC) and magnetic susceptibility (MS). The inverse modelling of FDEM data based on geostatistical techniques allows to go beyond conventional analyses of FDEM data. This geostatistical FDEM inversion method uses stochastic sequential simulation and co-simulation to perturbate the model parameter space and the corresponding FDEM forward model solutions, including both the synthetic FDEM responses and their sensitivity to changes on the physical properties of interest. A stochastic optimization driven by the misfit between true and synthetic FDEM data is applied to iterative towards a final subsurface model. This method not only improve the confidence of the obtained EC and MS inverted models but also allows to quantify the uncertainty related to them. Furthermore, taking into account spatial correlations enables more accurate prediction of the spatial distribution of subsurface properties and a more realistic reconstruction of small-scale spatial variations, even when considering highly heterogeneous near surface systems. Moreover, a main advantage of this iterative geostatistical FDEM inversion method is its ability to flexibly integrate data with different resolution in the same framework.</p><p>In this work, we apply this iterative geostatistical FDEM inversion technique, which has already been successfully demonstrated for one- and two-dimensional applications, to invert a real case FDEM data set in three dimensions. The FDEM survey data set was collected on a site located near Knowlton (Dorset, UK), which is geologically characterized by Cretaceous chalk overlain by Quaternary siliciclastic sand deposits. The subsurface at the site is known to contain several archaeological features, which produces strong local in-phase anomalies in the FDEM survey data. We discuss the particular challenges involved in the three-dimensional application of the inversion method to a real case data set and compare our results against previously obtained ones for one- and two-dimensional approximations.</p>

Kinematics and statistics of dense, slow granular flow through vertical channels

2008 ◽  
Vol 610 ◽  
pp. 69-97 ◽  
Author(s):  
ANANDA K. S. ◽  
SUDHESHNA MOKA ◽  
PRABHU R. NOTT
Keyword(s):  
Granular Materials ◽  
Spatial Correlation ◽  
Deformation Rate ◽  
Three Dimensional ◽  
Thin Layers ◽  
Image Processing Technique ◽  
Plasticity Model ◽  
Two Dimensional ◽  
Velocity Fluctuations ◽  
Macroscopic Deformation

We have investigated the flow of dry granular materials through vertical channels in the regime of dense slow flow using video imaging of the particles adjacent to a transparent wall. Using an image processing technique based on particle tracking velocimetry, the video movies were analysed to obtain the velocities of individual particles. Experiments were conducted in two- and three-dimensional channels. In the latter, glass beads and mustard seeds were used as model granular materials, and their translational velocities were measured. In the former, aluminium disks with a dark diametral stripe were used and their translational velocities and spin were measured. Experiments in the three-dimensional channels were conducted for a range of the channel width W, and for smooth and rough sidewalls. As in earlier studies, we find that shearing takes place predominantly in thin layers adjacent to the walls, while the rest of the material appears to move as a plug. However, there are large velocity fluctuations even in the plug, where the macroscopic deformation rate is negligibly small. The thickness of the shear layer, scaled by the particle diameter dp, increases weakly with W/dp. The experimental data for the velocity field are in good agreement with the Cosserat plasticity model proposed recently. We also measured the mean spin of the particles in the two-dimensional channel, and its deviation from half the vorticity. There is a clear, measurable deviation, which too is in qualitative agreement with the Cosserat plasticity model. The statistics of particle velocity and spin fluctuations in the two-dimensional channel were analysed by determining their probability distribution function, and their spatial and temporal correlation. They were all found to be broadly similar to previous observations for three-dimensional channels, but some differences are evident. The spatial correlation of the velocity fluctuations are much stronger in the two-dimensional channel, implying a pronounced solid-like motion superimposed over an uncorrelated fluid-like motion. The strong spatial correlation over large distances has led us to propose a mechanism for the production of velocity fluctuations in the absence of a macroscopic deformation rate.

Magnetic damping of jets and vortices

1995 ◽  
Vol 299 ◽  
pp. 153-186 ◽  
Author(s):  
P. A. Davidson
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Angular Momentum ◽  
Kinetic Energy ◽  
Lorentz Force ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Magnetic Damping ◽  
Field Lines ◽  
The Magnetic Field

It is well known that the imposition of a static magnetic field tends to suppress motion in an electrically conducting liquid. Here we look at the magnetic damping of liquid-mental flows where the Reynolds number is large and the magnetic Reynolds number is small. The magnetic field is taken as uniform and the fluid is either infinite in extent or else bounded by an electrically insulating surface S. Under these conditions, we find that three general principles govern the flow. First, the Lorentz force destroys kinetic energy but does not alter the net linear momentum of the fluid, nor does it change the component of angular momentum parallel to B. In certain flows, this implies that momentum, linear or angular, is conserved. Second, the Lorentz force guides the flow in such a way that the global Joule dissipation, D, decreases, and this decline in D is even more rapid than the corresponding fall in global kinetic energy, E. (Note that both D and E are quadratic in u). Third, this decline in relative dissipation, D / E, is essential to conserving momentum, and is achieved by propagating linear or angular momentum out along the magnetic field lines. In fact, this spreading of momentum along the B-lines is a diffusive process, familiar in the context of MHD turbulence. We illustrate these three principles with the aid of a number of specific examples. In increasing order of complexity we look at a spatially uniform jet evolving in time, a three-dimensional jet evolving in space, and an axisymmetric vortex evolving in both space and time. We start with a spatially uniform jet which is dissipated by the sudden application of a transverse magnetic field. This simple (perhaps even trivial) example provides a clear illustration of our three general principles. It also provides a useful stepping-stone to our second example of a steady three-dimensional jet evolving in space. Unlike the two-dimensional jets studied by previous investigators, a three-dimensional jet cannot be annihilated by magnetic braking. Rather, its cross-section deforms in such a way that the momentum flux of the jet is conserved, despite a continual decline in its energy flux. We conclude with a discussion of magnetic damping of axisymmetric vortices. As with the jet flows, the Lorentz force cannot destroy the motion, but rather rearranges the angular momentum of the flow so as to reduce the global kinetic energy. This process ceases, and the flow reaches a steady state, only when the angular momentum is uniform in the direction of the field lines. This is closely related to the tendency of magnetic fields to promote two-dimensional turbulence.

scholarly journals Analytical solutions for algebraic growth of disturbances in a stably stratified shear flow

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150267 ◽  
Author(s):  
Sharath Jose ◽  
Anubhab Roy ◽  
Rahul Bale ◽  
Rama Govindarajan
Keyword(s):  
Kinetic Energy ◽  
Linear Growth ◽  
Three Dimensional ◽  
Density Perturbation ◽  
Three Dimensions ◽  
Constant Density ◽  
Two Dimensional ◽  
Final Study ◽  
Density Flow ◽  
Diffusive Effects

We investigate analytically the short-time response of disturbances in a density-varying Couette flow without viscous and diffusive effects. The complete inviscid problem is also solved as an initial value problem with a density perturbation. We show that the kinetic energy of the disturbances grows algebraically at early times, contrary to the well-known algebraic decay at time tending to infinity. This growth can persist for arbitrarily long times in response to sharp enough initial perturbations. The simplest in our three-stage study is a model problem forced by a buoyancy perturbation in the absence of background stratification. A linear growth with time is obtained in the vertical velocity component. This model provides an analogy between the transient mechanism of kinetic energy growth in a two-dimensional density-varying flow and the lift-up mechanism of the three-dimensional constant density flow. Next we consider weak stable background stratification. Interestingly, the lowest order solution here is the same as that of the model flow. Our final study shows that a strong background stratification results in a sub-linear growth with time of the perturbation. A framework is thus presented where two-dimensional streamwise disturbances can lead to large transient amplification, unlike in constant density flow where three dimensions are required.

scholarly journals The Submesoscale Kinetic Energy Cascade: Mesoscale Absorption of Submesoscale Mixed Layer Eddies and Frontal Downscale Fluxes

2020 ◽  
Vol 50 (9) ◽  
pp. 2573-2589 ◽  
Author(s):  
René Schubert ◽  
Jonathan Gula ◽  
Richard J. Greatbatch ◽  
Burkard Baschek ◽  
Arne Biastoch
Keyword(s):  
Kinetic Energy ◽  
Mixed Layer ◽  
Current System ◽  
Mesoscale Eddies ◽  
Coarse Graining ◽  
Early Summer ◽  
Surface Fluxes ◽  
Energy Cascade ◽  
Near Surface ◽  
Agulhas Current

AbstractMesoscale eddies can be strengthened by the absorption of submesoscale eddies resulting from mixed layer baroclinic instabilities. This is shown for mesoscale eddies in the Agulhas Current system by investigating the kinetic energy cascade with a spectral and a coarse-graining approach in two model simulations of the Agulhas region. One simulation resolves mixed layer baroclinic instabilities and one does not. When mixed layer baroclinic instabilities are included, the largest submesoscale near-surface fluxes occur in wintertime in regions of strong mesoscale activity for upscale as well as downscale directions. The forward cascade at the smallest resolved scales occurs mainly in frontogenetic regions in the upper 30 m of the water column. In the Agulhas ring path, the forward cascade changes to an inverse cascade at a typical scale of mixed layer eddies (15 km). At the same scale, the largest sources of the upscale flux occur. After the winter, the maximum of the upscale flux shifts to larger scales. Depending on the region, the kinetic energy reaches the mesoscales in spring or early summer aligned with the maximum of mesoscale kinetic energy. This indicates the importance of submesoscale flows for the mesoscale seasonal cycle. A case study shows that the underlying process is the mesoscale absorption of mixed layer eddies. When mixed layer baroclinic instabilities are not included in the simulation, the open-ocean upscale cascade in the Agulhas ring path is almost absent. This contributes to a 20% reduction of surface kinetic energy at mesoscales larger than 100 km when submesoscale dynamics are not resolved by the model.

MAGNETIC COLLIMATION AND MAGNETOHYDRODYNAMIC KINK INSTABILITY DRIVEN BY DIFFERENTIAL ROTATION

2008 ◽  
Vol 17 (10) ◽  
pp. 1707-1713 ◽  
Author(s):  
C. S. CAREY ◽  
C. R. SOVINEC ◽  
S. HEINZ ◽  
J. E. EVERETT
Keyword(s):  
Growth Rate ◽  
Accretion Disk ◽  
Differential Rotation ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Small Scale ◽  
Two Dimensional ◽  
Extragalactic Jets ◽  
Magnetohydrodynamic Simulations ◽  
Kink Instability

We investigate the launching and stability of extragalactic jets through magnetohydrodynamic simulations of jet evolution. In these simulations, a small scale equilibrium magnetic corona is twisted by a differentially rotating accretion disk. Two-dimensional calculations show the formation of a collimated outflow. This outflow is divided into two regions by the Alfvén surface: a magnetically dominated Poynting region, and a kinetically dominated region. Three-dimensional calculations show that the outflow is unstable to the m = 1 kink instability, and that the growth rate of the kink instability decreases as the rotation rate of the accretion disk increases.

Investigation of residual stress distribution induced during deep rolling of Ti-6Al-4V alloy

2020 ◽  
Vol 235 (1-2) ◽  
pp. 186-197
Author(s):  
Kunpeng Han ◽  
Dinghua Zhang ◽  
Changfeng Yao ◽  
Liang Tan ◽  
Zheng Zhou ◽  
...  
Keyword(s):  
Residual Stress ◽  
Compressive Residual Stress ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Circumferential Direction ◽  
Two Dimensional ◽  
Deep Rolling ◽  
Three Dimensional Model ◽  
Surface Residual Stress ◽  
Near Surface

To clarify the effects of deep rolling parameters on residual stress, two-dimensional and three-dimensional finite element models were developed using the Chaboche hardening model. Both two-dimensional and three-dimensional simulation results were compared with experimental results. The three-dimensional model is more accurate, especially the 90° cut-out model. The maximum errors in the longitudinal and circumferential directions of 90° cut-out are 8.9% and 15.6%, respectively. Compared to 20 MPa, a rolling pressure of 38 MPa results in larger and deeper compressive residual stress in both directions, but lower surface residual stress in the circumferential direction. Compared to 30% overlap, 60% overlap produces larger compressive residual stress in the near surface region in the longitudinal direction and deeper residual stress with lower maximum compressive residual stress in the circumferential direction. The friction coefficient only slightly affects residual stress in the circumferential direction; increasing the rolling speed induces higher near surface residual stress in the circumferential direction. Compared to the HG6 tool, the HG8 tool generates decreasing surface residual stresses and deeper residual stress in both directions. Compared to one pass, two passes significantly increase the residual stress in circumferential direction, but only slightly increase the residual stress in the longitudinal direction.

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