scholarly journals Vertical Transition in Transport and Mixing in Baroclinic Flows

2008 ◽  
Vol 65 (4) ◽  
pp. 1137-1157 ◽  
Author(s):  
M. D. Greenslade ◽  
P. H. Haynes
Keyword(s):  
Relaxation Rate ◽  
Channel Model ◽  
Gaussian Function ◽  
Plane Channel ◽  
Lower Boundary ◽  
Thermal Relaxation ◽  
Vertical Shear ◽  
Large Set ◽  
Transport Barrier ◽  
Transport And Mixing

Abstract Numerical simulations in multilevel baroclinic turbulence in a β-plane channel model are discussed, focusing on the transport and mixing behavior. The temperature field in the model is relaxed toward a field consistent with a broad zonal jet with vertical shear that is a Gaussian function of the cross-channel coordinate. The resulting statistical equilibrium flow includes an active baroclinic eddy field. The transport and mixing properties are analyzed by considering the fields of potential vorticity and a passive tracer (from which effective diffusivities/equivalent lengths are calculated). The upper part of the flow organizes itself in such a way that there is a transport barrier in the center of the channel, with eddy mixing regions on either side. In the lower part of the flow the eddy mixing occurs across a single broad region, with no central transport barrier. The transition between these two regimes takes place abruptly at a height zT. A large set of simulations is used to map out the variation of zT as a function of external parameters including β, the thermal relaxation rate κT, and the (lower boundary) frictional relaxation rate κM (applied in the lowest model layer only). The transition height zT is argued to be relevant to sharp vertical transitions in transport and mixing observed in atmospheric and oceanic flows.

scholarly journals Instabilities of continuously stratified zonal equatorial jets in a periodic channel model

2002 ◽  
Vol 20 (5) ◽  
pp. 729-740 ◽  
Author(s):  
S. Masina
Keyword(s):  
Channel Model ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Maximum Velocity ◽  
Equatorial Region ◽  
Eastern Pacific ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Scale ◽  
Surface Jet

Abstract. Several numerical experiments are performed in a nonlinear, multi-level periodic channel model centered on the equator with different zonally uniform background flows which resemble the South Equatorial Current (SEC). Analysis of the simulations focuses on identifying stability criteria for a continuously stratified fluid near the equator. A 90 m deep frontal layer is required to destabilize a zonally uniform, 10° wide, westward surface jet that is symmetric about the equator and has a maximum velocity of 100 cm/s. In this case, the phase velocity of the excited unstable waves is very similar to the phase speed of the Tropical Instability Waves (TIWs) observed in the eastern Pacific Ocean. The vertical scale of the baroclinic waves corresponds to the frontal layer depth and their phase speed increases as the vertical shear of the jet is doubled. When the westward surface parabolic jet is made asymmetric about the equator, in order to simulate more realistically the structure of the SEC in the eastern Pacific, two kinds of instability are generated. The oscillations that grow north of the equator have a baroclinic nature, while those generated on and very close to the equator have a barotropic nature.  This study shows that the potential for baroclinic instability in the equatorial region can be as large as at mid-latitudes, if the tendency of isotherms to have a smaller slope for a given zonal velocity, when the Coriolis parameter vanishes, is compensated for by the wind effect.Key words. Oceanography: general (equatorial oceanography; numerical modeling) – Oceanography: physics (fronts and jets)

scholarly journals Nonlinear Saturation of Vertically Propagating Rossby Waves

2009 ◽  
Vol 66 (4) ◽  
pp. 915-934 ◽  
Author(s):  
Constantine Giannitsis ◽  
Richard S. Lindzen
Keyword(s):  
Wave Propagation ◽  
Channel Model ◽  
Plane Channel ◽  
Nonlinear Flow ◽  
Computational Domain ◽  
Mean Flow ◽  
Wave Interactions ◽  
Linear Solution ◽  
Wave Growth ◽  
Flow Interactions

Abstract The interaction between vertical Rossby wave propagation and wave breaking is studied in the idealized context of a beta-plane channel model. Considering the problem of propagation through a uniform zonal flow in an exponentially stratified fluid, where linear theory predicts exponential wave growth with height, the question is how wave growth is limited in the nonlinear flow. Using a numerical model, the authors examine the behavior of the flow as the bottom forcing increases through values bound to lead to a breakdown of the linear solution within the computational domain. Focusing on the equilibrium flow obtained for each value of the bottom forcing, an attempt is made to identify the mechanisms involved in limiting wave growth and examine in particular the importance of wave–wave interactions. The authors also examine the case in which forcing is continuously increasing with time so as to enhance effects peculiar to transiency; it does not significantly alter the main results. Wave–mean flow interactions are found to dominate the dynamics even for strong bottom forcing values. Ultimately, it is the modification of the mean flow that is found to limit the vertical penetration of the forced wave, through either increased wave absorption or downward reflection. Linear propagation theory is found to capture the wave structure surprisingly well, even when the total flow is highly deformed. Overall, the numerical results seem to suggest that wave–wave interactions do not have a strong direct effect on the propagating disturbance. Wave–mean flow interactions limit wave growth sufficiently that a strong additional nonlinear enstrophy sink, through downscale cascade, is not necessary. Quantitatively, however, wave–wave interactions, primarily among the lowest wavenumbers, prove important so as to sufficiently accurately determine the basic state and its influence on wave propagation.

scholarly journals Buoyancy-driven flow in a confined aquifer with a vertical gradient of permeability

2018 ◽  
Vol 848 ◽  
pp. 411-429 ◽  
Author(s):  
Edward M. Hinton ◽  
Andrew W. Woods
Keyword(s):  
Rarefaction Wave ◽  
Pore Space ◽  
Lower Boundary ◽  
Leading Edge ◽  
Vertical Gradient ◽  
Vertical Shear ◽  
Classical Solutions ◽  
The Novel ◽  
Two Fluids ◽  
Gradient Of Permeability

We examine the injection of fluid of one viscosity and density into a horizontal permeable aquifer initially saturated with a second fluid of different viscosity and density. The novel feature of the analysis is that we allow the permeability to vary vertically across the aquifer. This leads to recognition that the interface may evolve as either a rarefaction wave that spreads at a rate proportional to $t$, a shock-like front of fixed length or a mixture of shock-like regions and rarefaction-wave-type regions. The classical solutions in which there is no viscosity ratio between the fluids and in which the formation has constant permeability lead to an interface that spreads laterally at a rate proportional to $t^{1/2}$. However, these solutions are unstable to cross-layer variations in the permeability owing to the vertical shear which develops in the flow, causing the structure of the interface to evolve to the rarefaction wave or shock-like structure. In the case that the viscosities of the two fluids are different, it is possible that the solution involves a mixture of shock-like and rarefaction-type structures as a function of the distance above the lower boundary. Using the theory of characteristics, we develop a regime diagram to delineate the different situations. We consider the implications of such heterogeneity for the prediction of front locations during $\text{CO}_{2}$ sequestration. If we neglect the permeability fluctuations, the model always predicts rarefaction-type solutions, while even modest changes in the permeability across a layer can introduce shocks. This difference may be very significant since it leads to the $\text{CO}_{2}$ plume occupying a greater fraction of the pore space between the injector and the leading edge of the $\text{CO}_{2}$ front in a layer of the same mean permeability. This has important implications for estimates of the fraction of the pore space that the $\text{CO}_{2}$ may access.

Transport and Mixing in Kinematic and Dynamically Consistent Flows

2007 ◽  
Vol 64 (10) ◽  
pp. 3640-3651 ◽  
Author(s):  
P. H. Haynes ◽  
D. A. Poet ◽  
E. F. Shuckburgh
Keyword(s):  
Large Range ◽  
Vorticity Field ◽  
Transport Barrier ◽  
Multiple Jets ◽  
Mixing Behavior ◽  
Transport Barriers ◽  
Flow Evolution ◽  
Transport And Mixing ◽  
Dynamical Consistency ◽  
Strong Vorticity

Abstract The interplay between dynamics and transport in two-dimensional flows is examined by comparing the transport and mixing in a kinematic flow in which the velocity field is imposed as a given function of time with that in an analogous dynamically consistent flow in which the advected vorticity field controls the flow evolution. In both cases the variation of the transport and mixing behavior with a parameter ε governing the strength of the time dependence is considered. It is shown that dynamical consistency has the effect of (i) postponing the breaking of a central transport barrier as ε increases and (ii) removing the property of the kinematic flow that, for a large range of ε, a weakly permeable central barrier persists. The first effect is associated with the development of a strong vorticity gradient and the associated jet along the central transport barrier. The second effect is associated with the fact that, in the dynamically consistent flow, the breaking of the central barrier is accompanied by a drastic change in the vorticity field and hence in the structure of the flow. The relation between the vorticity field and transport barriers is further examined using a range of simple kinematic and dynamically consistent models. Implications for formulation of predictive models that represent the interactions between dynamics, transport, and mixing (and might be suggested as a basis for parameterizing eddies in flows that form multiple jets) are discussed.

scholarly journals Spatial Transformations in the Parietal Cortex Using Basis Functions

1997 ◽  
Vol 9 (2) ◽  
pp. 222-237 ◽  
Author(s):  
Alexandre Pouget ◽  
Terrence J. Sejnowski
Keyword(s):  
Parietal Cortex ◽  
Reference Frames ◽  
Gaussian Function ◽  
Basis Functions ◽  
Basis Set ◽  
Large Set ◽  
Sigmoid Function ◽  
Computationally Efficient ◽  
Function Decomposition ◽  
Sensorimotor Transformations

Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We compare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.

General Properties of Thermal-Relaxation Rate Equations

1973 ◽  
Vol 8 (7) ◽  
pp. 3487-3487
Author(s):  
M. W. P. Strandberg ◽  
J. R. Shane
Keyword(s):  
Relaxation Rate ◽  
Thermal Relaxation ◽  
Rate Equations ◽  
General Properties

scholarly journals Seasonal cycles and variability of O<sub>3</sub> and H<sub>2</sub>O in the UT/LMS during SPURT

2006 ◽  
Vol 6 (1) ◽  
pp. 109-125 ◽  
Author(s):  
M. Krebsbach ◽  
C. Schiller ◽  
D. Brunner ◽  
G. Günther ◽  
M. I. Hegglin ◽  
...  
Keyword(s):  
Trace Gases ◽  
Distribution Functions ◽  
Trace Gas ◽  
Large Set ◽  
Transport Barrier ◽  
Tropical Tropopause ◽  
Time Period ◽  
Data Coverage ◽  
Insight Into

Abstract. Airborne high resolution in situ measurements of a large set of trace gases including ozone (O3) and total water (H2O) in the upper troposphere and the lowermost stratosphere (UT/LMS) have been performed above Europe within the SPURT project. SPURT provides an extensive data coverage of the UT/LMS in each season within the time period between November 2001 and July 2003. In the LMS a distinct spring maximum and autumn minimum is observed in O3, whereas its annual cycle in the UT is shifted by 2–3 months later towards the end of the year. The more variable H2O measurements reveal a maximum during summer and a minimum during autumn/winter with no phase shift between the two atmospheric compartments. For a comprehensive insight into trace gas composition and variability in the UT/LMS several statistical methods are applied using chemical, thermal and dynamical vertical coordinates. In particular, 2-dimensional probability distribution functions serve as a tool to transform localised aircraft data to a more comprehensive view of the probed atmospheric region. It appears that both trace gases, O3 and H2O, reveal the most compact arrangement and are best correlated in the view of potential vorticity (PV) and distance to the local tropopause, indicating an advanced mixing state on these surfaces. Thus, strong gradients of PV seem to act as a transport barrier both in the vertical and the horizontal direction. The alignment of trace gas isopleths reflects the existence of a year-round extra-tropical tropopause transition layer. The SPURT measurements reveal that this layer is mainly affected by stratospheric air during winter/spring and by tropospheric air during autumn/summer. Normalised mixing entropy values for O3 and H2O in the LMS appear to be maximal during spring and summer, respectively, indicating highest variability of these trace gases during the respective seasons.

scholarly journals Inventory, Distribution and Geometric Characteristics of Landslides in Baoshan City, Yunnan Province, China

2020 ◽  
Vol 12 (6) ◽  
pp. 2433 ◽  
Author(s):  
Xiaoyi Shao ◽  
Siyuan Ma ◽  
Chong Xu ◽  
Lingling Shen ◽  
Yongkun Lu
Keyword(s):  
Spatial Distribution ◽  
Yunnan Province ◽  
Lower Boundary ◽  
Google Earth ◽  
Landslide Susceptibility Mapping ◽  
Slope Position ◽  
Large Set ◽  
Geologic Hazard ◽  
Geometric Characteristics ◽  
High Resolution Satellite Images

Inventorying landslides in mountainous areas is of great importance for prevention of geologic hazards. This study aimed to establish a detailed landslide inventory of Baoshan City, Yunnan Province, China, based on a large set of high-resolution satellite images from Google Earth. The landslides of this region were divided into two groups, i.e., recent landslides and old landslides. The spatial distribution and geometric characteristics of the two kinds of landslides were analyzed, respectively. Results show that 2427 landslides are present in the study area, including 2144 recent landslides and 283 old landslides with a total area of 7.2 km2 and 97.6 km2, respectively. The recent landslides occurred primarily at steep slopes with higher elevation, while old landslides took place at gentle terrains. For the slope position, most landslides, whether old or recent, cluster near ridges. The lower boundary of the recent landslides is far away from the valley, while the accumulation area of the old landslide is closer to the valley. The H/L (height to length) ratios are basically the same for all landslides, ranging from 0.2 to 0.5. Old landslides have larger mobility, as their travel distances are longer than recent landslides at the same height. The results would be helpful for further understanding the development and spatial distribution of the landslides in Southwest China, and also provide essential support for the subsequent landslide susceptibility mapping and geologic hazard assessment in this area.

General Properties of Thermal-Relaxation Rate Equations

1973 ◽  
Vol 7 (11) ◽  
pp. 4809-4812 ◽  
Author(s):  
M. W. P. Strandberg ◽  
J. R. Shane
Keyword(s):  
Relaxation Rate ◽  
Thermal Relaxation ◽  
Rate Equations ◽  
General Properties

Subduction channel vs. orogenic wedge model: numerical simulations, impact of serpentinites and application to the Alps

2020 ◽  
Author(s):  
Lorenzo G. Candioti ◽  
Stefan M. Schmalholz ◽  
Thibault Duretz
Keyword(s):  
Channel Model ◽  
Thermal Relaxation ◽  
Passive Margin ◽  
Crustal Material ◽  
Subduction Channel ◽  
Passive Margins ◽  
Coupled Equations ◽  
Orogenic Wedge ◽  
Simulation Results ◽  
The Impact

&lt;p&gt;In this study, we use a state-of-the-art 2D numerical algorithm solving the standard thermo-mechanically coupled equations of continuum mechanics for slow flowing viscoelastoplastic material to model the evolution of rifting, thermal relaxation and convergence-to-collision of Alpine-type orogens in three stages. (1) A ca. 360 km wide basin that is floored by exhumed mantle and bounded by two conjugate magma-poor hyper-extended passive margins is generated during a 50 Myrs rifting period. An absolute extension velocity of 1 cm/yr is applied. (2) The passive margin system is thermally equilibrated during a subsequent cooling period of 60 Myrs without significant deformation in the lithosphere (no extension velocity). At this stage, we parameterise a serpentinization front on top of the exhumed mantle by replacing the dry peridotitic mantle by serpentinized mantle in one series of simulations. The thermally equilibrated system is used as a self-consistently generated initial configuration for the subsequent period of convergence lasting for 70 Myrs applying an absolute convergence velocity of 1.5 cm/yr. Values for the duration of deformation periods and for deformation velocities are chosen to allow for comparison between simulation results and petrological data from the Central and Western Alps. Density of all materials is either precomputed for characteristic bulk rock compositions and read in from precomputed thermodynamic look-up tables (Perple_X), or calculated during run time via a linearized equation of state (EOS).&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;We quantify (1) the impact of a serpentinization front of the exhumed mantle on the subduction dynamics by increasing systematically the strength of the serpentinites, (2) the peak pressure and temperature conditions of subducted crustal material from the passive margins of the overriding and subducting plate by tracking pressure (P)-temperature (T)-time (t)-depth (z) paths of selected particles and (3) the driving forces of the system. Last, (4) the impact of metamorphic phase transitions is investigated by parameterising densification of crustal material. We compare the results of simulations in which density is computed as a simple linearized EOS to results of simulations in which density is a more realistic function of P and T using precomputed thermodynamic look-up tables.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;We discuss geometric similarities between the simulation results and 2D geodynamic reconstructions from field data, quantify the P-T-t-z-history of selected particles and compare it to P-T-t data obtained from natural rocks. First results indicate that the strength of the serpentinites controls whether the deformation within the orogenic core is driven by buoyancy forces (subduction channel model) or by far-field tectonic forces (orogenic wedge model). There is a transition from subduction channel to orogenic wedge model from low to intermediate strength of the serpentinites.&lt;/p&gt;

Sign in / Sign up

Export Citation Format

Share Document