The Mexico Earthquake of September 19, 1985—A Theoretical Investigation of Large- and Small-scale Amplification Effects in the Mexico City Valley

1988 ◽  
Vol 4 (3) ◽  
pp. 609-633 ◽  
Author(s):  
P-Y. Bard ◽  
M. Campillo ◽  
F. J. Chávez-Garcia ◽  
F. Sánchez-Sesma
Keyword(s):  
Mexico City ◽  
Large Scale ◽  
Small Scale ◽  
Clay Layer ◽  
Local Surface ◽  
One Dimensional ◽  
Mexico Earthquake ◽  
The One ◽  
Deep Sediments ◽  
Lateral Heterogeneities

The linear, large-scale and small-scale amplification effects in the Mexico City valley, related to both the surficial clay layer and the underlying thick sediments, are investigated with two-dimensional (2D) models and compared with the results of simple one-dimensional (1D) models. The deep sediments are shown to be responsible, on their own, for an amplification ranging between 3 and 7, a part of which is due to the 2D effects in case of low damping and velocity gradient. This result is consistent with the observed relative amplification around 0.5 Hz at CU stations with respect to TACY station. The amplification due to the clay layer is much larger (above 10), and the corresponding 2D effects have very peculiar characteristics. On the one hand, the local surface waves generated on any lateral heterogeneity exhibit a strong spatial decay, even in case of low damping (2%), and the motion at a given site is therefore affected only by lateral heterogeneities lying within a radius smaller than 1 km. On the other hand, these local 2D effects may be extremely large, either on the very edges of the lake-bed zone, or over localized thicker areas, where they induce a duration increase and an overamplification. The main engineering consequences of these results are twofold: i) microzoning studies in Mexico City should take into account the effects of deep sediments, and ii) as the surface motion in the lake-bed zone is extremely sensitive to local heterogeneities, 1D models are probably inappropriate in many parts of Mexico City.

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

Nonlinear dynamics over rough topography: homogeneous and stratified quasi-geostrophic theory

2003 ◽  
Vol 474 ◽  
pp. 299-318 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Nonlinear Dynamics ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Small Scale ◽  
Stratified Fluids ◽  
Homogeneous Case ◽  
Bottom Boundary ◽  
One Dimensional ◽  
Averaged Equations ◽  
Large Scale Flow

The weakly nonlinear dynamics of quasi-geostrophic flows over a one-dimensional, periodic or random, small-scale topography is investigated using an asymptotic approach. Averaged (or homogenized) evolution equations which account for the flow–topography interaction are derived for both homogeneous and continuously stratified quasi-geostrophic fluids. The scaling assumptions are detailed in each case; for stratified fluids, they imply that the direct influence of the topography is confined within a thin bottom boundary layer, so that it is through a new bottom boundary condition that the topography affects the large-scale flow. For both homogeneous and stratified fluids, a single scalar function entirely encapsulates the properties of the topography that are relevant to the large-scale flow: it is the correlation function of the topographic height in the homogeneous case, and a linear transform thereof in the continuously stratified case.Some properties of the averaged equations are discussed. Explicit nonlinear solutions in the form of one-dimensional travelling waves can be found. In the homogeneous case, previously studied by Volosov, they obey a second-order differential equation; in the stratified case on which we focus they obey a nonlinear pseudodifferential equation, which reduces to the Peierls–Nabarro equation for sinusoidal topography. The known solutions to this equation provide examples of nonlinear periodic and solitary waves in continuously stratified fluid over topography.The influence of bottom topography on large-scale baroclinic instability is also examined using the averaged equations: they allow a straightforward extension of Eady's model which demonstrates the stabilizing effect of topography on baroclinic instability.

The story of humanity and the challenge of posthumanity

2018 ◽  
Vol 32 (2) ◽  
pp. 101-120 ◽  
Author(s):  
Zoltán Boldizsár Simon
Keyword(s):  
Human Subject ◽  
Large Scale ◽  
Historical Narrative ◽  
Historical Narratives ◽  
Small Scale ◽  
Historical Understanding ◽  
New Era ◽  
And Gender ◽  
The One ◽  
Better Than

Today’s technological-scientific prospect of posthumanity simultaneously evokes and defies historical understanding. On the one hand, it implies a historical claim of an epochal transformation concerning posthumanity as a new era. On the other, by postulating the birth of a novel, better-than-human subject for this new era, it eliminates the human subject of modern Western historical understanding. In this article, I attempt to understand posthumanity as measured against the story of humanity as the story of history itself. I examine the fate of humanity as the central subject of history in three consecutive steps: first, by exploring how classical philosophies of history achieved the integrity of the greatest historical narrative of history itself through the very invention of humanity as its subject; second, by recounting how this central subject came under heavy criticism by postcolonial and gender studies in the last half-century, targeting the universalism of the story of humanity as the greatest historical narrative of history; and third, by conceptualizing the challenge of posthumanity against both the story of humanity and its criticism. Whereas criticism fragmented history but retained the possibility of smaller-scale narratives, posthumanity does not doubt the feasibility of the story of humanity. Instead, it necessarily invokes humanity, if only in order to be able to claim its supersession by a better-than-human subject. In that, it represents a fundamental challenge to the modern Western historical condition and the very possibility of historical narratives – small-scale or large-scale, fragmented or universal.

Process Optimization of One-Stage Propane Pre-Cooled MRC Cycle for Small-Scale LNG Plant

2012 ◽  
Vol 516-517 ◽  
pp. 1184-1187
Author(s):  
Heng Sun ◽  
Dan Shu ◽  
Hong Mei Zhu
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Process Parameters ◽  
Large Scale ◽  
High Energy ◽  
Small Scale ◽  
Main Process ◽  
One Stage ◽  
High Energy Efficiency ◽  
The One

One-stage pre-cooled mixture refrigerant cycle can be applied in small-scale LNG plant and be special suitable for skit mounted LNG plant. It has different character with the C3MR cycle used in large-scale LNG plant. The optimization of the mixture refrigerant is carried out using HYSYS software. The effect of the main process parameters on the performance of the cycle is calculated and discussed. The result shows that appropriate ranges of the process parameters exist. Higher and lower values of the parameters will increase the energy consumption significantly. The results also indicate that the optimization of the one-stage pre-cooled mixture refrigerant cycle can obtain rather high energy efficiency that is competitive with that of the SMR which is widely employed in small-scale LNG plant.

Response spectra of earthquakes on very soft clay

1964 ◽  
Vol 54 (3) ◽  
pp. 855-866
Author(s):  
J. I. Bustamante
Keyword(s):  
Mexico City ◽  
Soft Clay ◽  
Response Spectra ◽  
Wave Reflections ◽  
General Shape ◽  
Dimensional Theory ◽  
Multiple Wave ◽  
One Dimensional ◽  
Velocity Spectra ◽  
The One

Abstract The response spectra of two strong and two mild earthquakes recorded on the thick lacustrine formation of Mexico City in 1961 and 1962 are presented. The velocity spectra of the two strong ones are compared with studies made independently by Jennings. Discrepancies there-with are explained in terms of wave reflections. A criterion to simplify data reduction and spectrum computations is supported by these comparisons. Velocity and pseudovelocity spectra are practically alike. The period corresponding to the maximum peak and the general shape of these curves agree closely with those predicted applying the one-dimensional theory of multiple wave reflections to the formations in question.

Modeling Transient Churn-Annular Flows in a Long Vertical Pipe

2013 ◽  
Author(s):  
M. V. C. Alves ◽  
J. R. Barbosa ◽  
P. J. Waltrich ◽  
G. Falcone
Keyword(s):  
Annular Flow ◽  
Large Scale ◽  
Coefficient Matrix ◽  
Vertical Tube ◽  
Flow Conditions ◽  
Vertical Pipe ◽  
One Dimensional ◽  
The One ◽  
Energy Equations ◽  
Liquid Flows

A mathematical model is presented to describe the behavior of transient gas-liquid flows involving the churn and annular flow patterns in a long vertical tube. The HyTAF (Hyperbolic Transient Annular Flow) code, developed specifically for this study, is based on the one-dimensional multi-fluid formulation and takes account of hydrodynamic non-equilibrium flow conditions by means of relationships for the rates of droplet entrainment and deposition. A finite difference algorithm is employed to solve the hyperbolic system of mass, momentum and energy equations via the Split Coefficient Matrix Method. The modeling results are compared with experimental data for steady-state annular and churn flows obtained from the literature and with pressure and flow rate induced transient churn-annular flow data generated in a large scale facility (48-mm ID, 42-m long test section).

A power series formulation for two-dimensional wildfire shapes

2016 ◽  
Vol 25 (9) ◽  
pp. 970 ◽  
Author(s):  
J. E. Hilton ◽  
C. Miller ◽  
A. L. Sullivan
Keyword(s):  
Power Series ◽  
Small Scale ◽  
Two Dimensional ◽  
One Dimensional ◽  
Rate Of Spread ◽  
Mathematical Expressions ◽  
Fire Front ◽  
Small Set ◽  
Prediction Systems ◽  
The One

Computational simulations of wildfires require a model for the two-dimensional expansion of a fire perimeter. Although many expressions exist for the one-dimensional rate of spread of a fire front, there are currently no agreed mathematical expressions for the two-dimensional outward speed of a fire perimeter. Multiple two-dimensional shapes such as elliptical and oval-shaped perimeters have been observed and reported in the literature, and several studies have attempted to classify these shapes using geometric approximations. Here we show that a two-dimensional outward speed based on a power series results in a perimeter that can match many of these observed shapes. The power series is based on the dot product between the vector normal to the perimeter and a fixed wind vector. The formulation allows the evolution and shape of a fire perimeter to be expressed using a small set of scalar coefficients. The formulation is implemented using the level set method, and computed perimeters are shown to provide a good match to perimeters of small-scale experimental fires. The method could provide a framework for statistical matching of wildfire shapes or be used to improve current wildfire prediction systems.

Dynamics of interaction of vortices in shear turbulent flows

2021 ◽  
Vol 102 (2) ◽  
pp. 56-67
Author(s):  
A.Zh. Turmukhambetov ◽  
◽  
S.B. Otegenova ◽  
K.A. Aitmanova ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Equations Of Motion ◽  
Vortex Structures ◽  
Small Scale ◽  
Two Dimensional ◽  
Practical Applications ◽  
Kinematic Effect ◽  
The One

The paper analyzes the results of a theoretical study of quasi-two-dimensional turbulence, two-dimensional equations of motion of which contain additional terms. The regularities of the dynamic interaction of vortex structures in shear turbulent flows of a viscous liquid are established. Based on the model of quasi-twodimensional turbulence, numerical values of the spatial scales of intermittency are determined as an alternation of large-scale and small-scale pulsations of dynamic characteristics. The experimentally observed alternation of vortex structures and the idea of their self-organization form the basis of the assumption of the existence of a geometric parameter determined by the size of the vortex core and the distance between their centers. Therefore, the main attention is paid to the theoretical calculation of the minimum spatial scales of the intermittency of vortex clusters. As a simplification, the vortex pairs are located in a reference frame, relative to which the centers of the vortices are stationary. Thus, the kinematic effect of the transfer of one vortex into the field of another is excluded from consideration. The symmetric and unsymmetric interactions of vortices, taking into account the one-sided and opposite directions of their rotation, are considered as realizable cases. A successful attempt is made to study the influence of the internal structure of vortex clusters on the numerical values of the minimum intermittency scales. The obtained results are satisfactorily confirmed by known theoretical and experimental data. Consequently, they can be used in all practical applications, without exception, where the structure of turbulence is taken into account, as well as for improving and expanding existing semi-empirical theories.

Some comparisons between heterogeneous and homogeneous layers for nonlinear SH waves in terms of heterogeneous and nonlinear effects

2020 ◽  
pp. 108128652094635 ◽  
Author(s):  
Dilek Demirkuş
Keyword(s):  
Solitary Wave ◽  
Large Scale ◽  
Multiple Scales ◽  
Nonlinear Effects ◽  
Small Scale ◽  
Solitary Wave Solutions ◽  
Nls Equation ◽  
Sh Waves ◽  
Wave Solutions ◽  
The One

This paper aims to make some comparative studies between heterogeneous and homogeneous layers for nonlinear shear horizontal (SH) waves in terms of the heterogeneous and nonlinear effects. Therefore, with this aim, two layers are defined as follows: on the one hand, one layer consists of hyperelastic, isotropic, heterogeneous, and generalized neo-Hookean materials; on the other hand, another layer is made up of hyperelastic, isotropic, homogeneous, and generalized neo-Hookean materials. Moreover, it is assumed that upper boundaries are stress-free and lower boundaries are rigidly fixed. The method of multiple scales is used in both analyses, in addition to using the known solutions of the nonlinear Schrödinger (NLS) equation, called bright and dark solitary wave solutions; these comparisons are made, numerically, and then all results are given for the lowest branch of both dispersion relations, graphically. Moreover, these comparisons are observed both on a large scale and on a small scale, not only in terms of the bright and dark solitary wave solutions but also in terms of the heterogeneous and nonlinear effects.

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