On the stability of a plate under longitudinal compression on a two-layer half-space with lower layer prestressed by gravity forces

2008 ◽  
Vol 43 (3) ◽  
pp. 487-493
Author(s):  
V. M. Alexandrov ◽  
D. I. Zarubov
Keyword(s):  
Half Space ◽  
Lower Layer ◽  
Longitudinal Compression ◽  
Gravity Forces ◽  
The Stability

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

Instability of quasi-geostrophic vortices in a two-layer ocean with a thin upper layer

2003 ◽  
Vol 475 ◽  
pp. 303-331 ◽  
Author(s):  
E. S. BENILOV
Keyword(s):  
Boundary Value Problem ◽  
Lower Layer ◽  
Boundary Value ◽  
Stability Boundary ◽  
Normal Modes ◽  
Layer Depth ◽  
Asymptotic Results ◽  
Gaussian Profile ◽  
Swirl Velocity ◽  
The Stability

We examine the stability of a quasi-geostrophic vortex in a two-layer ocean with a thin upper layer on the f-plane. It is assumed that the vortex has a sign-definite swirl velocity and is localized in the upper layer, whereas the disturbance is present in both layers. The stability boundary-value problem admits three types of normal modes: fast (upper-layer-dominated) modes, responsible for equivalent-barotropic instability, and two slow baroclinic types (mixed- and lower-layer-dominated modes). Fast modes exist only for unrealistically small vortices (with a radius smaller than half of the deformation radius), and this paper is mainly focused on the slow modes. They are examined by expanding the stability boundary-value problem in powers of the ratio of the upper-layer depth to the lower-layer depth. It is demonstrated that the instability of slow modes, if any, is associated with critical levels, which are located at the periphery of the vortex. The complete (sufficient and necessary) stability criterion with respect to slow modes is derived: the vortex is stable if and only if the potential-vorticity gradient at the critical level and swirl velocity are of the same sign. Several vortex profiles are examined, and it is shown that vortices with a slowly decaying periphery are more unstable baroclinically and less barotropically than those with a fast-decaying periphery, with the Gaussian profile being the most stable overall. The asymptotic results are verified by numerical integration of the exact boundary-value problem, and interpreted using oceanic observations.

scholarly journals Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1267
Author(s):  
Mikhail A. Sokolovskiy ◽  
Xavier J. Carton ◽  
Boris N. Filyushkin
Keyword(s):  
Large Scale ◽  
Lower Layer ◽  
Middle Layer ◽  
Vortex Interaction ◽  
Vortex Dipoles ◽  
The North ◽  
Surface Cyclone ◽  
Vertical Density ◽  
Quasigeostrophic Model ◽  
The Stability

The three-layer version of the contour dynamics/surgery method is used to study the interaction mechanisms of a large-scale surface vortex with a smaller vortex/vortices of the middle layer (prototypes of intrathermocline vortices in the ocean) belonging to the middle layer of a three-layer rotating fluid. The lower layer is assumed to be dynamically passive. The piecewise constant vertical density distribution approximates the average long-term profile for the North Atlantic, where intrathermocline eddies are observed most often at depths of 300–1600 m. Numerical experiments were carried out with different initial configurations of vortices, to evaluate several effects. Firstly, the stability of the vortex compound was evaluated. Most often, it remains compact, but when unstable, it can break as vertically coupled vortex dipoles (called hetons). Secondly, we studied the interaction between a vertically tilted cyclone and lenses. Then, the lenses first undergo anticlockwise rotation determined by the surface cyclone. The lenses can induce alignment or coupling with cyclonic vorticity above them. Only very weak lenses are destroyed by the shear stress exerted by the surface cyclone. Thirdly, under the influence of lens dipoles, the surface cyclone can be torn apart. In particular, the shedding of rapidly moving vortex pairs at the surface reflects the presence of lens dipoles below. More slowly moving small eddies can also be torn away from the main surface cyclone. In this case, they do not appear to be coupled with middle layer vortices. They are the result of large shear-induced deformation. Common and differing features of the vortex interaction, modeled in the framework of the theory of point and finite-core vortices, are noted.

On the Development of Transverse Ridges on Rock Glaciers

1989 ◽  
Vol 35 (121) ◽  
pp. 383-391 ◽  
Author(s):  
Deborah S. Loewenherz ◽  
Christopher J. Lawrence ◽  
Richard L. Weaver
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
Lower Layer ◽  
Elastic Solid ◽  
Surface Region ◽  
Finite Amplitude ◽  
Climatic Conditions ◽  
Rock Glacier ◽  
Rock Glaciers ◽  
The Stability

AbstractThe stability of a low Reynolds number flow on an inclined plane is investigated with respect to modelling the initiation of transverse wave-like ridges which commonly occur on the surfaces of rock-glacier forms. In accordance with field observations indicating the presence of stratification in rock glaciers, two models of rock-glacier structure are considered, each stratified and possessing a lower layer which is treated as a Newtonian fluid. An upper, less compliant layer is treated, alternatively, as a Newtonian fluid of viscosity greater than that of the lower layer, or as an elastic solid under longitudinal compression induced by a decrease in the slope of the underlying incline. A linear stability analysis is used to examine the behaviour of each of the proposed models, and both are found to generate instabilities at wavelengths comparable to those associated with transverse surficial ridges on rock glaciers. The growth rates of a flow disturbance predicted by the viscous-stratified model appear to be too slow to account fully for the development of wave forms of finite amplitude, suggesting that other mechanisms are involved in the amplification of an initial disturbance. The results of the stability analysis of the elastic lamina model indicate that finite surficial ridges may develop on rock glaciers as a product of a buckling instability in the surface region if there is a decrease in the slope of the underlying incline. Both of the analyses illustrate that transverse ridges can occur on the surface of a rock glacier in the absence of any variations in debris supply to the system. The results further imply that the use of these features in the paleoreconstruction of Holocene climatic conditions must entail an assessment of the relative roles of external climatically driven forcingversusinternal Theologically derived instability.

The Alekseev–Mikhailenko method applied to P–SV wave propagation in an elastic medium

1988 ◽  
Vol 25 (2) ◽  
pp. 226-234
Author(s):  
L. J. Pascoe ◽  
F. Hron ◽  
P. F. Daley
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Half Space ◽  
Elastic Half Space ◽  
Low Velocity ◽  
Seismic Modelling ◽  
Wave Propagation Problem ◽  
Modelling Techniques ◽  
Explicit Finite Difference ◽  
The Stability

The Alekseev–Mikhailenko method (AMM) is the name given to a series of algorithms that use one or more finite spatial transforms to reduce the dimensionality of a wave-propagation problem to that of one space dimension and time. This reduced equation is then solved using finite-difference techniques, and the space–time solution is recovered by applying inverse finite spatial transform(s). In this paper the elastodynamic wave equation that governs the coupled P–Sv motion in an isotropic, vertically inhomogeneous elastic half space is investigated using the AMM. Two types of impulsive body forces that may be used to excite the medium are examined, as is the problem of obtaining accurate transformed finite-difference analogues at the free surface. The second of these is accomplished by introducing the boundary conditions that the shear and normal stress must vanish here and by incorporating their transforms into the transformed elastodynamic equations. The stability criterion for the explicit finite-difference method is given cursory treatment, as detailed discussion of this aspect may be found in many texts that deal with the subject of finite differences.A coal-seam model (two thin, low-velocity layers embedded in a half space) illustrates the method. Both horizontal and vertical seismic traces are computed for this model and the results examined in relation to other seismic-modelling techniques.

scholarly journals То the synchronous work of pulsed sources of seismic waves

2019 ◽  
pp. 75-79
Author(s):  
S. P. Ekomasov
Keyword(s):  
Control System ◽  
Response Time ◽  
Half Space ◽  
Seismic Waves ◽  
Time Interval ◽  
Shock Interaction ◽  
Seismic Efficiency ◽  
Pulse Type ◽  
The Stability ◽  
The Moment

Researches have been made with the use of a hydropneumatic source of seismic waves. This source on the realized efforts of the shock interaction with a soil half-space considerably exceeds all known designs of radiators (sources) of pulse type. In this regard it shows higher seismic efficiency. The most important characteristic of the work of the pulse sources of seismic waves is a stability of the response time — a time interval from the moment of giving of a signal for producing of the blow until the very blow. Only with the achievement of the necessary stability the work in the mode of grouping of sources and accumulation of signals is possible. Features of the formation of response time of a hydropneumatic source are given. The analysis of the assessment of the parameters of synchronism of the pulse sources is made by a modem control system of their work. An influence of the rigidity of the soil on the assessment of stability of the response time and synchronism is shown. The system of the assessment of the stability used in the existing pulse sources at its application does not reflect the actual stability of response time in the radiators possessing a big force of blow.

scholarly journals The critical reflection theorem

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 965-972 ◽  
Author(s):  
Jacob T. Fokkema ◽  
Anton Ziolkowski
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Critical Reflection ◽  
Lower Layer ◽  
Plane Waves ◽  
Source Spectrum ◽  
Demarcation Criterion ◽  
The Earth ◽  
Reflection Theorem ◽  
Uppermost Layer

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

scholarly journals Upper-Bound Finite Element Adaptive Analysis of Plane Strain Heading in Soil with a Soft Upper Layer and Hard Lower Layer

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Zhang ◽  
Li Ding ◽  
Yu Liang ◽  
Jingyao Zong ◽  
Zhenya Li
Keyword(s):  
Finite Element ◽  
Failure Mechanism ◽  
Upper Bound ◽  
Lower Layer ◽  
Adaptive Strategy ◽  
Tunnel Face ◽  
Slip Lines ◽  
The Stability ◽  
Tunnel Depth ◽  
Soil Interface

This paper investigates the stability of a rectangular tunnel face affected by surcharge loading in soil with a soft upper layer and hard lower layer using upper-bound finite element methods with a plastic-dissipation-based mesh adaptive strategy (UBFEM-PDMA). Seven different positions for the soil interface are selected to study this problem. The upper bounds on the ultimate surcharge loads σs are presented in terms of dimensionless stability charts. The σs increases with tunnel depth, and it increases when the position of the soil interface moves up along the tunnel face. The failure mechanism primarily involves a wedge-shaped zone around the tunnel face and two slip lines originating from the top and bottom of the tunnel face, and it is mainly influenced by three factors, i.e., the position of the soil interface, the soil properties, and the tunnel depth. In contrast to the failure mechanism for uniform soil, multiple slip lines exist in the tunnel face in soil with a soft upper layer and hard lower layer. The results compare reasonably well with those in the literature and those from the numerical method.

On the Development of Transverse Ridges on Rock Glaciers

1989 ◽  
Vol 35 (121) ◽  
pp. 383-391
Author(s):  
Deborah S. Loewenherz ◽  
Christopher J. Lawrence ◽  
Richard L. Weaver
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
Lower Layer ◽  
Elastic Solid ◽  
Surface Region ◽  
Finite Amplitude ◽  
Climatic Conditions ◽  
Rock Glacier ◽  
Rock Glaciers ◽  
The Stability

AbstractThe stability of a low Reynolds number flow on an inclined plane is investigated with respect to modelling the initiation of transverse wave-like ridges which commonly occur on the surfaces of rock-glacier forms. In accordance with field observations indicating the presence of stratification in rock glaciers, two models of rock-glacier structure are considered, each stratified and possessing a lower layer which is treated as a Newtonian fluid. An upper, less compliant layer is treated, alternatively, as a Newtonian fluid of viscosity greater than that of the lower layer, or as an elastic solid under longitudinal compression induced by a decrease in the slope of the underlying incline. A linear stability analysis is used to examine the behaviour of each of the proposed models, and both are found to generate instabilities at wavelengths comparable to those associated with transverse surficial ridges on rock glaciers. The growth rates of a flow disturbance predicted by the viscous-stratified model appear to be too slow to account fully for the development of wave forms of finite amplitude, suggesting that other mechanisms are involved in the amplification of an initial disturbance. The results of the stability analysis of the elastic lamina model indicate that finite surficial ridges may develop on rock glaciers as a product of a buckling instability in the surface region if there is a decrease in the slope of the underlying incline. Both of the analyses illustrate that transverse ridges can occur on the surface of a rock glacier in the absence of any variations in debris supply to the system. The results further imply that the use of these features in the paleoreconstruction of Holocene climatic conditions must entail an assessment of the relative roles of external climatically driven forcing versus internal Theologically derived instability.

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