Marginal stability curve of a deformable bubble

2017 ◽  
Vol 89 ◽  
pp. 218-227 ◽  
Author(s):  
W. Zhou ◽  
J. Dušek
Keyword(s):  
Marginal Stability ◽  
Stability Curve

Time-dependent isolated anomalies in zonal flows

1993 ◽  
Vol 251 ◽  
pp. 377-409 ◽  
Author(s):  
Karl R. Helfrich ◽  
Joseph Pedlosky
Keyword(s):  
Solitary Waves ◽  
Analytical Solutions ◽  
Coherent Structures ◽  
Initial Conditions ◽  
Zonal Flow ◽  
Critical Value ◽  
Time Dependent ◽  
Marginal Stability ◽  
Zonal Flows ◽  
Stability Curve

A theory is developed for time-dependent coherent structures in a marginally stable atmospheric zonal flow. The coherent structures have the form of solitary waves travelling in the zonal direction. Analytical solutions are found for stationary solitary waves but these are shown to be always unstable. The instability manifests itself either as a fission of the structure subsequently emitting two oppositely directed travelling solitary waves or as an implosion in which the structure becomes increasingly more narrow and intense. Which of the two occurs depends sensitively on initial conditions. These solitary waves are stable in head-on collisions only if their joint zonally integrated amplitude is less than a critical value; otherwise, the implosion instability occurs. General initial conditions can give rise to solitary waves which either split, implode, or break down to form a train of nonlinear wave packets. A scenario for the birth and decay of isolated disturbances is given, utilizing the slow parametric transit of the marginal stability curve of the background zonal flow.

Transition in Convective Flows Heated Internally

2002 ◽  
Vol 124 (4) ◽  
pp. 635-642 ◽  
Author(s):  
Masato Nagata ◽  
Sotos Generalis
Keyword(s):  
Hopf Bifurcation ◽  
Secondary Flow ◽  
Linear Stability ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Grashof Number ◽  
Stability Curve ◽  
Convective Flows

The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.

THE APPROACHES TO THE SOLVING ENVIRONMENTAL AND ECONOMIC PROBLEMS OF SUSTAINABLE DEVELOPMENT ON THE SHELF OF THE ARCTIC SEAS OF THE RUSSIAN FEDERATION

2017 ◽  
Author(s):  
Alexander Krivichev ◽  
Alexander Krivichev
Keyword(s):  
Continental Shelf ◽  
Oil Spill ◽  
The Arctic ◽  
Marginal Stability ◽  
Environmental Benefit ◽  
Arctic Seas ◽  
Dynamic Simulations ◽  
Economic Problems ◽  
Technogenic Loads ◽  
Oil Spill Response

Russian Arctic shelf - rich larder of the hydrocarbons, at the same time Northern Sea Route (NSR) - a strategically important route for transporting them. The extraction and the transportation of the hydrocarbons along the NSR requires the solution of a number of ecological and economic problems in the first place to ensure environmental and technogenic safety. For the solving of these problems on the continental shelf it is required a system of comprehensive measures: - the development of the regulatory framework for environmental support oil and gas projects; - the introduction and use of integrated methods for monitoring environmental conditions at the sites of technogenic loads on the shelf of the Arctic seas, including the use of drones; - creating different models for assessing the marginal stability of ecosystems to technogenic loads during production and transportation of hydrocarbons on the continental shelf based on systems of dynamic simulations; - the development and use of sensitivity maps of coastal areas of the Arctic seas during oil spill response; - accounting of the results of the analysis of the total environmental benefit in the development of oil spill response plans; - application of the principle of "zero" resetting, due to the high fishery valuation in Barents and Kara seas and the conservation of marine biological resources.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

Mixed bottom-friction–Kelvin–Helmholtz destabilization of source-driven abyssal overflows in the ocean

2009 ◽  
Vol 626 ◽  
pp. 33-66 ◽  
Author(s):  
GORDON E. SWATERS
Keyword(s):  
Water Column ◽  
Thermohaline Circulation ◽  
Unstable Mode ◽  
Stability Boundary ◽  
Phase Speed ◽  
Bottom Friction ◽  
Marginal Stability ◽  
Time Variability ◽  
Gravitational Acceleration ◽  
Overlying Water

Source-driven ocean currents that flow over topographic sills are important initiation sites for the abyssal component of the thermohaline circulation. These overflows exhibit vigorous space and time variability over many scales as they progress from a predominately gravity-driven downslope flow to a geostrophic along-slope current. Observations show that in the immediate vicinity of a sill, grounded abyssal ocean overflows can possess current speeds greater than the local long internal gravity wave speed with bottom friction and downslope gravitational acceleration dominating the flow evolution. It is shown that these dynamics lead to the mixed frictionally induced and Kelvin–Helmholtz instability of grounded abyssal overflows. Within the overflow, the linearized instabilities correspond to bottom-intensified baroclinic roll waves, and in the overlying water column amplifying internal gravity waves are generated. The stability characteristics are described as functions of the bottom drag coefficient and slope, Froude, bulk Richardson and Reynolds numbers associated with the overflow and the fractional thickness of the abyssal current compared to the mean depth of the overlying water column. The marginal stability boundary and the boundary separating the parameter regimes in which the most unstable mode has a finite or infinite wavenumber are determined. When it exists, the high-wavenumber cutoff is obtained. Conditions for the possible development of an ultraviolet catastrophe are determined. In the infinite-Reynolds-number limit, an exact solution is obtained which fully includes the effects of mean depth variations in the overlying water column associated with a sloping bottom. For parameter values characteristic of the Denmark Strait overflow, the most unstable mode has a wavelength of about 19 km, a geostationary period of about 14 hours, an e-folding amplification time of about 2 hours and a downslope phase speed of about 74 cm s−1.

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