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1.
The mechanisms and structural elements of instability whose evolution results in the occurrence of the collapse are studied in the scope of the rotating shallow water model with a horizontally nonuniform density. The diagram stability based on the integral collapse criterion is suggested to explain system behavior in the space of constants of motion. Analysis of the instability shows that two collapse scenarios are possible. One scenario implies anisotropic collapse during which the contact area of a collapsing drop-like fragment with the bottom contracts into a rotating segment. The other implies isotropic contraction of the area into a point. 相似文献
2.
B. Dipierro M. Abid 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(2):69
Using linear instability theory and nonlinear dynamics, the Rayleigh-Taylor instability
of variable density swirling flows is studied. It is found that the flow topology could be
predicted, when the instability sets in, using a function χ dependent on
density and axial and azimuthal velocities. It is shown that even when the inner
axial-flow is heavier than the outer one (a favorable case for the development of the
Rayleigh-Taylor instability thanks to the centrifugal force) the instability is not
necessarily Rayleigh-Taylor-dominated. It is also shown that when the Rayleigh-Taylor
instability develops, it is helical. 相似文献
3.
Jian Guo Zhou 《Journal of computational physics》2011,230(2):394-401
In the lattice Boltzmann method for the shallow water equations (LABSWE), the force term involves the first order derivative related to a bed slope, which has to be determined using the centred scheme for an accurate solution. However, such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice Boltzmann method. This paper shows how to remove this drawback from the LABSWE by incorporating the bed level into the lattice Boltzmann equation in a consistent manner with the lattice Boltzmann approach. Three numerical tests have been presented to verify the proposed method. 相似文献
4.
A novel 2D numerical model for vertically homogeneous shallow flows with variable horizontal density is presented. Density varies according to the volumetric concentration of different components or species that can represent suspended material or dissolved solutes. The system of equations is formed by the 2D equations for mass and momentum of the mixture, supplemented by equations for the mass or volume fraction of the mixture constituents. A new formulation of the Roe-type scheme including density variation is defined to solve the system on two-dimensional meshes. By using an augmented Riemann solver, the numerical scheme is defined properly including the presence of source terms involving reaction. The numerical scheme is validated using analytical steady-state solutions of variable-density flows and exact solutions for the particular case of initial value Riemann problems with variable bed level and reaction terms. Also, a 2D case that includes interaction with obstacles illustrates the stability and robustness of the numerical scheme in presence of non-uniform bed topography and wetting/drying fronts. The obtained results point out that the new method is able to predict faithfully the overall behavior of the solution and of any type of waves. 相似文献
5.
K. V. Karelsky A. S. Petrosyan A. V. Chernyak 《Journal of Experimental and Theoretical Physics》2012,114(6):1058-1071
The system of the equations of motion for a compressible gas in the gravitational field over a smooth underlying surface has been analyzed in the shallow water approximation. All continuous centered self-similar solutions and all discontinuous self-similar solutions have been obtained. The problem of the decay of an arbitrary discontinuity for the equations of motion of the compressible gas has been solved in the explicit form in the shallow water approximation. The existence of four different configurations implementing the solution of the problem of the decay of an arbitrary discontinuity has been demonstrated. The conditions necessary and sufficient for the implementation of each configuration have been determined. 相似文献
6.
K. V. Karelsky A. S. Petrosyan S. V. Tarasevich 《Journal of Experimental and Theoretical Physics》2011,113(3):530-542
The system of the magnetohydrodynamic equations for a heavy fluid has been analyzed in the shallow water approximation. All
discontinuous self-similar solutions and all continuous centered self-similar solutions have been found. It has been shown
that magnetogravity compression waves are broken with the formation of a magnetogravity shock wave. The initial decay discontinuity
problem for the magnetohydrodynamic equations has been solved in the explicit form in the shallow water approximation. The
existence of five different configurations implementing the solution of the decay of an arbitrary discontinuity has been demonstrated.
The conditions necessary and sufficient for the implementation of each configuration have been found. 相似文献
7.
D. A. Klimachkov A. S. Petrosyan 《Journal of Experimental and Theoretical Physics》2016,123(3):520-539
Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case. 相似文献
8.
A new instability predicte by theory to occur in rotating shallow water in which the rotation velocity has a discontinuity, in a regime where the flow velocity exceeds the characteristics velocity of the waves, has been found experimentally. The instability develops when the radial gradient of the angular velocity across the discontinuity is negative; such an instability is likely to be responsible for the formation of the spiral structure in galaxies which have a similar rotational velocity profile. 相似文献
9.
Guglielmo Stecca Annunziato Siviglia Eleuterio F. Toro 《Journal of computational physics》2010,229(18):6362-6380
In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple-space dimensions on structured meshes. The proposed method is an extension of the multidimensional FORCE flux developed by Toro et al. (2009) [14]. Here we introduce upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. For the linear advection equation, the proposed UFORCE method reproduces exactly the upwind Godunov method. Extension to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. Second order of accuracy in space and time on structured meshes is obtained in the framework of finite volume methods. The proposed method improves the accuracy of the solution for small Courant numbers and intermediate waves associated with linearly degenerate fields (contact discontinuities, shear waves and material interfaces). It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the schemes is assessed on a suite of test problems for the two-dimensional shallow water equations. 相似文献
10.
K. V. Karelsky A. S. Petrosyan S. V. Tarasevich 《Journal of Experimental and Theoretical Physics》2014,119(2):311-325
Magnetohydrodynamic equations for a heavy fluid over an arbitrary surface are studied in the shallow water approximation. While solutions to the shallow water equations for a neutral fluid are well known, shallow water magnetohydrodynamic (SMHD) equations over a nonflat boundary have an additional dependence on the magnetic field, and the number of equations in the magnetic case exceeds that in the neutral case. As a consequence, the number of Riemann invariants defining SMHD equations is also greater. The classical simple wave solutions do not exist for hyperbolic SMHD equations over an arbitrary surface due to the appearance of a source term. In this paper, we suggest a more general definition of simple wave solutions that reduce to the classical ones in the case of zero source term. We show that simple wave solutions exist only for underlying surfaces that are slopes of constant inclination. All self-similar discontinuous and continuous solutions are found. Exact explicit solutions of the initial discontinuity decay problem over a slope are found. It is shown that the initial discontinuity decay solution is represented by one of four possible wave configurations. For each configuration, the necessary and sufficient conditions for its realization are found. The change of dependent and independent variables transforming the initial equations over a slope to those over a flat plane is found. 相似文献
11.
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13.
Rogue waves in shallow water 总被引:1,自引:0,他引:1
T. Soomere 《The European physical journal. Special topics》2010,185(1):81-96
Most of the processes resulting in the formation of unexpectedly high surface waves in deep water (such as dispersive and
geometrical focusing, interactions with currents and internal waves, reflection from caustic areas, etc.) are active also
in shallow areas. Only the mechanism of modulational instability is not active in finite depth conditions. Instead, wave amplification
along certain coastal profiles and the drastic dependence of the run-up height on the incident wave shape may substantially
contribute to the formation of rogue waves in the nearshore. A unique source of long-living rogue waves (that has no analogues
in the deep ocean) is the nonlinear interaction of obliquely propagating solitary shallow-water waves and an equivalent mechanism
of Mach reflection of waves from the coast. The characteristic features of these processes are (i) extreme amplification of
the steepness of the wave fronts, (ii) change in the orientation of the largest wave crests compared with that of the counterparts
and (iii) rapid displacement of the location of the extreme wave humps along the crests of the interacting waves. The presence
of coasts raises a number of related questions such as the possibility of conversion of rogue waves into sneaker waves with
extremely high run-up. Also, the reaction of bottom sediments and the entire coastal zone to the rogue waves may be drastic. 相似文献
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16.
A. M. Balonishnikov 《Technical Physics》2005,50(2):262-263
Analysis of a simplified equation derived previously for small-scale velocity components shows that any turbulent flow of
an incompressible liquid becomes unstable against infinitesimal perturbations of small-scale velocity components if the strain
rate tensor for the large-scale velocity is high. Such a statement comes into conflict with the classical stability theory,
which specifically asserts that the Poiseuille flow in a circular tube is linearly stable against infinitesimal perturbations. 相似文献
17.
Graham MD 《Chaos (Woodbury, N.Y.)》1999,9(1):154-163
Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. (c) 1999 American Institute of Physics. 相似文献
18.
Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose
directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory
and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in
one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by
other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results
show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary
geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the
disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow
andvice versa.
Paper presented at the 1o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome. 相似文献
19.
V. S. Grach A. G. Demekhov V. Yu. Trakhtengerts 《Radiophysics and Quantum Electronics》2006,49(11):851-865
We consider the possible mechanism of generation of charged-particle density irregularities and electric field in the middle
atmosphere based on the development of the dissipative instability of a flow of large charged aerosols. A dispersion equation
describing the properties of the spectral component of a quasi-static electric field with allowance for the aerosol charging
inertia is obtained. This equation is used to study characteristics of the instability threshold. It is shown that the charging
inertia and the presence of photoelectrons lead to an increase and a decrease in the threshold plasma frequency of the aerosols,
respectively. It is found that there exist optimal combinations of such parameters as the radius of spherical aerosols and
the mass of heavy ion clusters for which the instability threshold is minimum. It is also shown that the instability threshold
is lower for the particles stretched along the motion direction. Quantitative estimates are given for medium parameters necessary
for the excitation of instability in the region of existence of polar mesospheric summer echo as well as for spatial scales
of unstable perturbations.
__________
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 942–957, November 2006. 相似文献
20.
使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态. 相似文献