Instability convective

Thermally driven convective instabilities in fluid flow, and, more specifically, Rayleigh-B6nard instabilities are favorite working examples in the area of low-dimensional dynamics of distributed systems (see (14 and references therein). By appropriately choosing the cell dimensions (aspect ratio) we can either drive the system to temporal chaos while keeping it spatially coherent, or, alternatively, produce complex spatial patterns. 

Little is known about the interactions between the transport properties in the melt and the production of defects at the melt-crystal interface. An exception is the swirl microdefect seen during processing of dislocation-free silicon wafers (118). The origins of this defect (119) are related to temperature oscillations and remelting of the interface. Kuroda and Kozuka (120) have studied the dependence of temperature oscillations on operating parameters in a CZ system but have not linked the oscillations to convective instabilities in the melt. 

Theoretical analysis indicates that occurrence of such convective instabilities depends on anisotropy of electrical conductivity and dielectric properties in the initial aligned nematic material. That is, conductivity parallel to the direction of alignment must differ from conductivity perpendicular to this direction. Calculation of the stability condition requires knowledge not only of these anisotropic electrical properties but also of anisotropic elastic and viscous properties which oppose disruption of the alignment and flow. 

The Sierra Nevada provide an example of the perils of relating erosion rates to relief. They are thought to have persisted since 60-80 Ma with high (1.5 km) relief over long wavelengths ( 50 km), but erosion rates over these timescales are estimated to have been only 0.03-0.08 mm/yr (House et al. 1997, 2001 Clark et al. 2005). Incision rates may have been higher ( 0.2 mm/yr) in the Pliocene (Stock et al. 2004), possibly aided by convective instability at depth (e.g., Ducea and Saleeby 1996), but this is still slow relative to erosion rates in many other tectonically active and inactive regions, and similar to some with much lower relief (e.g., Heffern et al. 2007). 

Regarding the classification of instabilities into convective and absolute instability, one can now see the difference clearer in terms of the group velocity. For absolute instability the group velocity is found to be zero, so that the disturbances do not get swept away, as in convective instability and continue to grow in the place of their origin. However, in many flow systems, these two aspects can remain simultaneously. 

Instead of using this equation, in the literature, there are few models proposed by which the frequency or Strouhal number of the shedding is fixed. Koch (1985) proposed a resonance model that fixes it for a particular location in the wake by a local linear stability analysis. Upstream of this location, flow is absolutely unstable and downstream, the flow displays convective instability. Nishioka Sato (1973) proposed that the frequency selection is based on maximum spatial growth rate in the wake. The vortex shedding phenomenon starts via a linear instability and the limit cycle-like oscillations result from nonlinear super critical stability of the flow, describ-able by Eqn. (5.3.1). 

Huerre, P. and Monkewitz, PA. (1985). Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151. 

Formation of various patterns like the honeycomb structure mentioned above can originate from gradients in surface tension or density due to temperature variations caused by solvent evaporation. Both effects can produce convection instability, namely Marangoni [295] and Rayleigh [296] convection. In thin films Marangoni convection predominates. 

Vertical convectively driven turbulence. While differential rotation may inhibit convective motions in the radial direction in a disk, motions parallel to the rotation axis are relatively unaffected by rotation. In a disk where heat is being generated near the midplane, and where dust grains are the dominant source of opacity, the disk is likely to be unstable to convective motions in the vertical direction, which carry the heat away from the disk s midplane and deposit it close to the disk s surface, where it can be radiated away. Convective instability was conjectured to lead to sufficiently robust turbulence for the resulting... 

Wilson M. and Patterson R. (2001) Intraplate magmatism related to short-wavelength convective instabilities in the upper mantle evidence from the Tertiary—Quaternary volcanic province of western and central Europe. In Mantle Plumes Their Identification through Time, Geol Soc. Amer. Spec. Paper 352 (eds. R. E. Ernst and K. L. Buchan). Geological Society of America, Boulder, CO, pp. 37—58. 

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