On triply diffusive convection in completely confined fluids

The present paper carries forward Prakash et al. [21] analysis for triple diffusive convection problem in completely confined fluids and derives upper bounds for the complex growth rate of an arbitrary oscillatory disturbance which may be neutral or unstable through the use of some non-trivial integral estimates obtained from the coupled system of governing equations of the problem.

Plasma stability theory including the resistive wall effects

Plasma stabilization due to a nearby conducting wall can provide access to better performance in some scenarios in tokamaks. This was proved by experiments with an essential gain in${\it\beta}$and demonstrated as a long-lasting effect at sufficiently fast plasma rotation in the DIII-D tokamak (see, for example, Straitet al.,Nucl. Fusion, vol. 43, 2003, pp. 430–440). The rotational stabilization is the central topic of this review, though eventually the mode rotation gains significance. The analysis is based on the first-principle equations describing the energy balance with dissipation in the resistive wall. The method emphasizes derivation of the dispersion relations for the modes which are faster than the conventional resistive wall modes, but slower than the ideal magnetohydrodynamics modes. Both the standard thin wall and ideal-wall approximations are not valid in this range. Here, these are replaced by an approach incorporating the skin effect in the wall. This new element in the stability theory makes the energy sink a nonlinear function of the complex growth rate. An important consequence is that a mode rotating above a critical level can provide a damping effect sufficient for instability suppression. Estimates are given and applications are discussed.

Linear stability analysis for monami in a submerged seagrass bed

The onset of monami – the synchronous waving of seagrass beds driven by a steady flow – is modelled as a linear instability of the flow. Unlike previous works, our model considers the drag exerted by the grass in establishing the steady flow profile, and in damping out perturbations to it. We find two distinct modes of instability, which we label modes 1 and 2. Mode 1 is closely related to Kelvin–Helmholtz instability modified by vegetation drag, whereas mode 2 is unrelated to Kelvin–Helmholtz instability and arises from an interaction between the flow in the vegetated and unvegetated layers. The vegetation damping, according to our model, leads to a finite threshold flow for both of these modes. Experimental observations for the onset and frequency of waving compare well with model predictions for the instability onset criteria and the imaginary part of the complex growth rate respectively, but experiments lie in a parameter regime where the two modes can not be distinguished.

On the Modulation of Oscillation in Thermohaline Convection Problems Using Temperature Dependent Viscosity

The present paper mathematically investigates the effect of temperature dependent viscosity on the onset of instability in thermohaline convection problems of Veronis and Stern type configurations, using linear stability theory. A sufficient condition for the stability of oscillatory modes for thermohaline configuration is derived. When the compliment of this sufficient condition is true, the oscillatory motions of neutral or growing amplitude may exist, and hence the bounds for the complex growth rate of these neutral or unstable modes are derived, when viscosity of the fluid is an arbitrary function of temperature. Some general conclusions for the cases of linear and exponential variations of viscosity are worked out. The present analysis thus shows that the oscillations in thermohaline convection problems can be modulated or arrested by considering the temperature dependent viscosity of the fluid.

Transverse instabilities of deep-water solitary waves

The dynamics of a one-dimensional slowly modulated, nearly monochromatic localized wave train in deep water is described by a one-dimensional soliton solution of a two-dimensional nonlinear Schrödinger (NLS) equation. In this paper, the instability of such a wave train with respect to transverse perturbations is examined numerically in the context of the NLS equation, using Hill's method. A variety of instabilities are obtained and discussed. Among these, we show that the solitary wave is susceptible to an oscillatory instability (complex growth rate) due to perturbations with arbitrarily short wavelength. Further, there is a cut-off on the instability with real growth rates. We show analytically that the nature of this cut-off is different from what is claimed in previous works.

Surface Reaction Mechanisms in Chemical Beam Epitaxy

ABSTRACTSurface reaction mechanisms which underly the growth of III-V semiconductors by chemical beam epitaxy have been investigated using a combination of surface spectroscopic techniques in conjunction with modulated molecular beam scattering techniques. Emphasis is placed on understanding the complex growth rate effects observed during the growth of Ga(Al,In)As and the origin of selected area epitaxy. These effects are shown to arise from the surface sensitive nature of the decomposition of the group III alkyl source chemicals used in CBE.