International Science Index
Sediment Patterns from Fluid-Bed Interactions: A Direct Numerical Simulations Study on Fluvial Turbulent Flows
We present results on the initial formation of ripples from an initially flattened erodible bed. We use direct numerical simulations (DNS) of turbulent open channel flow over a fixed sinusoidal bed coupled with hydrodynamic stability analysis. We use the direct forcing immersed boundary method to account for the presence of the sediment bed. The resolved flow provides the bed shear stress and consequently the sediment transport rate, which is needed in the stability analysis of the Exner equation. The approach is different from traditional linear stability analysis in the sense that the phase lag between the bed topology, and the sediment flux is obtained from the DNS. We ran 11 simulations at a fixed shear Reynolds number of 180, but for different sediment bed wavelengths. The analysis allows us to sweep a large range of physical and modelling parameters to predict their effects on linear growth. The Froude number appears to be the critical controlling parameter in the early linear development of ripples, in contrast with the dominant role of particle Reynolds number during the equilibrium stage.
Triple Diffusive Convection in a Vertically Oscillating Oldroyd-B Liquid
The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.
Study of Rayleigh-Bénard-Brinkman Convection Using LTNE Model and Coupled, Real Ginzburg-Landau Equations
A local nonlinear stability analysis using a eight-mode
expansion is performed in arriving at the coupled amplitude equations
for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence
of LTNE effects. Streamlines and isotherms are obtained in the
two-dimensional unsteady finite-amplitude convection regime. The
parameters’ influence on heat transport is found to be more
pronounced at small time than at long times. Results of the
Rayleigh-Bénard convection is obtained as a particular case of
the present study. Additional modes are shown not to significantly
influence the heat transport thus leading us to infer that five minimal
modes are sufficient to make a study of RBBC. The present problem
that uses rolls as a pattern of manifestation of instability is a needed
first step in the direction of making a very general non-local study of
two-dimensional unsteady convection. The results may be useful in
determining the preferred range of parameters’ values while making
rheometric measurements in fluids to ascertain fluid properties such
as viscosity. The results of LTE are obtained as a limiting case of
the results of LTNE obtained in the paper.
Influence of Internal Heat Source on Thermal Instability in a Horizontal Porous Layer with Mass Flow and Inclined Temperature Gradient
An investigation has been presented to analyze the
effect of internal heat source on the onset of Hadley-Prats flow in
a horizontal fluid saturated porous medium. We examine a better
understanding of the combined influence of the heat source and mass
flow effect by using linear stability analysis. The resultant eigenvalue
problem is solved by using shooting and Runga-Kutta methods for
evaluate critical thermal Rayleigh number with respect to various
flow governing parameters. It is identified that the flow is switch from
stabilizing to destabilizing as the horizontal thermal Rayleigh number
is enhanced. The heat source and mass flow increases resulting a
stronger destabilizing effect.
Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow
Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.
Uniform Solution on the Effect of Internal Heat Generation on Rayleigh-Benard Convection in Micropolar Fluid
The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.
Role of Viscosity Ratio in Liquid-Liquid Jets under Radial Electric Field
The effect of viscosity ratio (λ, defined as viscosity of surrounding medium/viscosity of fluid jet) on stability of axisymmetric (m=0) and asymmetric (m=1) modes of perturbation on a liquid-liquid jet in presence of radial electric field (E0 ), is studied using linear stability analysis. The viscosity ratio is shown to have a damping effect on both the modes of perturbation. However
the effect was found more pronounced for the m=1 mode as compared to m=1 mode. Investigating the effect of both E0 and λ
simultaneously, an operating diagram is generated, which clearly shows the regions of dominance of the two modes for a range of
electric field and viscosity ratio values.
Linear Stability of Convection in a Viscoelastic Nanofluid Layer
This paper presents a linear stability analysis of
natural convection in a horizontal layer of a viscoelastic
nanofluid. The Oldroyd B model was utilized to describe the
rheological behavior of a viscoelastic nanofluid. The model
used for the nanofluid incorporated the effects of Brownian
motion and thermophoresis. The onset criterion for stationary
and oscillatory convection was derived analytically. The effects
of the Deborah number, retardation parameters, concentration
Rayleigh number, Prandtl number, and Lewis number on the
stability of the system were investigated. Results indicated that
there was competition among the processes of thermophoresis,
Brownian diffusion, and viscoelasticity which caused
oscillatory rather than stationary convection to occur.
Oscillatory instability is possible with both bottom- and
top-heavy nanoparticle distributions. Regimes of stationary and
oscillatory convection for various parameters were derived and
are discussed in detail.
Linear Instability of Wake-Shear Layers in Two-Phase Shallow Flows
Linear stability analysis of wake-shear layers in twophase
shallow flows is performed in the present paper. Twodimensional
shallow water equations are used in the analysis. It is
assumed that the fluid contains uniformly distributed solid particles.
No dynamic interaction between the carrier fluid and particles is
expected in the initial moment. The stability calculations are
performed for different values of the particle loading parameter and
two other parameters which characterize the velocity ratio and the
velocity deficit. The results show that the particle loading parameter
has a stabilizing effect on the flow while the increase in the velocity
ratio or in the velocity deficit destabilizes the flow.