A note on surface water waves for finite depth in the presence of an ice-cover

A class of I boundary value problems involving propagation of two-dimensional surface water waves, associated with water of uniform finite depth, against a plane vertical wave maker is investigated under the assumption that the surface is covered by a thin sheet of ice. It is assumed that the ice-cover behaves like a thin isotropic elastic plate. Then the problems under consideration lead to those of solving the two-dimensional Laplace equation in a semi-infinite strip, under Neumann boundary conditions on the vertical boundary as well as on one of the horizontal boundaries, representing the bottom of the fluid region, and a condition involving upto fifth order derivatives of the unknown function on the top horizontal ice-covered boundary, along with the two appropriate edge-conditions, at the ice-covered corner, ensuring the uniqueness of the solutions. The mixed boundary value problems are solved completely, by exploiting the regularity property of the Fourier cosine transform.

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Transition to turbulence in the free convection boundary layers on an inclined heated plate

An experimental study has been made of transition to turbulence in the free convective flows on a heated plate. Observations have been made with the plate vertical and inclined at angles up to about 50° to the vertical, both above and below the plate. A fibre anemometer was used to survey the region of intermittent turbulence. Information has thus been obtained about the range of Grashof numbers over which transition takes place. Even when the plate is vertical the region of intermittent turbulence is long. When it is inclined, this region becomes still longer in the flow below the plate as a result of the stabilizing stratification, a Richardson number effect. It is possible to have a whole flow such that it should be described as transitional, not laminar or turbulent. It was noticed that in this flow and the vertical plate one, the velocity during the laminar periods could be either of two characteristic values, one of them close to zero. The behaviour above an inclined plate could be interpreted largely as a trend towards the behaviour described in a preceding paper.

Turbulent free convection above a heated plate inclined at a small angle to the horizontal Journal

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion. Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments. The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

Turbulent flow computations using upwind RANS technique for a flat plate and an airfoil

Reynolds Averaged Navier Stokes (RANS) equations are solved using third order upwind biased Roe's scheme for the inviscid fluxes and second order central difference scheme for the viscous fluxes. The Baldwin & Lomax turbulence model is employed for Reynolds stresses. The governing equations are solved using finite-volume implicit scheme in body fitted curvilinear coordinate O-grid system. Computations axe reported for a flat plate apart from RAE 2822 and NACA 0012 airfoils. Results for the flat plate at M = 0.3, R-c = 4.0 x 10(6) compare favourably with the analytical solution. Results for the two airfoils are compared with experiment. There is a good agreement in C-p distribution between experiment and computation for both the airfoils. Comparison of C-f distribution with experiment for RAE 2822 airfoil is reasonable.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Analysis of Serpentine folded-waveguide slow-wave structures by elliptical conformal transformation

Analysis of the serpentine folded-waveguide slow-wave structure was carried out using elliptical conformal transformation, for the dispersion and interaction impedance characteristics of the structure. The results obtained from the present analysis were compared with those from 3D electromagnetic simulation using MAFIA.

Axial wave propagation in coupled nanorod system with nonlocal small scale effects

This article deals with the axial wave propagation properties of a coupled nanorod system with consideration of small scale effects. The nonlocal elasticity theory has been incorporated into classical rod/bar model to capture unique features of the coupled nanorods under the umbrella of continuum mechanics theory. Nonlocal rod model is developed for coupled nanorods. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behavior of nanorods from those of macroscopic rods. Explicit expressions are derived for wavenumber, cut-off frequency and escape frequency of nanorods. The analysis shows that the wave characteristics of nanorods are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial or longitudinal wave mode, where no wave propagation occurs. This is manifested in the spectrum cures as the region, where the wavenumber tends to infinite or wave speed tends to zero. The effect of the coupled spring stiffness is also capture in the present analysis. It has been also shown that the cut-off frequency increases as the stiffness of the coupled spring increases and also the coupled spring stiffness has no effect on escape frequency of the axial wave mode in the nanorod. This cut-off frequency is also independent of the nonlocal small scale parameter. The present study may bring in helpful insights while investigating multiple-nanorod-system-models for future nano-optomechanical systems applications. The results can also provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of coupled single-walled carbon nanotubes or coupled nanorods. (C) 2011 Elsevier Ltd. All rights reserved.