Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Vertical uplift capacity of horizontal anchors

The method of characteristics coupled with a log-spiral failure surface was used to develop a theory for vertical uplift capacity of shallow horizontal strip anchors in a general c-phi soil. Uplift-capacity factors F(c), F(q) and F(gamma), for the effects of cohesion, surcharge, and density, respectively, have been established as functions of embedment ratio lambda and angle of friction phi. The extent of the failure surface at the ground has also been determined. Comparisons made with existing test results support the predictive capability of the theory, and comparisons with the analysis proposed by Meyerhof and Adams show the proposed analysis provides slightly more conservative predictions of pullout capacity.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds acid precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%-20% weaker than observed, The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a targe amount of high-frequency intraseasonal variations, While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency EI Nino-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15 degrees west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Nonsimilar solutions for mixed convection in non-Newtonian fluids along horizontal surfaces in porous media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Airborne measurements of aerosol scattering properties above the MABL over Bay of Bengal during W_ICARB - characteristics and spatial gradients

Realizing the importance of aerosol characterization and addressing its spatio-temporal heterogeneities over Bay of Bengal (BoB), campaign mode observations of aerosol parameters were carried out using simultaneous cruise, aircraft and land-based measurements during the Winter Integrated Campaign for Aerosols gases and Radiation Budget (W_ICARB). Under this, airborne measurements of total and hemispheric backscatter coefficients were made over several regions of coastal India and eastern BoB using a three wavelength integrating nephelometer. The measurements include high resolution multi-level (ML) sorties for altitude profiles and bi-level (BL) sorties for spatial gradients within and above the Marine Atmospheric Boundary Layer (MABL) over BoB. The vertical profiles of the scattering coefficients are investigated in light of the information on the vertical structure of the atmospheric stability, which was derived from the collocated GPS (Global Positioning System) aided radiosonde ascents. In general, the altitude profiles revealed that the scattering coefficient remained steady in the convectively well-mixed regions and dropped off above the MABL. This decrease was quite rapid off the Indian mainland, while it was more gradual in the eastern BoB. Investigation on horizontal gradients revealed that the scattering coefficients over northern BoB are 3 to 4 times higher compared to that of central BoB within and above the MABL. A north-south gradient in scattering coefficients is observed over Port Blair in the eastern BoB, with values decreasing from south to north, which is attributed to the similar gradient in the surface wind speed, which can be replicated in the sea salt abundance. The gradients are parameterized using best-fit analytical functions.

Seismic horizontal pullout capacity of vertical anchors in sands

The problem of finding the horizontal pullout capacity of vertical anchors embedded in sands with the inclusion of pseudostatic horizontal earthquake body forces, was tackled in this note. The analysis was carried out using an upper bound limit analysis, with the consideration of two different collapse mechanisms: bilinear and composite logarithmic spiral rupture surfaces. The results are presented in nondimensional form to find the pullout resistance with changes in earthquake acceleration for different combinations of embedment ratio of the anchor (lambda), friction angle of the soil (phi), and the anchor-soil interface wall friction angle (delta). The pullout resistance decreases quite substantially with increases in the magnitude of the earthquake acceleration. For values of delta up to about 0.25-0.5phi, the bilinear and composite logarithmic spiral rupture surfaces gave almost identical answers, whereas for higher values of delta, the choice of the logarithmic spiral provides significantly smaller pullout resistance. The results compare favorably with the existing theoretical data.

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.

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.

Impact of satellite observed microwave SST on the simulation of tropical cyclones

The impact of realistic representation of sea surface temperature (SST) on the numerical simulation of track and intensity of tropical cyclones formed over the north Indian Ocean is studied using the Weather Research and Forecast (WRF) model. We have selected two intense tropical cyclones formed over the Bay of Bengal for studying the SST impact. Two different sets of SSTs were used in this study: one from TRMM Microwave Imager (TMI) satellite and other is the weekly averaged Reynold's SST analysis from National Center for Environmental Prediction (NCEP). WRF simulations were conducted using the Reynold's and TMI SST as model boundary condition for the two cyclone cases selected. The TMI SST which has a better temporal and spatial resolution showed sharper gradient when compared to the Reynold's SST. The use of TMI SST improved the WRF cyclone intensity prediction when compared to that using Reynold's SST for both the cases studied. The improvements in intensity were mainly due to the improved prediction of surface latent and sensible heat fluxes. The use of TMI SST in place of Reynold's SST improved cyclone track prediction for Orissa super cyclone but slightly degraded track prediction for cyclone Mala. The present modeling study supports the well established notion that the horizontal SST gradient is one of the major driving forces for the intensification and movement of tropical cyclones over the Indian Ocean.