Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.     

EFFECT OF VERTICAL CONTACT ON WENNER RESISTIVITY SOUNDINGS*

The allowance for the influence of a vertical contact is evaluated on Wenner resistivity sounding curves, which are graphically constructed on bilogarithmic paper over simple composite earth models consisting of a vertical contact separating two- or three layered earth on one side and a homogeneous medium on the other side. The error incurred in the graphical constructions is explored. Finally, the use of these graphically constructed sounding curves is shown in the interpretation of two Wenner field soundings measured in a complex geologic area.     

DIRECT INTERPRETATION OF TWO-ELECTRODE RESISTIVITY SOUNDINGS *

This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).     

Eurasian snow cover and seasonal forecast of Indian summer monsoon rainfall

Abstract

This paper presents the relationship between Indian summer monsoon total rainfall and two parameters from Eurasian snow cover, one being the winter snow cover extent and the other the area of spring snowmelt. Satellite-derived Eurasian snow cover extent and Indian monsoon rainfall data were obtained from the NOAA/NESDIS and the India Meteorological Department (IMD) for the period 1966–1985. Seasonal cyclic variations of snow cover showed a higher swing in both the winter and the spring seasons of the cycle as compared to the remaining seasons of the year in the lower region of the cycle. The established inverse relation between winter snow cover and monsoon rainfall during June to September is further extended. Winter snow cover is very strongly correlated with spring snowmelt over Eurasia. Spring snowmelt area is obtained by subtracting the May snow cover extent from that of the previous February. The variations of spring snowmelt were also compared with Indian total monsoon rainfall. The detected correlation is stronger between snowmelt and monsoon rainfall than between the winter snow cover and the monsoon rainfall. There is also a significant multiple correlation among winter snow cover, spring snowmelt and monsoon rainfall. Lastly, a significant multiple correlation suggested a multiple regression equation which might improve the climatic prediction of monsoon rainfall over India.     

Near shore waves,long-shore currents and sediment transport along micro-tidal beaches,central west coast of India

Coastlines are undergoing constant geomorphologic changes with respect to the incident wave climate.Based on waves measured at 9 m water depth,simulation of near shore wave transformation is done using REFDIF-1numerical model and the near shore breaker parameters are estimated at two micro-tidal beaches along central west coast of India.Model results are validated with measured values.From the breaker parameters,long-shore current and long-shore sediment transport rates（LSTR） are computed by using semi-empirical equations.Estimated long-shore current and LSTR are showing dramatic variations with respect to seasons.Predominant direction of LSTR is observed towards north since the approach waves are from south-west direction during pre-monsoon and post monsoon.During monsoon season,waves are from west south-west and resulted in southerly transport.The estimated annual net and gross LSTR by Cambridge Environmental Research Consultants（CERC） at two locations are in the same order whereas LSTR estimated by Walton ＆ Bruno and Kamphuis equations are showing different estimations because of difference in surf-zone width and foreshore slope between the two locations.For micro-tidal beaches with length less than 6 km,Kamphuis equation is giving agreeable estimation of LSTR.Sensitivity analysis of LSTR estimate shows that coastal inclination is the prominent factor in determining LSTR than incident wave angle.