Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

Stokes problem for a porous vertical plate with heat sinks by finite difference method

The effect of heat sinks on the free-convection flow of an incompressible viscous fluid past an impulsively started infinite vertical porous plate is considered. Finite difference method has been used to obtain the numerical solution of the governing equations. The influence of the various parameters, occurring into the problem, on the velocity field, the temperature field and on their related quantities is extensively discussed with the help of graphs and tables.     

Note on nonlinear Rayleigh-Taylor instability

Shivamoggi (1983) has used the method of strained coordinates in investigating the nonlinear Rayleigh-Taylor instability problem. After incorporating the corrections pointed out by Malik and Singh (1983) he obtained a revised expression for the nonlinear cut off wavenumber which separates the region of stability from that of instability.     

Use of Roche coordinates in the problems of small oscillations of tidally-distorted stellar models

Kopal's method of Roche coordinates used by us in an earlier paper (Mohan and Singh, 1978) to study the problems of small oscillations of tidally-distorted stars has been extended further to take into account the effect of second-order terms in tidal distortion. Our results show that the effect of including terms of second order of smallness in tidal distortion in the metric coefficients of the Roche coordinates of tidally distorted stars is quite significant, especially in case of stars with extended envelopes and (or) larger values of the mass ratio of the companion star producing tidal distortion. Some of the models which were earlier found stable against small perturbations now become dynamically unstable with the inclusion of the terms of second order of smallness in tidal effects.At present on leave of absence with the department of Mathematics, College of Science, Baghdad, Iraq.     

Relationships between three dispersion measures used in flood frequency analysis

Three dispersion measures of a random variable, i.e., the standard deviation, the mean deviation (MD) about the mean and the second L-moment, are analyzed in terms of their properties and mutual relationships. Emphasis is placed on the MD, as it is less recognized than two other dispersion measures. The relationships between the dispersion measures are derived for distributions commonly applied in flood frequency analysis (FFA). For distributions that are unbounded, there is a distribution-dependent constant value of the ratio of dispersion measures, or equivalently of respective coefficients of variation. For two-parameter distributions that are lower-bounded, the relationship between the coefficients of variation is also distribution dependent and is not linear. For lower-bounded three-parameter distributions, the dispersion measure ratios, or equivalently the ratios of coefficients of variation, depend on the coefficient of skewness and show a strong distributional dependence. For selected distributions, the three dispersion measures are compared both in terms of the robustness to the largest samples element and the accuracy of upper quantile estimation. The MD statistics may be highly competitive to the two other dispersion measure statistics if applied in FFA for parameters estimation.     

Microwave response of seasonal snow-cover measured by using a ground-based radiometer at 6.93 and 18.7 ghz frequencies and at dual polarization

Snow cover is an important variable for climatic and hydrologic models due to its effects on surface albedo, energy, and moisture budgets. Passive microwave sensors can be used to monitor temporal and spatial variations in large-scale snow cover parameters, avoiding problems of cloud cover and polar nights. In the present study, brightness temperature values were estimated (using calibration curves) for moist snow on natural and blackbody/metal surface. T_B response on snow depth, density, SWE and angular variation from nadir were measured and found that T_B decreases with increase of snow depth and with increase of angle from nadir. Empirical relations were used to estimate emissivity, dielectric constant and dielectric loss factor. It was observed that emissivity decreases with the increase of dielectric constant. The dielectric constant and dielectric loss factor both increases with the increase of density. Experiments were performed during winter of year 2005 at Dhundi and Solang (H.P.), India, using ground based passive microwave radiometer having 6.9 and 18.7 GHz antenna frequencies at dual polarization.