ALBERT

Description: The response of eight long-duration pigeonpea [Cajanus cajan (L) Millsp.] genotypes to irrigation was studied at Gwalior in Central India during the 1990–91, 1991–92 and 1992–93 growing seasons on an Inceptisol. The crop was grown at two spacings as it was expected that crop density could interact with the crop's ability to extract soil moisture. The irrigation treatment received furrow irrigation four times during the 1990–91 and 1992–93 seasons and twice during the 1991–92 season. Grain yields of all genotypes were 11 % higher when planted at higher density than at low density. There was a differential variation in yield and harvest index among genotypes due to season but not due to spacing and irrigation suggesting the validity of the present approach of testing genotypes under optimum conditions. Grain yield declined by 21 % from the 1990 to 1992 season. The decline was 〉 1 t/ha in some cultivars (ICPL 366, GW3), and between 0·5 and 1·0 t/ha in others (NP [WR] 15, ICP 87143 and ICPL 84072). In others (Bahar, ICP 9174, ICP 8860) the yield fluctuation was 〈 0·5 t/ha. The genotypes' mean yields were as high as 2·7 t/ha for ICPL 87143, ICPL 84072 and ICPL 366. There was a significant reduction in both grain yield (16 %), and also above-ground plant dry mass (18 %) due to soil moisture limitation in the unirrigated treatment. Both the above-ground plant dry mass and grain yields were significantly more at high plant density than at lower plant density especially with irrigation. The genotypes were found to differ in their response to production environment (irrigation, spacing and to the undefined differences of the 3 years). Genotypic variation in yield within a production environment was found to vary in relation to changes in harvest index and across environment (irrigation, seasons) due to variation in total dry matter production. A lack of negative relationship between the total dry matter and harvest index suggests the possibility of optimizing both for obtaining higher yield from long-duration genotypes.

Description: For the understanding of longshore currents along a natural beach, the effects of bottom unevenness are considered to be important, especially for the flow in the swash zone. Currents in the swash zone are strongly influenced by the bed slope because the effect of gravity overwhelms the effect of the depth change. In the present paper, we investigate these effects and focus on waves propagating from offshore over a flat ocean basin of constant depth to a beach with a sloping wavy bottom. The waves are incident at a small angle to the beach normal, and the bed slope in the alongshore direction is varied slowly. To simplify the problem, only cnoidal waves and solitary waves are considered and the bed level is varied sinusoidally in the longshore direction. A perturbation method is applied to the two-dimensional nonlinear shallow water equation (two-dimensional NLSWE) for the wave motion in order to generate a more simplified model of wave dynamics consisting of a one-dimensional NLSWE for the direction normal to the beach and an equation for the alongshore direction. The first equation, the one-dimensional NLSWE, is solved by Carrier and Greenspan's transformation. The solution of the second one is found by extending Brocchini and Peregrine's solution for a flat beach. Two methods for the solution of the one-dimensional NLSWE are introduced in order to get a solution applicable to large-amplitude swash motions, where the amplitude is comparable to the beach length. One is the Maclaurin expansion of the solution around the moving shoreline, and the other is Riemann's representation of the solution, which exactly satisfies the one-dimensional NLSWE and the boundary conditions. After doing a consistency check by confirming that Riemann's method, a numerical solution, agrees with the exact solution for an infinitely long, sloping beach, we assumed that the Maclaurin series solution can also describe wave motion in the swash zone properly not only for this model but also for our 'wavy', finite beach model. The solution obtained from the Maclaurin series is then plugged into the equation for the alongshore direction to calculate the shore currents induced by wave run-up and back-wash motions, where a 'weakly two-dimensional solution' is derived from geometrical considerations. The results show that since the water depth near the shoreline is comparable to the bed level fluctuations, the flow is strongly affected by the bed unevenness, leading to recognizable changes in shoreline movement and the time-averaged velocity and the mass flux of the flow in the swash zone. More specifically, the inhomogeneity of the alongshore mass flux generates offshore currents because of the continuity condition for the fluid mass.

Description: Granular surface flows are important in industrial practice and natural systems, but the understanding of such flows is at present incomplete. We present a combined theoretical and experimental study of quasi-two-dimensional heap formation by pouring particles continuously at a point. Two cases are considered: open systems and closed systems. Experimental results show that the shear rate in the flowing layer is nearly independent of the mass flow rate, and the angle of static friction at the bed-layer interface increases with flow rate. Predictions of the model for the flowing layer thickness and interface angles are in good agreement with experiments.

Description: Even though the first theoretical example of chaotic advection was a three-dimensional flow (Henon 1966), the number of theoretical studies addressing chaos and mixing in three-dimensional flows is small. One problem is that an experimentally tractable three-dimensional system that allows detailed experimental and computational investigation had not been available. A prototypical, bounded, three-dimensional, moderate-Reynolds-number flow is presented; this system lends itself to detailed experimental observation and allows high-precision computational inspection of geometrical and dynamical effects. The flow structure, captured by means of cuts with a laser sheet (experimental Poincare section), is visualized via continuously injected fluorescent dye streams, and reveals detailed chaotic structures and chains of high-period islands. Numerical experiments are performed and compared with particle image velocimetry (PIV) and flow visualization results. Predictions of existing theories for chaotic advection in three-dimensional volume-preserving flows are tested. The ratio of two frequencies of particle motion - the frequency of motion around the vertical axis and the frequency of recirculation in the plane containing the axis - is identified as the crucial parameter. Using this parameter, the number of islands in the chain can be predicted. The same parameter - using as a base-case the integrable motion - allows the identification of operating conditions where small perturbations lead to nearly complete mixing.

Description: The theoretical study and experimental investigation of the reflection of asymmetric shock waves in steady flows reported by Li et al. (1999) are complemented by a numerical simulation. All the findings reported in both the theoretical study and the experimental investigation were also evident in the numerical simulation. In addition to weak regular reflection and Mach reflection wave configurations, strong regular reflection and inverse-Mach reflection wave configurations were recorded numerically. The hysteresis phenomenon, which was hypothesized in the course of the theoretical study and then verified in the experimental investigation, was also observed in the numerical simulation.

Description: An explicit solution is provided for the scattering of an obliquely incident flexural-gravity wave by a narrow straight-line crack separating two semi-infinite thin elastic plates floating on water of finite depth. By first separating the solution into the sum of symmetric and antisymmetric parts it is shown that a simple form for each part can be derived in terms of a rapidly convergent infinite series multiplied by a fundamental constant of the problem. This constant is simply determined by applying an appropriate edge condition. Curves of reflection and transmission coefficients are presented, showing how they vary with plate properties and angle of incidence. It is also shown that in the absence of incident waves and for certain relations between their wavelength and frequency, symmetric edge waves exist which travel along the crack and decay in a direction normal to the crack.