The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
The tiller emergence in seedling nursery beds and field, and panicle formation in the field were investigated under scattered-planting with seedling dry-raised on plastic trays in double-season rice. A significant dif...The tiller emergence in seedling nursery beds and field, and panicle formation in the field were investigated under scattered-planting with seedling dry-raised on plastic trays in double-season rice. A significant difference was noted in the non-synchronously-emerged tillers （the tillers that formed from latent buds and did not emerge following the normal tillering law on seedling nursery beds and recovered to grow after scattered-planting or transplanting） as well as the percentage of the available synchronously-emerged tillers between seedlings raised on plastic trays under dry-land conditions （DPT） and seedlings raised on nursery beds under wetland conditions （WB）. The seedlings under DPT had some non-synchronously-emerged tillers, but those under WB had not. Therefore, the traditional formula for determining the number of rice seedlings was improved, and the formula for determining the number of basic seedlings under scattered planting with DPT in double-season rice was introduced. For early rice, it was X=Y/{（I＋t1r1）[1＋（N-n-SN）Rr2]＋（SN-3-t1）R2r5}, and for late rice, it was X=Y/{（1＋t1r1）[1＋（N-n-SN）Rr2]＋（N-n-SN-3）Rr2R1r3＋（SN-3-t1）R2r5}. Where, X represents reasonable number of basic seedlings per unit area at scattered-planting; Y, number of fitting panicles per unit area; t1, total number of tillers per plant; r1, percentage of the total available tillers; N, total number of leaves of the main culm; n, total number of elongated internodes in the main culm; SN, seedling leaf ages at scattered-planting; R, percentage of the primary tillers emerged in available node-position; r2, percentage of the available primary tillers; R1, percentage of the secondary tillers in the field （except the secondary tillers of the seedlings）; r3, percentage of the available secondary tillers; R2, percentage of the asynchronously-emerged tillers after scattered-planting; r5, percentage of the available non-synchronously-emerged tillers after scattered-planting.展开更多
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
文摘The tiller emergence in seedling nursery beds and field, and panicle formation in the field were investigated under scattered-planting with seedling dry-raised on plastic trays in double-season rice. A significant difference was noted in the non-synchronously-emerged tillers （the tillers that formed from latent buds and did not emerge following the normal tillering law on seedling nursery beds and recovered to grow after scattered-planting or transplanting） as well as the percentage of the available synchronously-emerged tillers between seedlings raised on plastic trays under dry-land conditions （DPT） and seedlings raised on nursery beds under wetland conditions （WB）. The seedlings under DPT had some non-synchronously-emerged tillers, but those under WB had not. Therefore, the traditional formula for determining the number of rice seedlings was improved, and the formula for determining the number of basic seedlings under scattered planting with DPT in double-season rice was introduced. For early rice, it was X=Y/{（I＋t1r1）[1＋（N-n-SN）Rr2]＋（SN-3-t1）R2r5}, and for late rice, it was X=Y/{（1＋t1r1）[1＋（N-n-SN）Rr2]＋（N-n-SN-3）Rr2R1r3＋（SN-3-t1）R2r5}. Where, X represents reasonable number of basic seedlings per unit area at scattered-planting; Y, number of fitting panicles per unit area; t1, total number of tillers per plant; r1, percentage of the total available tillers; N, total number of leaves of the main culm; n, total number of elongated internodes in the main culm; SN, seedling leaf ages at scattered-planting; R, percentage of the primary tillers emerged in available node-position; r2, percentage of the available primary tillers; R1, percentage of the secondary tillers in the field （except the secondary tillers of the seedlings）; r3, percentage of the available secondary tillers; R2, percentage of the asynchronously-emerged tillers after scattered-planting; r5, percentage of the available non-synchronously-emerged tillers after scattered-planting.
