Analytical Models for Velocity Distributions in Compound Channels with Emerged and Submerged Vegetated Floodplains

The lateral distributions of depth-averaged velocity in open compound channels with emerged and submerged vegetated floodplains were analyzed based on the analytical solution of the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term to account for the effects of vegetation.The three cases considered for open channels were two-stage rectangular channel with emerged vegetated floodplain,rectangular channel with submerged vegetated corner,and two-stage rectangular channel with submerged vegetated floodplain,respectively.To predict the depth-averaged velocity with submerged vegetated floodplains,we proposed a new method based on a two-layer approach where flow above and through the vegetation layer was described separately.Moreover,further experiments in the two-stage rectangular channel with submerged vegetated floodplain were carried out to verify the results.The analytical solutions of the cases indicated that the corresponding analytical depth-averaged velocity distributions agree well with the simulated and experimental prediction.The analytical solutions of the cases with theoretical foundation and without programming calculation were reasonable and applicable,which were more convenient than numerical simulations.The analytical solutions provided a way for future researches to solve the problems of submerged vegetation and discontinuous phenomenon of depth-averaged velocity at the stage point for compound channels.Understanding the hydraulics of flow in compound channels with vegetated floodplains is very important for supporting the management of fluvial processes.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

Breather molecules and localized interaction solutions in the(2+1)-dimensional BLMP equation

The(2+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation is an important integrable model.In this paper,we obtain the breather molecule,the breather-soliton molecule and some localized interaction solutions to the BLMP equation.In particular,by employing a compound method consisting of the velocity resonance,partial module resonance and degeneration of the breather techniques,we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump,as well as a bell-shaped soliton and lump.Due to the lack of the long wave limit,it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump.The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically.The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations.