Modeling of Waves Propagating in Water with a Crushed Ice Layer on the Free Surface

A transformation of gravitational waves in fluid of constant depth with a crushed ice layer floating on the free fluid surface is considered. The propagating waves undergo a slight damping along their path of propagation. The main goal of the study is to construct an approximate descriptive model of this phenomenon.With regard to small displacements of the free surface, a viscous type model of damping is considered, which corresponds to a continuous distribution of dash-pots at the free surface of the fluid. A constant parameter of the dampers is assumed in advance as known parameter of damping. This parameter may be obtained by means of experiments in a laboratory flume.

Stationary ideal flow on a free surface of a given shape

We study the stationary, ideal flow on a free fluid surface with a prescribed shape. It is demonstrated that the flow is governed by a self-contained set of equations for the surface flow field without any reference to the bulk flow. To write down these equations for arbitrary surfaces, we apply a covariant formulation using Riemannian geometry and we show how to include surface tension and velocity-dependent forces such as the Coriolis force. We write down explicitly the equations for cases where the surface elevation can be written as function of either Cartesian or polar coordinates in the plane, and we obtain solutions for the important case of rotational symmetry and the perturbed flow when this symmetry is slightly broken. To understand the general character and solubility of the equations, we introduce the associated dynamical system describing the motion along the streamlines. The existence of orbits with transversal intersections, as well as quasi-periodic and chaotic solutions, show that not all boundary value problems are well-posed. In the particular case of unforced motion the streamlines are geodesic curves and in this case the existence of a non-trivial surface velocity field requires that the surface can be foliated by a family of non-intersecting geodesic curves.

Simulation of of 3D Flood Waves by Gas-Liquid Two-Phase Model

This paper is concerned with a gas-liquid two-phase model combining with the k–ε turbulent model for numerical simulation of 3D flood waves due to complete or partial dam-break. The flow equations are solved with the finite volume method and solved by the pressure-correction algorithm of the SIMPLE-type. The free fluid surface is simulated by the the volume of fluid(VOF) method. The comparisons with other numerical results show that the proposed method is accurate, reliable and effective in simulation of dam-break flood waves.

Large Eddy Simulation of Gas-Liquid Two-Phase Flow for a Nested Type Fixed-Cone Valve

large eddy simulation cooperated with a physical fractional-step method is applied to simulate steady flow around a nested type fixed-cone valve; and the equations are solved with the finite volume method. The free fluid surface is simulated by the VOF method. The pressure contours and vorticity magnitude are obtained. The modeling results conform to physical law, and show that the large eddy simulation theory has powerful capacity in simulation of microstructures of turbulent flows, and the function of the nested type fixed-cone valve for energy dissipating is good.

On Nonlinear Dynamics in a Free Fluid Surface of a Tank Excited by a Non-Ideal Power Source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor.