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Flow with a free surface
Published in Bernard S. Massey, John Ward-Smith, Mechanics of Fluids, 2018
Bernard S. Massey, John Ward-Smith
Waves whose properties are primarily determined by gravitational effects are referred to as gravity waves. Surface tension effects can then be ignored and eqn 10.54 reduces to () c2=gλ2πtanh(2hπλ)
Hybridizing FDM and FVM scheme of high-precision interface fast capture for mixed free-surface-pressurized flow in large cascade water delivery system
Published in Journal of Hydraulic Research, 2023
Yifei Huang, Guanghua Guan, Kang Wang, Zhonghao Mao, Zhonghua Yang
This phenomenon was caused by the Riemann problem. When a mixed free-surface-pressurized flow occurred, the gravity wave and pressure wave velocities significantly differed, leading to initial discontinuity. When solving the Riemann problem, if the value of Δx/Δt was close to the movement speed of the initial discontinuity, as determined by mass conservation, using difference instead of differentiation can cause the discontinuity of each step to be fixed in several adjacent grids. This will help in obtaining the numerical result close to the analytical result. When the value of Δx/Δt was greater than the discontinuous motion speed, the discontinuity position calculated by the analytical solution was not at the boundary of adjacent grids. However, it fixed to the closest grid boundary, dislocating the position, which made the interface divergent. When the movement speed was less than the discontinuous motion speed, the discontinuous position of the analytical solution calculation was inside the grid, and the numerical solution of the difference solution was only at the grid boundary. Therefore, the number of iterations increased, the calculation efficiency decreased, and the discontinuous motion speed became faster than that in the FVM results. In addition, severe numerical oscillations occurred at the interface between the free-surface flow and the interface, and the numerical oscillations of the pressurized flow part eased.
Effects of bottom permeability on wave generation by a moving oscillatory disturbance in magneto-hydrodynamics
Published in Waves in Random and Complex Media, 2022
Selina Hossain, Sandip Paul, Soumen De
In the field of linearised water wave theory an ocean with permeable bottom is quite feasible and has been considered by many researchers. For example, Mase and Takeba [11] analyzed wave transformations over a permeable seabed with slowly varying depth. Martha et al. [17] considered water-wave scattering problem with a porous sea-bed. Wave scattering problem in a multi-layered fluid with porous undulating bed was considered by Paul and De [20]. Not only in wave scattering problems, there were many works on wave generation problem in which a porous bottom was assumed. Kundu and Mandal [23] considered an ocean with porous bottom to study the wave generation problem by an axisymmetric initial disturbance on the surface. Mohanty and Sidharth [24] studied the transient flexural gravity wave motion in an ocean with a permeable bed in the presence of current. Later, Mohanty [26] discussed the time-dependent capillary gravity wave motion in the presence of undulated permeable ocean bottom.
On the evolution of global ocean tides
Published in Geophysical & Astrophysical Fluid Dynamics, 2021
The thickness of fluid layer, namely ocean depth, influences the natural frequency of surface gravity wave and hence tidal resonances. On a long geologic timescale ocean depth changes. According to Hallam (1984) ocean in the history was about 600 metres higher. In the future, ocean can be shallower because of evaporation. We do not know the accurate change of ocean depth and so we assume the change of metres as reference. Figure 3 shows the evolution of tides on the long timescale of Earth's rotation with the three ocean depths for comparison with the present depth 3688 metres. It shows that for both lunar and solar tides a deeper ocean advances resonance while a shallower ocean postpones resonance. As stated, the tidal wave is a mixed mode of inertial wave and surface gravity wave. The frequency of the latter is scaled by its phase speed , and therefore, a deeper ocean corresponds to a higher frequency of surface gravity wave and hence a higher eigenfrequency of tidal wave, as shown in Figure 3. However, the change of ocean depth does not radically change tidal resonances, i.e. it cannot strongly suppress tidal resonances.