Application of a Hybrid SPH - Boussinesq model to predict the lifecycle of landslide-generated waves

2021 ◽  
Vol 223 ◽  
pp. 108658
Author(s):  
Chuan Lin ◽  
Xiangyu Wang ◽  
Manuel Pastor ◽  
Ting Zhang ◽  
Tongchun Li ◽  
...  
Keyword(s):  
Boussinesq Model

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

Laminar natural convection about an isothermally heated sphere at small Grashof number

1968 ◽  
Vol 34 (1) ◽  
pp. 163-176 ◽  
Author(s):  
Francis E. Fendell
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Outer Sphere ◽  
Convective Transport ◽  
Convection Flow ◽  
Constant Density ◽  
Boussinesq Model ◽  
Grashof Number ◽  
Recirculating Flow

The flow induced by gravity about a very small heated isothermal sphere introduced into a fluid in hydrostatic equilibrium is studied. The natural-convection flow is taken to be steady and laminar. The conditions under which the Boussinesq model is a good approximation to the full conservation laws are described. For a concentric finite cold outer sphere with radius, in ratio to the heated sphere radius, roughly less than the Grashof number to the minus one-half power, a recirculating flow occurs; fluid rises near the inner sphere and falls near the outer sphere. For a small heated sphere in an unbounded medium an ordinary perturbation expansion essentially in the Grashof number leads to unbounded velocities far from the sphere; this singularity is the natural-convection analogue of the Whitehead paradox arising in three-dimensional low-Reynolds-number forced-convection flows. Inner-and-outer matched asymptotic expansions reveal the importance of convective transport away from the sphere, although diffusive transport is dominant near the sphere. Approximate solution is given to the nonlinear outer equations, first by seeking a similarity solution (in paraboloidal co-ordinates) for a point heat source valid far from the point source, and then by linearization in the manner of Oseen. The Oseen solution is matched to the inner diffusive solution. Both outer solutions describe a paraboloidal wake above the sphere within which the enthalpy decays slowly relative to the rapid decay outside the wake. The updraft above the sphere is reduced from unbounded growth with distance from the sphere to constant magnitude by restoration of the convective accelerations. Finally, the role of vertical stratification of the ambient density in eventually stagnating updrafts predicted on the basis of a constant-density atmosphere is discussed.

scholarly journals Generation of upstream advancing solitons by moving disturbances

1987 ◽  
Vol 184 ◽  
pp. 75-99 ◽  
Author(s):  
T. Yao-Tsu Wu
Keyword(s):  
Solitary Waves ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Theoretical Models ◽  
Computer Code ◽  
Basic Mechanism ◽  
Stationary Solutions ◽  
Boussinesq Model ◽  
Dispersive Waves ◽  
Fkdv Equation

This study investigates the recently identified phenomenon whereby a forcing disturbance moving steadily with a transcritical velocity in shallow water can generate, periodically, a succession of solitary waves, advancing upstream of the disturbance in procession, while a train of weakly nonlinear and weakly dispersive waves develops downstream of a region of depressed water surface trailing just behind the disturbance. This phenomenon was numerically discovered by Wu & Wu (1982) based on the generalized Boussinesq model for describing two-dimensional long waves generated by moving surface pressure or topography. In a joint theoretical and experimental study, Lee (1985) found a broad agreement between the experiment and two theoretical models, the generalized Boussinesq and the forced Korteweg-de Vries (fKdV) equations, both containing forcing functions. The fKdV model is applied in the present study to explore the basic mechanism underlying the phenomenon.To facilitate the analysis of the stability of solutions of the initial-boundary-value problem of the fKdV equation, a family of forced steady solitary waves is found. Any such solution, if once established, will remain permanent in form in accordance with the uniqueness theorem shown here. One of the simplest of the stationary solutions, which is a one-parameter family and can be scaled into a universal similarity form, is chosen for stability calculations. As a test of the computer code, the initially established stationary solution is found to be numerically permanent in form with fractional uncertainties of less than 2% after the wave has traversed, under forcing, the distance of 600 water depths. The other numerical results show that when the wave is initially so disturbed as to have to rise from the rest state, which is taken as the initial value, the same phenomenon of the generation of upstream-advancing solitons is found to appear, with a definite time period of generation. The result for this similarity family shows that the period of generation, Ts, and the scaled amplitude α of the solitons so generated are related by the formula Ts = const α−3/2. This relation is further found to be in good agreement with the first-principle prediction derived here based on mass, momentum and energy considerations of the fKdV equation.

Natural convection in porous media: effect of weak dispersion on bifurcation

1990 ◽  
Vol 216 ◽  
pp. 285-298 ◽  
Author(s):  
Xiaowei S. He ◽  
John G. Georgiadis
Keyword(s):  
Effective Conductivity ◽  
Horizontal Layer ◽  
Hydrodynamic Dispersion ◽  
The Novel ◽  
Media Effect ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Volumetric Heating ◽  
Pitchfork Bifurcations ◽  
The Impact

We use weakly nonlinear analysis via a two-parameter expansion to study bifurcation of conduction into cellular convection of an internally heated fluid in a porous medium that forms a horizontal layer between two isothermal walls. The Darcy–Boussinesq model of convection is enhanced by including two nonlinear terms: (i) quadratic (Forchheimer) drag; and (ii) hydrodynamic dispersion enhancement of the thermal conductivity described by a weak linear relationship between effective conductivity and local amplitude of filtration velocity. The impact of the second term on the shape of the bifurcation curve for two-dimensional rolls is profound in the presence of uniform volumetric heating. The resulting bifurcation structure is unlike any pitchfork bifurcations typical of the classical Bénard problem. Although direct experimental validation of the novel bifurcation is not available, we would like to register it as an alternative or a supplement to models of small imperfections, and as an attempt to account for the scatter of observed critical values for the first bifurcation.

scholarly journals TSUNAMI PHASE SPEED REDUCTION DUE TO WATER COMPRESSIBILTY

2018 ◽  
pp. 9
Author(s):  
Ali Abdolali ◽  
James T. Kirby
Keyword(s):  
Arrival Time ◽  
Phase Speed ◽  
Propagation Speed ◽  
Frequency Dispersion ◽  
Wave Theory ◽  
Polar Coordinates ◽  
Ocean Bottom ◽  
Tsunami Propagation ◽  
Boussinesq Model ◽  
Tsunami Waves

Most existing tsunami propagation models consider the ocean to be an incompressible, homogenous medium. Recently, it has been shown that a number of physical features can slow the propagation speed of tsunami waves, including wave frequency dispersion, ocean bottom elasticity, water compressibility and thermal or salinity stratification. These physical effects are secondary to the leading order, shallow water or long wave behavior, but still play a quantifiable role in tsunami arrival time, especially at far distant locations. In this work, we have performed analytical and numerical investigations and have shown that consideration of those effects can actually improve the prediction of arrival time at distant stations, compared to incompressible forms of wave equations. We derive a modified Mild Slope Equation for Weakly Compressible fluid following the method proposed by Sammarco et al. (2013) and Abdolali et al. (2015) using linearized wave theory, and then describe comparable extensions to the Boussinesq model of Kirby et al. (2013). Both models account for water compressibility and compression of static water column to simulate tsunami waves. The mild slope model is formulated in plane Cartesian coordinates and is thus limited to medium propagation distances, while the Boussinesq model is formulated in spherical polar coordinates and is suitable for ocean scale simulations.

Wave Simulations in Ponce de Leon Inlet Using Boussinesq Model

2003 ◽  
Vol 129 (3) ◽  
pp. 124-135 ◽  
Author(s):  
Fengyan Shi ◽  
James T. Kirby ◽  
Robert A. Dalrymple ◽  
Qin Chen
Keyword(s):  
Boussinesq Model
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