scholarly journals MODELING TURBULENT BORE PROPAGATION IN THE SURF ZONE

1984 ◽  
Vol 1 (19) ◽  
pp. 7
Author(s):  
David R. Basco ◽  
Ib A. Svendsen
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Surf Zone ◽  
Momentum Balance ◽  
Correction Coefficient ◽  
Nonlinear Shallow Water Equations ◽  
Horizontal Momentum ◽  
T Distribution ◽  
The Waves ◽  
Turbulent Bore

Initial efforts to numerically simulate surf zone waves by using a modified form of the nonlinear shallow water equations are described. Turbulence generated at the front of the moving bore-like wave spreads vertically downward to significantly alter the velocity profile and hence the horizontal momentum flux. This influence of turbulence is incorporated into the momentum balance equation through a momentum correction coefficient, a which is prescribed based in part upon the theoretical a(x) distribution beneath stationary hydraulic jumps. The numerical results show that with a suitably chosen a(x) distribution, the equations not only dissipate energy as the waves propagate, but also that the wave shape stabilizes as a realistic profile rather than progressively steepening as when the nonlinear shallow water equations are employed. Further research is needed to theoretically determine the appropriate a(x,t) distribution.

A shock solution for the nonlinear shallow water equations

2010 ◽  
Vol 658 ◽  
pp. 166-187 ◽  
Author(s):  
MATTEO ANTUONO
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Theoretical Analysis ◽  
Asymptotic Behaviour ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Boundary Data ◽  
Depth Analysis ◽  
Nonlinear Shallow Water Equations ◽  
Shock Solution

A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the main quantities along and behind the bore. The theoretical analysis is then applied to the specific case in which the water at the front of the shock wave is still. A comparison with the Shen & Meyer (J. Fluid Mech., vol. 16, 1963, p. 113) solution reveals that such a solution can be regarded as a specific case of the more general solution proposed here. The results obtained can be regarded as a useful benchmark for numerical solvers based on the NSWEs.

Dispersive Nonlinear Shallow-Water Equations

2009 ◽  
Vol 122 (1) ◽  
pp. 1-28 ◽  
Author(s):  
M. Antuono ◽  
V. Liapidevskii ◽  
M. Brocchini
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Nonlinear Shallow Water Equations

A turbulent bore on a beach

1984 ◽  
Vol 148 ◽  
pp. 73-96 ◽  
Author(s):  
I. A. Svendsen ◽  
P. A. Madsen
Keyword(s):  
Theoretical Model ◽  
Energy Dissipation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Present Model ◽  
Finite Amplitude ◽  
Shear Stresses ◽  
Flow Conditions ◽  
Physical Conditions ◽  
Turbulent Bore

A theoretical model is developed giving a moderately detailed description of the flow in a turbulent bore, the velocity profiles, the shear stresses, the energy dissipation, etc. An analysis of the flow conditions at the toe of the turbulent front indicates significant differences from the usual description based on the finite-amplitude shallow-water equations, and it is shown that the present model gives a closer description of the actual physical conditions. Finally, numerical results are presented that illustrate how the model works, and test its validity on an example with known properties.

Computational study of some nonlinear shallow water equations

Open Physics ◽  
2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Ali Bhrawy ◽  
Mohamed Abdelkawy
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Periodic Solutions ◽  
Shallow Water Equations ◽  
Computational Study ◽  
Expansion Method ◽  
Coastal Areas ◽  
Atmospheric Modeling ◽  
Hydraulic Engineering ◽  
Nonlinear Shallow Water Equations

AbstractThe shallow water equations have wide applications in ocean, atmospheric modeling and hydraulic engineering, also they can be used to model flows in rivers and coastal areas. In this article we obtained exact solutions of three equations of shallow water by using $\frac{{G'}} {G} $-expansion method. Hyperbolic and triangular periodic solutions can be obtained from the $\frac{{G'}} {G} $-expansion method.

scholarly journals Seiche in the Gulf of Tonkin

1996 ◽  
Vol 18 (1) ◽  
pp. 27-33
Author(s):  
Pham Van Ninh ◽  
Tran Thi Ngoc Duyet
Keyword(s):  
Boundary Condition ◽  
Numerical Modelling ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Forced Oscillation ◽  
Two Dimensional ◽  
Nonlinear Shallow Water Equations ◽  
Liquid Boundary ◽  
Gulf Of Tonkin

Steichen in the Gulf of Tonkin has been studied by numerical modelling based on the two-dimensional nonlinear shallow water equations system with liquid boundary condition given in the form of forced oscillation. The main proper periods have been defined as follows: 23-25 hours, 1-12 hours, 5-7 hours, 2-4 hours. Among them the 23 hours period is the most evident. The obtained results coincide with observed ones at the long shore hydrometeological stations of the Gulf.

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