The effect of a submerged barrier on the natural freqencies and radiation damping of a shallow basin connected to open water

AbstractA theory is provided for the natural seiching frequencies and radiative decay rates for a shallow-water basin whose connection to open water is restricted by a submerged wall or reef. The transition from an essentially-open basin to a closed basin, as the aperture reduces to zero, is discussed using a matching procedure. Graphs of frequencies and damping factors as functions of aperture size are obtained for idealized two-dimensional shelf configurations, involving a constant-depth shallow basin connected to constant-depth, but not necessarily shallow, open water.

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A new well-balanced finite-volume scheme on unstructured triangular grids for two-dimensional two-layer shallow water flows with wet-dry fronts

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110380 ◽

2021 ◽

Vol 438 ◽

pp. 110380

Author(s):

Xin Liu

Keyword(s):

Shallow Water ◽

Finite Volume ◽

Finite Volume Scheme ◽

Two Dimensional ◽

Volume Scheme ◽

Water Flows ◽

Triangular Grids ◽

Shallow Water Flows

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Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽

10.3390/w13162152 ◽

2021 ◽

Vol 13 (16) ◽

pp. 2152

Author(s):

Gonzalo García-Alén ◽

Olalla García-Fonte ◽

Luis Cea ◽

Luís Pena ◽

Jerónimo Puertas

Keyword(s):

Experimental Data ◽

Shallow Water ◽

Shallow Water Equations ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Experimental Dataset ◽

River Hydraulics ◽

Shallow Water Models ◽

Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

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Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽

10.3390/math9121439 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1439

Author(s):

Chaudry Masood Khalique ◽

Karabo Plaatjie

Keyword(s):

Differential Equation ◽

Wave Equation ◽

Shallow Water ◽

Water Wave ◽

Elliptic Integral ◽

Momentum Conservation ◽

Two Dimensional ◽

Order Ordinary Differential Equation ◽

Closed Form Solutions ◽

Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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