Linear long wave propagation over discontinuous submerged shallow water topography

Shankar, Ravi; Yan, Shuangqin; Golbek, Megan; Hartland, Tucker; Gerrodette, Peter; Fomin, Sergei; Чугунов, В. А.

doi:10.1016/j.amc.2014.11.034

Cited by 4 publications

(3 citation statements)

References 22 publications

(61 reference statements)

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“…It is found that the recovery coefficient of anchor chain shows strong nonlinear characteristics, and the influence of geometric nonlinearity cannot be ignored in the course of research. 1 Kaplon 2 studied the different types of cables based on catenary equation and derived the analytical expressions of cable tension distribution and geometry. Zarruk et al 3 used a set of parameters to approximate the external excitation of the anchor cable, taking into account external forces.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamic response analysis of submerged multi-body structure considering the uncertainty of connection gap

Zhou

Fang

et al. 2019

Noise & Vibration Worldwide

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The aim of this study is to determine the stochastic dynamic characteristics of the system due to the uncertainty of the gap contact between the mooring cable and the structural body of the submerged multi-body structure. The sag effect caused by the light, flexible, and low damping characteristics of the mooring cable and its dynamic elongation under the action of the flow field and the impact of the gap connection is considered. The sag effect is corrected using the equivalent elastic modulus method; the stochastic generalized non-deterministic dynamic model of the system considering the dynamic elongation and clearance contact of the mooring cable is established; and the Newmark-β method and the interval algorithm are used to solve the problem. The calculation results show that the mean and peak values of the kinematic parameters of the structure are larger than the ideal articulated state; the dynamic tension is changed randomly; and the deflection angle of the gap-contact state is greater than that of the articulated state, which may lead to the instability of the system. Therefore, when studying the concrete structure in water, we should consider the contact state of the joint and analyze its stochastic dynamic characteristics.

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Section: Introductionmentioning

confidence: 99%

Stochastic dynamic response analysis of submerged multi-body structure considering the uncertainty of connection gap

Zhou

Fang

et al. 2019

Noise & Vibration Worldwide

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“…For linear equations where wave collapse doesn't occur, numerical solutions have been widely studied in various contexts (see e.g. [9]). In contrast, there have only been a few attempts to develop numerical methods for predicting the time of nonlinear wave collapse.…”

Section: Introductionmentioning

confidence: 99%

Numerical Computation of Wave Breaking Times

2015

SIURO

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The time of nonlinear wave collapse is computed numerically for the Hopf equation. Previous numerical criteria for locating the time of wave collapse are either computationally prohibitive to implement or give erroneous results. A new criterion for this purpose is developed analytically using asymptotic analysis of the wave shock development shortly after breaking. The criterion defines the wave breaking time as the onset of energy dissipation. This onset results in a singularity in the third derivative of the energy function, the location of which yields the breaking time. A numerical criterion is formulated from this analytical result and tested against the exact analytical value of the breaking time. This is done by first solving the differential equation with a finite difference method. Then, to compensate for numerical error, a moving average method is developed to refine the energy data. The obtained results give visible convergence to the analytical breaking time as the numerical mesh is refined.

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“…We further simplify our non-dimensional model by using scale analysis on equations (1) and (2) [5], [8].…”

Section: Non-dimensional Modelmentioning

confidence: 99%

Modeling Tsunami Run-Up and Draw-Down on the Beach

Noland¹

2018

SIURO

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Previous literature has investigated the run-up and draw-down of tsunami waves on a one-dimensional, constant-sloped beach, but the existing solutions are complex and computationally unwieldy. Our research aims to establish a simpler model while still obtaining accurate results. We do so by using a quasi-linear theory derived from the nonlinear shallow-water wave equations. These equations are considered over a linear beach with properly imposed initial and boundary conditions. The main difficulty in solving this problem is the moving boundary associated with the shoreline motion. To eliminate this difficulty, we apply an appropriate substitution to the spatial variable, and thus replace the moving boundary of the computational domain with a stationary boundary. A key feature of our tsunami problem is the presence of the small parameter ε = η 0 h 0 , where η0 is the characteristic amplitude of the wave and h0 is the characteristic depth of the ocean. Due to the presence of this small parameter, the problem can be essentially linearized using the method of perturbations and then solved analytically via an integral transformation. Our explicit solution enables us to swiftly predict the behavior of the wave using an essentially linear model. We test the accuracy of our model against the numerical solution obtained using Mathematica, and find minimal discrepancies. Finally, we extend our results to a modified beach configuration that more accurately reflects real-world shoreline topography.

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Linear long wave propagation over discontinuous submerged shallow water topography

Cited by 4 publications

References 22 publications

Stochastic dynamic response analysis of submerged multi-body structure considering the uncertainty of connection gap

Stochastic dynamic response analysis of submerged multi-body structure considering the uncertainty of connection gap

Numerical Computation of Wave Breaking Times

Modeling Tsunami Run-Up and Draw-Down on the Beach

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