The Sensitivity of Set-Up/Set-Down and Wave-Driven Currents to Different Breaking Models

2007 ◽  
Author(s):  
Carl Newell ◽  
Thomas Mullarkey
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Wave Breaking ◽  
Velocity Potential ◽  
Interaction Model ◽  
Radiation Stress ◽  
Current Interaction ◽  
Wave Breaking Model ◽  
Set Up ◽  
Derivatives Of

The authors have developed a wave-current interaction model. It includes a wave sub-model based on the elliptic form of the mild slope wave equation with a parabolic mild slope wave equation as a boundary condition. It also includes a hydrodynamic sub-model which has been developed to examine set-up, set-down and currents in the coastal zone. The wave breaking model used in the wave sub-model affects the results of set-up, set-down and current obtained using the hydrodynamic sub-model. This paper examines a number of different breaking models and compares the set-up, set-down and currents obtained using radiation stress values which are calculated from derivatives of velocity potential. The velocity potential is obtained in the wave sub-model using the various breaking models being examined. The results show a number of possible breaking models for set-up and set-down calculation and also shows shortcomings in various breaking models when it comes to calculation of longshore currents.

Wave Breaking Dissipation in the Wave-Driven Ocean Circulation

2007 ◽  
Vol 37 (7) ◽  
pp. 1749-1763 ◽  
Author(s):  
Juan M. Restrepo
Keyword(s):  
Time Scales ◽  
Ocean Circulation ◽  
Wave Breaking ◽  
Interaction Model ◽  
Stokes Drift ◽  
Dissipative Term ◽  
Flow Vorticity ◽  
Proper Mass ◽  
Long Time ◽  
Current Interaction

Abstract If wave breaking modifies the Lagrangian fluid paths by inducing an uncertainty in the orbit itself and this uncertainty on wave motion time scales is observable as additive noise, it is shown that within the context of a wave–current interaction model for basin- and shelf-scale motions it persists on long time scales. The model of McWilliams et al. provides the general framework for the dynamics of wave–current interactions. In addition to the deterministic part, the vortex force, which couples the total flow vorticity to the residual flow due to the waves, will have a part that is associated with the dissipative mechanism. At the same time the wave field will experience dissipation, and tracer advection is affected by the appearance of a dissipative term in the Stokes drift velocity. Consistency leads to other dynamic consequences: the boundary conditions are modified to take into account the diffusive process and proper mass/momentum balances at the surface of the ocean. In addition to formulating how a wave–current interaction model is modified by the presence of short-time events that induce dissipation, this study proposes a stochastic parameterization of dissipation. Its relation to other alternative parameterizations is given. Two focal reasons make stochastic parameterizations attractive: one can draw from extensive practical modeling experience in other fields, and it ties in a very natural way to a wealth of observational data via statistics.

scholarly journals Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture

1963 ◽  
Vol 3 (3) ◽  
pp. 325-339 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Elastic Waves ◽  
Scattered Field ◽  
Velocity Potential ◽  
Elastic Solid ◽  
Step Function ◽  
Free Surface Waves ◽  
Dependent Variables ◽  
Smooth Plane ◽  
New Feature ◽  
Set Up

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.

An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Wave Motion ◽  
2014 ◽  
Vol 51 (1) ◽  
pp. 168-192 ◽  
Author(s):  
Silvia Falletta ◽  
Giovanni Monegato
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Time Dependent

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

scholarly journals An analytical solution for solving a new wave equation within Lorenzo-Hartley kernel

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3739-3744
Author(s):  
Feng Gao
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Fractional Order ◽  
New Wave ◽  
Liouville Type ◽  
Derivatives Of

In this article we investigate the general fractional-order derivatives of the Riemann-Liouville type via Lorenzo-Hartley kernel, general fractional-order integrals and the new general fractional-order wave equation defined on the definite domain with the analytical soluton.

scholarly journals Determine of the wave equation in the task of electrical oscillations

2018 ◽  
Vol 184 ◽  
pp. 01023
Author(s):  
Gordana V. Jelić ◽  
Vladica Stanojević ◽  
Dragana Radosavljević
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Mathematical Physics ◽  
Equation Of Motion ◽  
Independent Variables ◽  
Equations Of Mathematical Physics ◽  
Basic Equations ◽  
Derivatives Of ◽  
Two Independent Variables ◽  
Transverse Oscillations

One of the basic equations of mathematical physics (for instance function of two independent variables) is the differential equation with partial derivatives of the second order (3). This equation is called the wave equation, and is provided when considering the process of transverse oscillations of wire, longitudinal oscillations of rod, electrical oscillations in a conductor, torsional vibration at waves, etc… The paper shows how to form the equation (3) which is the equation of motion of each point of wire with abscissa x in time t during its oscillation. It is also shown how to determine the equation (3) in the task of electrical oscillations in a conductor. Then equation (3) is determined, and this solution satisfies the boundary and initial conditions.

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