scholarly journals EVOLUTION OF DAMAGED ARMOR LAYER PROFILE

2011 ◽  
Vol 1 (32) ◽  
pp. 40
Author(s):  
Ali Farhadzadeh ◽  
Nobuhisa Kobayashi ◽  
Jeffrey Melby
Keyword(s):  
Water Depth ◽  
Hydrodynamic Model ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Irregular Wave ◽  
Progression Model ◽  
Damage Progression ◽  
Dry Zone ◽  
The Mean ◽  
Exponential Probability

A probabilistic hydrodynamic model for the wet and dry zone on a permeable structure is developed to predict irregular wave action on the structure above the still water level. The model is based on the time-averaged continuity and momentum equations for nonlinear shallow-water waves coupled with the exponential probability distribution of the water depth. The model predicts the cross-shore variations of the mean and standard deviation of the water depth and horizontal velocity. Damage progression of a stone armor layer is predicted by modifying a formula for bed load on beaches with input from the hydrodynamic model. The damage progression model is compared with three tests by Melby and Kobayashi (1998) that lasted up to 28.5 hours. The model predicts the temporal progression of the eroded area quite well. The numerical model is very efficient and suited for a risk-based design of rubble mound structures.

Hydraulic control of homogeneous shear flows

2003 ◽  
Vol 475 ◽  
pp. 163-172 ◽  
Author(s):  
CHRIS GARRETT ◽  
FRANK GERDES
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Water Waves ◽  
Flow Speed ◽  
Hydraulic Control ◽  
Mean Flow ◽  
Shallow Water Waves ◽  
Homogeneous Fluid ◽  
Apparent Paradox ◽  
The Mean

If a shear flow of a homogeneous fluid preserves the shape of its velocity profile, a standard formula for the condition for hydraulic control suggests that this is achieved when the depth-averaged flow speed is less than (gh)1/2. On the other hand, shallow-water waves have a speed relative to the mean flow of more than (gh)1/2, suggesting that information could propagate upstream. This apparent paradox is resolved by showing that the internal stress required to maintain a constant velocity profile depends on flow derivatives along the channel, thus altering the wave speed without introducing damping. By contrast, an inviscid shear flow does not maintain the same profile shape, but it can be shown that long waves are stationary at a position of hydraulic control.

scholarly journals APPLICATIONS OF A NUMERICAL SHALLOW WATER WAVES MODEL

1982 ◽  
Vol 1 (18) ◽  
pp. 54
Author(s):  
A. Hauguel ◽  
Ph. Pechon
Keyword(s):  
Numerical Model ◽  
Water Waves ◽  
Breaking Waves ◽  
Scale Model ◽  
Dimensional Model ◽  
Longshore Current ◽  
Shallow Water Waves ◽  
Storm Waves ◽  
Mean Sea Surface ◽  
The Mean

This paper relates three applications of a numerical model of storm waves in shallow waters developed in LNH. The equations are recalled at first and then the applications performed are presented. The numerical model has been used in the case of the port of Fecamp, on the English Channel coast, on which the results of a scale model were available. The computed results compare well with the scale model measurements. The second case is the s imulation of a t sumami induced by a submarine landslide which appeared in 1979 near Nice ; the mode 1 has permitted the simulation of the rising of the wave. The last applications consisted in simulating breaking waves by introducing a dispersion term in the equations. This simulation has been tested with a one-dimensional model at first. The results show that the numerical model reproduces the elevation of the mean sea surface due to the loss of energy in breakings. Then the longshore current induced by breaking waves coming obliquely over a rectilinear sloping shore has been reproduced with a two dimensional model. The results show that the model is able to compute with a good accuracy re fraction, diffraction and reflection, and that it appears to be very interesting for longshore currents simulation.

scholarly journals Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Mathias Klahn ◽  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Water Waves ◽  
Second Order ◽  
Wave Number ◽  
Order Effects ◽  
Wave Fields ◽  
Fully Nonlinear ◽  
Vertical Coordinate ◽  
Irregular Wave ◽  
Mean And Variance ◽  
The Mean

In this paper, we study the mean and variance of the Eulerian and Lagrangian fluid velocities as a function of depth below the surface of directionally spread irregular wave fields given by JONSWAP spectra in deep water. We focus on the behaviour of these quantities in the bulk of the water, and using second-order potential flow theory we derive new simple asymptotic approximations for their decay in the limit of large depth below the surface. Specifically, we show that when the depth is greater than about 1.5 peak wavelengths, the variance of the Eulerian velocity decays in proportion to exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) , and the mean Lagrangian velocity decays in proportion to 1 ( − k p z ) 1 / 6 exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) . Here, k p is the peak wave number and z is the vertical coordinate measured positively upwards from the still water level. We test the accuracy of the second-order formulation against new fully nonlinear simulations of both short crested and long crested irregular wave fields and find a good match, even when the simulations are known to be affected substantially by third-order effects. To our knowledge, this marks the first fully nonlinear investigation of the Eulerian and Lagrangian velocities below the surface in irregular wave fields.

Cloaking in shallow-water waves via nonlinear medium transformation

2015 ◽  
Vol 778 ◽  
pp. 273-287 ◽  
Author(s):  
Ahmad Zareei ◽  
Mohammad-Reza Alam
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Governing Equation ◽  
Water Waves ◽  
Electromagnetic Waves ◽  
Nonlinear Transformation ◽  
Gravitational Acceleration ◽  
Shallow Water Waves ◽  
Variable Permeability ◽  
Single Polarization

A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell’s equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell’s equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. We show that with this nonlinear transformation an object can be cloaked from any wave that merely satisfies the long-wave assumption. The presented transformation can be applied as well for the design of non-magnetic optical cloaks for electromagnetic waves.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach

Integrable Models

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solution ◽  
Water Waves ◽  
Heisenberg Model ◽  
Kdv Equation ◽  
Short Review ◽  
Lax Pair ◽  
Shallow Water Waves ◽  
Initial Value ◽  
The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

Sign in / Sign up

Export Citation Format

Share Document