scholarly journals NUMERICAL ANALYSES ON PROPAGATION OF NONLINEAR INTERNAL WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 24
Author(s):  
Kei Yamashita ◽  
Taro Kakinuma ◽  
Keisuke Nakayama
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Wave Equations ◽  
Vertical Wall ◽  
Submerged Breakwater ◽  
Wave Trough ◽  
Water Region ◽  
Wave Nonlinearity ◽  
Sloping Beach

A set of nonlinear surface/internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of surface/internal waves propagating through a shallow- or a deep-water region in a tank. Internal waves propagating over a submerged breakwater or a uniformly sloping beach are also simulated. The internal progressive wave shows remarkable shoaling when the interface reaches the critical level, after which physical variables including wave celerity become unstable near the wave-breaking point. In the case of the internal-wave trough reflecting at the vertical wall, the vertical velocities of water particles in the vicinity of the interface are different from that of the moving interface at the wall near the wave breaking, which means that the kinematic boundary condition on the interface of trough has been unsatisfied.

scholarly journals SHOALING OF NONLINEAR INTERNAL WAVES ON A UNIFORMLY SLOPING BEACH

2012 ◽  
Vol 1 (33) ◽  
pp. 72 ◽  
Author(s):  
Kei Yamashita ◽  
Taro Kakinuma ◽  
Keisuke Nakayama
Keyword(s):  
Experimental Data ◽  
Internal Waves ◽  
Wave Height ◽  
Wave Breaking ◽  
Critical Level ◽  
Lower Layer ◽  
Strong Nonlinearity ◽  
Initial Wave ◽  
Wave Nonlinearity ◽  
Sloping Beach

The internal waves in the two-layer systems have been numerically simulated by solving the set of nonlinear equations in consideration of both strong nonlinearity and strong dispersion of waves. After the comparison between the numerical results and the BO solitons, as well as the experimental data, the internal waves propagating over the uniformly sloping beach are simulated including the cases of the mild and long slopes. The internal waves show remarkable shoaling after the interface touches the critical level. In the lower layer, the horizontal velocity becomes larger than the local linear celerity of internal waves in shallow water just before the crest peak and the position is defined as the wave-breaking point when the ratio of nonlinear parameter to beach slope is large. The ratio of initial wave height to wave-breaking depth becomes larger as the slope is milder and the wave nonlinearity is stronger. The wave height does not increase so much before wave-breaking on the mildest slope.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

Models of energy loss from internal waves breaking in the ocean

2017 ◽  
Vol 836 ◽  
pp. 72-116 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Exact Solution ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Convective Instability ◽  
Helmholtz Instability ◽  
Turbulent Dissipation ◽  
The Waves ◽  
Data Representative ◽  
Made In

The supply of energy to the internal wave field in the ocean is, in total, sufficient to support the mixing required to maintain the stratification of the ocean, but can the required rates of turbulent dissipation in mid-water be sustained by breaking internal waves? It is assumed that turbulence occurs in regions where the field of motion can be represented by an exact solution of the equations that describe waves propagating through a uniformly stratified fluid and becoming unstable. Two instabilities leading to wave breaking are examined, convective instability and shear-induced Kelvin–Helmholtz instability. Models are constrained by data representative of the mid-water ocean. Calculations of turbulent dissipation are first made on the assumption that all the waves representing local breaking have the same steepness, $s$, and frequency, $\unicode[STIX]{x1D70E}$. For some ranges of $s$ and $\unicode[STIX]{x1D70E}$, breaking can support the required transfer of energy to turbulence. For convective instability this proves possible for sufficiently large $s$, typically exceeding 2.0, over a range of $\unicode[STIX]{x1D70E}$, while for shear-induced instability near-inertial waves are required. Relaxation of the constraint that the model waves all have the same $s$ and $\unicode[STIX]{x1D70E}$ requires new assumptions about the nature and consequences of wave breaking. Examples predict an overall dissipation consistent with the observed rates. Further observations are, however, required to test the validity of the assumptions made in the models and, in particular, to determine the nature and frequency of internal wave breaking in the mid-water ocean.

scholarly journals Scattering of Low-Mode Internal Waves at Finite Isolated Topography

2014 ◽  
Vol 44 (1) ◽  
pp. 359-383 ◽  
Author(s):  
Sonya Legg
Keyword(s):  
Internal Wave ◽  
Froude Number ◽  
Internal Waves ◽  
Wave Breaking ◽  
Internal Tides ◽  
Relative Height ◽  
Incoming Wave ◽  
Topographic Slope ◽  
Height Increase ◽  
Incoming Energy

Abstract A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h0/H0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h0/H0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h0/H0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.

scholarly journals Nonlinear Characteristics of Internal Waves in a Deep-Water Region or near a Wave-Breaking Point

2010 ◽  
Vol 66 (1) ◽  
pp. 26-30
Author(s):  
Kei YAMASHITA ◽  
Taro KAKINUMA ◽  
Keisuke NAKAYAMA ◽  
Masayuki OIKAWA ◽  
Hidekazu TSUJI ◽  
...  
Keyword(s):  
Internal Waves ◽  
Deep Water ◽  
Wave Breaking ◽  
Breaking Point ◽  
Nonlinear Characteristics ◽  
Water Region

scholarly journals Sensitivity of internal wave energy distribution over seabed corrugations to adjacent seabed features

2017 ◽  
Vol 824 ◽  
pp. 74-96 ◽  
Author(s):  
Farid Karimpour ◽  
Ahmad Zareei ◽  
Joël Tchoufag ◽  
Mohammad-Reza Alam
Keyword(s):  
Steady State ◽  
Energy Distribution ◽  
Internal Wave ◽  
Internal Waves ◽  
Bragg Reflection ◽  
Vertical Wall ◽  
Internal Gravity Waves ◽  
Destructive Interference ◽  
Complete Disappearance ◽  
Reflected Waves

Here we show that the distribution of energy of internal gravity waves over a patch of seabed corrugations strongly depends on the distance of the patch to adjacent seafloor features located downstream of the patch. Specifically, we consider the steady state energy distribution due to an incident internal wave arriving at a patch of seabed ripples neighbouring (i) another patch of ripples (i.e. a second patch) and (ii) a vertical wall. Seabed undulations with dominant wavenumber twice as large as overpassing internal waves reflect back part of the energy of the incident internal waves (Bragg reflection) and allow the rest of the energy to transmit downstream. In the presence of a neighbouring topography on the downstream side, the transmitted energy from the patch may reflect back; partially if the downstream topography is another set of seabed ripples or fully if it is a vertical wall. The reflected wave from the downstream topography is again reflected back by the patch of ripples through the same mechanism. This consecutive reflection goes on indefinitely, leading to a complex interaction pattern including constructive and destructive interference of multiply reflected waves as well as an interplay between higher mode internal waves resonated over the topography. We show here that when steady state is reached both the qualitative and quantitative behaviour of the energy distribution over the patch is a strong function of the distance between the patch and the downstream topography: it can increase or decrease exponentially fast along the patch or stay (nearly) unchanged. As a result, for instance, the local energy density in the water column can become an order of magnitude larger in certain areas merely based on where the downstream topography is. This may result in the formation of steep waves in specific areas of the ocean, leading to breaking and enhanced mixing. At a particular distance, the wall or the second patch may also result in a complete disappearance of the trace of the seabed undulations on the upstream and the downstream wave field.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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