scholarly journals The Effect of a Variable Background Density Stratification and Current on Oceanic Internal Solitary Waves

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 96
Author(s):  
Zihua Liu ◽  
Roger Grimshaw ◽  
Edward Johnson
Keyword(s):  
Internal Waves ◽  
Variable Coefficient ◽  
Vries Equation ◽  
State Density ◽  
Density Stratification ◽  
Internal Solitary Waves ◽  
Climatological Data ◽  
Horizontal Variation ◽  
Background Density ◽  
Background State

Large amplitude, horizontally propagating internal waves are commonly observed in the coastal ocean. They are often modelled by a variable-coefficient Korteweg–de Vries equation to take account of a horizontally varying background state. Although this equation is now well-known, a term representing non-conservative effects, arising from horizontal variation in the underlying basic state density stratification and current, has often been omitted. In this paper, we examine the possible significance of this term using climatological data for several typical oceanic sites where internal waves have been observed.

scholarly journals The Propagation of Internal Solitary Waves over Variable Topography in a Horizontally Two-Dimensional Framework

2018 ◽  
Vol 48 (2) ◽  
pp. 283-300 ◽  
Author(s):  
Chunxin Yuan ◽  
Roger Grimshaw ◽  
Edward Johnson ◽  
Xueen Chen
Keyword(s):  
Solitary Wave ◽  
Wave Field ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Transverse Direction ◽  
Density Stratification ◽  
Internal Solitary Waves ◽  
Two Dimensional ◽  
Petviashvili Equation ◽  
Background Density

AbstractThis paper presents a horizontally two-dimensional theory based on a variable-coefficient Kadomtsev–Petviashvili equation, which is developed to investigate oceanic internal solitary waves propagating over variable bathymetry, for general background density stratification and current shear. To illustrate the theory, a typical monthly averaged density stratification is used for the propagation of an internal solitary wave over either a submarine canyon or a submarine plateau. The evolution is essentially determined by two components, nonlinear effects in the main propagation direction and the diffraction modulation effects in the transverse direction. When the initial solitary wave is located in a narrow area, the consequent spreading effects are dominant, resulting in a wave field largely manifested by a significant diminution of the leading waves, together with some trailing shelves of the opposite polarity. On the other hand, if the initial solitary wave is uniform in the transverse direction, then the evolution is more complicated, though it can be explained by an asymptotic theory for a slowly varying solitary wave combined with the generation of trailing shelves needed to satisfy conservation of mass. This theory is used to demonstrate that it is the transverse dependence of the nonlinear coefficient in the Kadomtsev–Petviashvili equation rather than the coefficient of the linear transverse diffraction term that determines how the wave field evolves. The Massachusetts Institute of Technology (MIT) general circulation model is used to provide a comparison with the variable-coefficient Kadomtsev–Petviashvili model, and good qualitative and quantitative agreements are found.

scholarly journals The modified Korteweg - de Vries equation in the theory of large - amplitude internal waves

1997 ◽  
Vol 4 (4) ◽  
pp. 237-250 ◽  
Author(s):  
R. Grimshaw ◽  
E. Pelinovsky ◽  
T. Talipova
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
Large Amplitude ◽  
Nonlinear Term ◽  
Vries Equation ◽  
Nonlinear Effects ◽  
Wave Generation ◽  
Density Stratification ◽  
De Vries

Abstract. The propagation of large- amplitude internal waves in the ocean is studied here for the case when the nonlinear effects are of cubic order, leading to the modified Korteweg - de Vries equation. The coefficients of this equation are calculated analytically for several models of the density stratification. It is shown that the coefficient of the cubic nonlinear term may have either sign (previously only cases of a negative cubic nonlinearity were known). Cubic nonlinear effects are more important for the high modes of the internal waves. The nonlinear evolution of long periodic (sine) waves is simulated for a three-layer model of the density stratification. The sign of the cubic nonlinear term influences the character of the solitary wave generation. It is shown that the solitary waves of both polarities can appear for either sign of the cubic nonlinear term; if it is positive the solitary waves have a zero pedestal, and if it is negative the solitary waves are generated on the crest and the trough of the long wave. The case of a localised impulsive initial disturbance is also simulated. Here, if the cubic nonlinear term is negative, there is no solitary wave generation at large times, but if it is positive solitary waves appear as the asymptotic solution of the nonlinear wave evolution.

scholarly journals Painleve analysis for a forced Korteveg-de Vries equation arisen in fluid dynamics of internal solitary waves

2015 ◽  
Vol 19 (4) ◽  
pp. 1223-1226 ◽  
Author(s):  
Sheng Zhang ◽  
Mei-Tong Chen ◽  
Wei-Yi Qian
Keyword(s):  
Fluid Dynamics ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Internal Solitary Waves ◽  
Painlevé Analysis ◽  
New Exact Solutions ◽  
De Vries ◽  
Painleve Analysis ◽  
Truncated Painlevé Expansion

In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.

Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves

2004 ◽  
Vol 34 (12) ◽  
pp. 2774-2791 ◽  
Author(s):  
Roger Grimshaw ◽  
Efim Pelinovsky ◽  
Tatiana Talipova ◽  
Audrey Kurkin
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Asymptotic Theory ◽  
Vries Equation ◽  
Internal Solitary Waves ◽  
Variable Depth ◽  
North West ◽  
Wave Parameters ◽  
De Vries

Abstract Internal solitary waves transform as they propagate shoreward over the continental shelf into the coastal zone, from a combination of the horizontal variability of the oceanic hydrology (density and current stratification) and the variable depth. If this background environment varies sufficiently slowly in comparison with an individual solitary wave, then that wave possesses a soliton-like form with varying amplitude and phase. This stage is studied in detail in the framework of the variable-coefficient extended Korteweg–de Vries equation where the variation of the solitary wave parameters can be described analytically through an asymptotic description as a slowly varying solitary wave. Direct numerical simulation of the variable-coefficient extended Korteweg–de Vries equation is performed for several oceanic shelves (North West shelf of Australia, Malin shelf edge, and Arctic shelf) to demonstrate the applicability of the asymptotic theory. It is shown that the solitary wave may maintain its soliton-like form for large distances (up to 100 km), and this fact helps to explain why internal solitons are widely observed in the world's oceans. In some cases the background stratification contains critical points (where the coefficients of the nonlinear terms in the extended Korteweg–de Vries equation change sign), or does not vary sufficiently slowly; in such cases the solitary wave deforms into a group of secondary waves. This stage is studied numerically.

Resonantly generated internal waves in a contraction

1994 ◽  
Vol 274 ◽  
pp. 139-161 ◽  
Author(s):  
S. R. Clarke ◽  
R. H. J. Grimshaw
Keyword(s):  
Critical Point ◽  
Internal Waves ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Negative Polarity ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
Analytical Approximations

The near-resonant flow of a stratified fluid through a localized contraction is considered in the long-wavelength weakly nonlinear limit to investigate the transient development of nonlinear internal waves and whether these might lead to local steady hydraulic flows. It is shown that under these circumstances the response of the fluid will fall into one of three categories, the first governed by a forced Korteweg–de Vries equation and the latter two by a variable-coefficient form of this equation. The variable-coefficient equation is discussed using analytical approximations and numerical solutions when the forcing is of the same (positive) and of opposite (negative) polarity to that of free solitary waves in the fluid. For positive and negative forcing, strong and weak resonant regimes will occur near the critical point. In these resonant regimes for positive forcing the flow becomes locally steady within the contraction, while for negative forcing it remains unsteady within the contraction. The boundaries of these resonant regimes are identified in the limits of long and short contractions, and for a number of common stratifications.

Study Based on FLUENT of Broken Internal Waves in Different Slope Angles

2014 ◽  
Vol 638-640 ◽  
pp. 1769-1777
Author(s):  
Zi Tong Yan ◽  
Liang Qiu Cheng ◽  
Feng Yi ◽  
Tai Zhong Chen ◽  
Han Sun ◽  
...  
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Slope Angle ◽  
Ecological Environment ◽  
Internal Solitary Waves ◽  
Propagation Process ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
New Methods

Internal waves will break in the process of communication, the broken will make water in upper and lower mixing, which has significant influence on the hydrodynamic and layered characteristics of density stratification of the water. In order to reveal the propagation of internal solitary waves, a 3d numerical wave flume was built. The research of the propagation of internal solitary waves in the regular topography and broken on slopes was based on FLUENT. Comparing the fragmentation degree of different slope angle and researching the energy dissipation of the wave propagation process , which are supposed to successfully match the results with the experiment results, can provide new methods and means for the further study of internal wave breaking characteristics and the improvement of ecological environment of water bodies.

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