A Study of Internal Waves and Turbulence Above Irregular, Sloping Bathymetry: A Contribution to the Littoral Internal Wave Initiative (LIWI)

1997 ◽  
Author(s):  
Kurt L. Polzin ◽  
John M. Toole ◽  
Raymond W. Schmitt
Keyword(s):  
Internal Wave ◽  
Internal Waves

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.

Density Wave Measurements in a Rectangular Clarifier

1983 ◽  
Vol 18 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Mark K. Watson ◽  
R.R. Hudgins ◽  
P.L. Silveston
Keyword(s):  
Power Spectrum ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Motion ◽  
Wave Amplitude ◽  
Suspended Solids ◽  
Small Volume ◽  
Density Wave ◽  
Measure Concentration ◽  
Wave Measurements

Abstract Internal wave motion was studied in a laboratory rectangular, primary clarifier. A photo-extinction device was used as a turbidimeter to measure concentration fluctuations in a small volume within the clarifier as a function of time. The signal from this device was fed to a HP21MX minicomputer and the power spectrum plotted from data records lasting approximately 30 min. Results show large changes of wave amplitude as frequency increases. Two distinct regions occur: one with high amplitudes at frequencies below 0.03 Hz, the second with very small amplitudes appears for frequencies greater than 0.1 Hz. The former is associated with internal waves, the latter with flow-generated turbulence. Depth, velocity in the clarifier and inlet suspended solids influence wave amplitudes and the spectra. A variation with position or orientation of the probe was not detected. Contradictory results were found for the influence of flow contraction baffles on internal wave amplitude.

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

Study of Nonlinear Internal Waves and Impact on Offshore Drilling Units

2011 ◽  
Author(s):  
Nishu V. Kurup ◽  
Shan Shi ◽  
Zhongmin Shi ◽  
Wenju Miao ◽  
Lei Jiang
Keyword(s):  
Numerical Model ◽  
South China Sea ◽  
Internal Wave ◽  
Internal Waves ◽  
South China ◽  
Andaman Sea ◽  
Offshore Drilling ◽  
Nonlinear Internal Waves ◽  
Drilling Operations ◽  
Drilling System

Internal waves near the ocean surface have been observed in many parts of the world including the Andaman Sea, Sulu Sea and South China Sea among others. The factors that cause and propagate these large amplitude waves include bathymetry, density stratification and ocean currents. Although their effects on floating drilling platforms and its riser systems have not been extensively studied, these waves have in the past seriously disrupted offshore exploration and drilling operations. In particular a drill pipe was ripped from the BOP and lost during drilling operations in the Andaman sea. Drilling riser damages were also reported from the south China Sea among other places. The purpose of this paper is to present a valid numerical model conforming to the physics of weakly nonlinear internal waves and to study the effects on offshore drilling semisubmersibles and riser systems. The pertinent differential equation that captures the physics is the Korteweg-de Vries (KdV) equation which has a general solution involving Jacobian elliptical functions. The solution of the Taylor Goldstein equation captures the effects of the pycnocline. Internal wave packets with decayed oscillations as observed from satellite pictures are specifically modeled. The nonlinear internal waves are characterized by wave amplitudes that can exceed 50 ms and the present of shearing currents near the layer of pycnocline. The offshore drilling system is exposed to these current shears and the associated movements of large volumes of water. The effect of internal waves on drilling systems is studied through nonlinear fully coupled time domain analysis. The numerical model is implemented in a coupled analysis program where the hull, moorings and riser are considered as an integrated system. The program is then utilized to study the effects of the internal wave on the platform global motions and drilling system integrity. The study could be useful for future guidance on offshore exploration and drilling operations in areas where the internal wave phenomenon is prominent.

scholarly journals On Internal Waves Propagating across a Geostrophic Front

2019 ◽  
Vol 49 (5) ◽  
pp. 1229-1248 ◽  
Author(s):  
Qiang Li ◽  
Xianzhong Mao ◽  
John Huthnance ◽  
Shuqun Cai ◽  
Samuel Kelly
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
Horizontal Shear ◽  
Mixing Rate ◽  
Reflection And Transmission ◽  
Topographic Slope ◽  
Virtual Boundary ◽  
The Impact

AbstractReflection and transmission of normally incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal wave theory in the absence of a front. The equation type is determined by a parameter Δ, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave, and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the Northern Hemisphere, positive vorticity of the front may produce Δ ≤ 0, that is, a “forbidden zone,” in which wave solutions are not permitted. Thus, Δ = 0 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom boundaries in buoyancy coordinates (or the slope of the virtual boundary if a forbidden zone is present) determine wave reflection and transmission. The reflection coefficient for normally incident internal waves depends on rotation, isopycnal slope, topographic slope, and incident mode number. The scattering rate to high vertical modes allows a bulk estimate of the mixing rate, although the impact of internal wave-driven mixing on the geostrophic front is neglected.

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