scholarly journals A NUMERICAL CALCULATION FOR INTERNAL WAVES OVER TOPOGRAPHY

2018 ◽  
pp. 64
Author(s):  
Taro Kakinuma ◽  
Naoto Ochi ◽  
Kei Yamashita ◽  
Keisuke Nakayama
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Critical Level ◽  
Wave Train ◽  
Strong Nonlinearity ◽  
Long Wave ◽  
Fluid Systems ◽  
Steep Decrease ◽  
Shallow Area ◽  
Fundamental Equations

The internal waves propagating from the deep to shallow, and the shallow to deep, areas in the two-layer fluid systems, have been numerically simulated by solving the set of nonlinear equations, based on the variational principle in consideration of both the strong nonlinearity and strong dispersion of internal waves. The incident wave in the deep area, is the BO-type downward convex internal wave, which is the numerical solution obtained for the present fundamental equations. In the cases where the interface elevation is below, or equal to, the critical level in the shallow area, the disintegration of the internal waves occurs remarkably, leading to a long wave train. The lowest elevation of the interface, increases after its gradual decrease in the shallow area, where the interface is above the critical level, while the lowest elevation of the interface, increases through the internal-wave propagation in the shallow area, where the interface elevation is below, or equal to, the critical level, after its steep decrease around the boundary between the area over the upslope, and the shallow region.

scholarly journals Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break

2013 ◽  
Vol 43 (12) ◽  
pp. 2641-2660 ◽  
Author(s):  
Weifeng G. Zhang ◽  
Timothy F. Duda
Keyword(s):  
Internal Wave ◽  
Energy Conversion ◽  
Internal Waves ◽  
Shelf Break ◽  
Internal Tides ◽  
Vertical Shear ◽  
Spectral Structure ◽  
Strong Nonlinearity ◽  
Momentum Exchange ◽  
Baroclinic Energy Conversion

Abstract To quantify dynamical aspects of internal-tide generation at the Mid-Atlantic Bight shelf break, this study employs an idealized ocean model initialized by climatological summertime stratification and forced by monochromatic barotropic tidal currents at the offshore boundary. The Froude number of the scenario is subunity, and the bathymetric slope offshore of the shelf break is supercritical. A barotropic-to-baroclinic energy conversion rate of 335 W m−1 is found, with 14% of the energy locally dissipated through turbulence and bottom friction and 18% radiated onto the shelf. Consistent with prior studies, nonlinear effects result in additional super- and subharmonic internal waves at the shelf break. The subharmonic waves are subinertial, evanescent, and mostly trapped within a narrow beam of internal waves at the forcing frequency. They likely result from nonresonant triad interaction associated with strong nonlinearity. Strong vertical shear associated with the subharmonic waves tends to enhance local energy dissipation and turbulent momentum exchange (TME). A simulation with reduced tidal forcing shows an expected diminished level of harmonic energy. A quasi-linear simulation verifies the role of momentum advection in controlling the relative phases of internal tides and the efficiency of barotropic-to-baroclinic energy conversion. The local TME is tightly coupled with the internal-wave dynamics: for the chosen configuration, neglecting TME causes the internal-wave energy to be overestimated by 12%, and increasing it to high levels damps the waves on the continental shelf. This work implies a necessity to carefully consider nonlinearity and turbulent processes in the calculation of internal tidal waves generated at the shelf break.

Internal Waves Impact on the Sea Surface

2011 ◽  
Author(s):  
Igor V. Shugan ◽  
Hwung-Hweng Hwung ◽  
Ray-Yeng Yang
Keyword(s):  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
High Frequency ◽  
Wave Train ◽  
Sea Surface ◽  
Wave Excitation ◽  
Wave Modulation ◽  
The Impact ◽  
Current Zone

The impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves is theoretically analyzed. An analytical and numerical solution of the modulation equations are found under the conditions close to the group velocity resonance. It is shown that smoothing of the down current surface waves is accompanied by a relatively high-frequency modulation while the profile of the opposing current is reproduced by the surface wave’s envelope. The possibility of generation of an internal wave forerunner, that is a modulated surface wavepacket, is established. Long surface waves can form the wave modulation forerunner ahead of the internal wave, while the relatively short surface waves create the trace of the internal wave. Modulation of surface waves by the periodic internal wave train may have the characteristic period less than the internal wave period and be no uniform while crossing the current zone. Surface wave excitation by internal waves, observable at their group resonance is efficient only on the opposing current.

Numerical study of internal wave–caustic and internal wave–shear interactions in a stratified fluid

2000 ◽  
Vol 415 ◽  
pp. 89-116 ◽  
Author(s):  
A. JAVAM ◽  
J. IMBERGER ◽  
S. W. ARMFIELD
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Turning Point ◽  
Critical Level ◽  
Numerical Study ◽  
Shear Instability ◽  
Level Energy ◽  
Mean Flow ◽  
Reflected Waves ◽  
The Mean

The behaviour of internal waves at a caustic level, turning point and critical layer have been investigated numerically. At a caustic reflection, a triad interaction was formed within the reflection region and the internal wave energy was transferred to lower frequencies (subharmonics). This resulted in a local subharmonic instability. One of the excited internal waves penetrated the caustic level and propagated downwards. This downward propagating wave then produced a second caustic where further reflection could take place. At a turning point, nonlinear interaction between the incident and reflected waves transferred energy to higher frequencies (evanescent trapped waves) which resulted in a superharmonic instability. At the critical level, energy was transferred to the mean flow. As the degree of nonlinearity increased, more energy was found to be transferred and overturning resulted due to a shear instability.

scholarly journals Laboratory investigations on the resonant feature of ‘dead water’ phenomenon

2019 ◽  
Vol 61 (1) ◽  
Author(s):  
Karim Medjdoub ◽  
Imre M. Jánosi ◽  
Miklós Vincze
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Train ◽  
Interfacial Wave ◽  
Maritime Literature ◽  
Propagating Waves ◽  
Lee Waves ◽  
Vertical Density ◽  
Resonant Feature ◽  
Dead Water

Abstract Interfacial internal wave excitation in the wake of towed ships is studied experimentally in a quasi-two-layer fluid. At a critical ‘resonant’ towing velocity, whose value depends on the structure of the vertical density profile, the amplitude of the internal wave train following the ship reaches a maximum, in unison with the development of a drag force acting on the vessel, known in the maritime literature as ‘dead water’. The amplitudes and wavelengths of the emerging internal waves are evaluated for various ship speeds, ship lengths and stratification profiles. The results are compared to linear two- and three-layer theories of freely propagating waves and lee waves. We find that despite the fact that the observed internal waves can have considerable amplitudes, linear theories can still provide a surprisingly adequate description of subcritical-to-supercritical transition and the associated amplification of internal waves. We argue that the latter can be interpreted as a coalescence of frequencies of two fundamental stable wave motions, namely lee waves and propagating interfacial wave modes. Graphic abstract

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.

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.

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