scholarly journals On the Coriolis Effect for Internal Ocean Waves

2022 ◽  
Author(s):  
R. Ivanov
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Coriolis Force ◽  
Water Wave ◽  
Small Amplitude ◽  
Ocean Waves ◽  
Coriolis Effect ◽  
Wave Dynamics ◽  
Ostrovsky Equation ◽  
Physical Variables

Abstract. A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.

scholarly journals Internal Wave Dynamics Over Isolated Seamount and Its Influence on Coral Larvae Dispersion

2021 ◽  
Vol 8 ◽  
Author(s):  
Nataliya Stashchuk ◽  
Vasiliy Vlasenko
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Tidal Flow ◽  
Winter Season ◽  
Internal Tides ◽  
Coral Larvae ◽  
Volcanic Origin ◽  
Wave Dynamics ◽  
Short Scale ◽  
Tracking Model

The internal wave dynamics over Rosemary Bank Seamount (RBS), North Atlantic, were investigated using the Massachusetts Institute of Technology general circulation model. The model was forced by M2-tidal body force. The model results are validated against the in-situ data collected during the 136th cruise of the RRS “James Cook” in June 2016. The observations and the modeling experiments have shown two-wave processes developed independently in the subsurface and bottom layers. Being super-critical topography for the semi-diurnal internal tides, RBS does not reveal any evidence of tidal beams. It was found that below 800-m depth, the tidal flow generates bottom trapped sub-inertial internal waves propagated around RBS. The tidal flow interacting with a cluster of volcanic origin tall bottom cones generates short-scale internal waves located in 100 m thick seasonal pycnocline. A weakly stratified layer separates the internal waves generated in two waveguides. Parameters of short-scale sub-surface internal waves are sensitive to the season stratification. It is unlikely they can be observed in the winter season from November to March when seasonal pycnocline is not formed. The deep-water coral larvae dispersion is mainly controlled by bottom trapped tidally generated internal waves in the winter season. A Lagrangian-type passive particle tracking model is used to reproduce the transport of generic deep-sea water invertebrate species.

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.

Numerical Studies of Internal Wave Dynamics

1997 ◽  
Author(s):  
George F. Carnevale ◽  
M. C. Hendershott
Keyword(s):  
Internal Wave ◽  
Wave Dynamics ◽  
Numerical Studies

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.

Shallow water wave generation by unsteady flow

1968 ◽  
Vol 31 (4) ◽  
pp. 779-788 ◽  
Author(s):  
J. E. Ffowcs Williams ◽  
D. L. Hawkings
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Point Of View ◽  
Sound Waves ◽  
Aerodynamic Sound ◽  
Shallow Layer ◽  
Sound Theory ◽  
Water Simulation

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

1993 ◽  
Vol 251 ◽  
pp. 21-53 ◽  
Author(s):  
Sergei I. Badulin ◽  
Victor I. Shrira
Keyword(s):  
Shear Flow ◽  
Internal Wave ◽  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Energy Concentration ◽  
Local Analysis ◽  
Mean Flow ◽  
Wave Trapping ◽  
Wave Dynamics

The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

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