The generation of internal waves by the diurnal barotropic tide in the area of extensive irregularity of the bottom topography

1993 ◽  
Vol 4 (5) ◽  
pp. 339-348 ◽  
Author(s):  
S. V. Dovgaya ◽  
L. V. Cherkesov
Keyword(s):  
Internal Waves ◽  
Bottom Topography ◽  
Barotropic Tide

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.

Tidal Internal Waves in the Bransfield Strait, Antarctica

2021 ◽  
Author(s):  
Eugene Morozov ◽  
Dmitry Frey ◽  
Elizaveta Khimchenko
Keyword(s):  
Internal Waves ◽  
Bottom Topography ◽  
Pressure Sensors ◽  
Internal Tide ◽  
Internal Tides ◽  
South Shetland Islands ◽  
Flat Bottom ◽  
Bransfield Strait ◽  
Vertical Displacements ◽  
Rfbr Grant

<p>Observations of tidal internal waves in the Bransfield Strait, Antarctica, are analyzed. The measurements were carried out for 14 days on a moored station equipped with five autonomous temperature and pressure sensors. The mooring was deployed on the slope of Nelson Island (South Shetland Islands archipelago) over a depth of 70 m at point 62°21ꞌ S, 58°49ꞌ W. Analysis is based on the fluctuations of isotherms.  Vertical displacements of temperature revealed that strong internal vertical oscillations up to 30–40 m are caused by the diurnal internal tide. Spectral analysis of vertical displacements of the 0.9°C isotherm showed a clear peak at a period of 24 h. It is known that the tides in the Bransfield Strait are mostly mixed diurnal and semidiurnal, but during the Antarctic summer, diurnal tide component may intensify. The velocity ellipses of the barotropic tidal currents were estimated using the global tidal model TPXO9.0. It was found that tidal ellipses rotate clockwise with a period of 24 h and anticlockwise with a period of 12 h. The waves are forced due to the interaction of the barotropic tide with the bottom topography. Diurnal internal tides do not develop at latitudes higher than 30º over flat bottom. The research was supported by RFBR grant 20-08-00246.</p>

Spatio-temporal variability of internal waves in the Caspian Sea

2020 ◽  
Author(s):  
Olga Lavrova ◽  
Andrey Kostianoy
Keyword(s):  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Internal Waves ◽  
Satellite Data ◽  
Caspian Sea ◽  
Bottom Topography ◽  
Sea Surface ◽  
Anthropogenic Factors ◽  
Landsat 8 ◽  
The Caspian Sea

<p>Internal waves (IWs) are an intrinsic feature of all density stratified water bodies: oceans, seas, lakes and reservoirs. IWs occur due to various causes. Among them are tides and inertial motions, variations in atmospheric pressure and wind, underwater earthquakes, water flows over bottom topography, anthropogenic factors, etc. In coastal areas of oceans and tidal seas,  IWs induced by tidal currents over shelf edge predominate. Such IWs are well-studied in multiple field, laboratory and numerical experiments. However, the data on IWs in non-tidal seas, such as the Black, Baltic and Caspian Seas, are scarce. Meanwhile, our multi-year satellite observations prove IWs to be quite a characteristic hydrophysical phenomenon of the Caspian Sea. The sea is considered non-tidal because tide height does not exceed 12 cm at the coastline. And yet surface manifestations of IWs are regularly observed in satellite data, both radar and visible. The goal of our study was to reveal spatial, seasonal and interannual variability of IW surface manifestations in the Caspian Sea in the periods of 1999-2012 and 2018-2019 from the analysis of satellite data. All available satellite radar and visible data were used, that is data from ERS1/2 SAR; Envisat ASAR; Sentinel-1A,1B SAR-C; Landsat-4,5 TM; Landsat-7 ETM+; Landsat-8 OLI; Sentinel-2A,2B MSI sensors. During the year, IWs were observed from the beginning of May to mid-September. In certain years, depending on hydrometeorological conditions, such as water heating, wind field, etc., no IWs could be seen in May or September. IWs regularly occur in the east of Middle Caspian and in the northeast of South Caspian. In North Caspian, due to its shallowness and absence of pronounced stratification, IWs are not generated, at least their surface signatures cannot be found in satellite data. In the west of the sea, IWs are scarcely observed, primarily at the beginning of the summer season. IW trains propagate toward the coast, their generation sites are mainly over the depths of 50-200 m.</p><p>According to the available data for the studied periods, the time of the first appearance of IW signatures differs significantly from year to year. For example, in 1999 and 2000 it happened only in July.</p><p>Since no in situ measurements were conducted in the sites of regular IW manifestations, an attempt  was made to establish the dependence of IW occurrence frequency  on seasonal and interannual variations of sea surface temperature, an indirect indicator of the depth of the diurnal or seasonal thermocline, that is where IW were generated. Sea surface temperature was also estimated from satellite data.</p><p>Another issue addressed in the work was the differentiation between the sea surface signatures of IWs in the atmosphere and the sea. The Caspian Sea is known for their close similarity in spatial characteristics.</p><p>The work was carried out with financial support of the Russian Science Foundation grant #19-77-20060.  Processing of satellite data was carried out by Center for Collective Use “IKI-Monitoring” with the use of “See The Sea” system, that was implemented in frame of Theme “Monitoring”, State register No. 01.20.0.2.00164.</p>

Propagation and transformation of nonlinear internal waves of tidal origin observed in the northeastern East China Sea

2020 ◽  
Author(s):  
Seung-Woo Lee ◽  
SungHyun Nam
Keyword(s):  
East China Sea ◽  
Internal Waves ◽  
Bottom Topography ◽  
Wave Interaction ◽  
Propagation Speed ◽  
East China ◽  
Modal Interactions ◽  
Nonlinear Internal Waves ◽  
China Sea ◽  
Mode 2

<p>Oceanic nonlinear internal waves (NLIWs) play an important role in regional circulation, biogeochemistry, energetics, vertical mixing, and underwater acoustics, causing hazards to marine engineering and submarine navigation. Mainly generated by the interaction of the barotropic tides with the bottom topography, they propagate and transform due to wave-wave interaction process. Here, we present characteristics of first two modes of NLIWs observed using high-resolution spatiotemporal data collected in a relatively flat area in the northeastern East China Sea in May 2015. Six groups of NLIWs were identified from the observations: four groups of mode-1 and two groups of mode-2. The amplitude, propagation speed, and characteristic width of mode-1 NLIWs had ranges of 4–16 m, 0.53–0.56 m s<sup>-1</sup>, and 310–610 m, respectively. The mode-2 NLIWs propagate eastward slowly with a speed less than 0.37 m s<sup>-1</sup> with a comparable amplitude of 4–14 m and longer characteristic width of 540–1920 m. Intermodal interactions may take a role in the evolution of mode-1 NLIWs west of the observational area. Our results characterizing the two modes of NLIWs highlight the significance of propagation and transformation of NLIWs and their modal interactions on a broad and shallow shelf.</p>

Scattering of Internal Waves with Frequency Change over Rough Topography

2009 ◽  
Vol 39 (7) ◽  
pp. 1574-1594
Author(s):  
Tomohiro Nakamura ◽  
Toshiyuki Awaji
Keyword(s):  
Internal Waves ◽  
Incident Wave ◽  
Doppler Shift ◽  
Bottom Topography ◽  
Wave Frequency ◽  
Frequency Change ◽  
Background Flow ◽  
Energy Redistribution ◽  
Boundary Mixing ◽  
Incident Waves

Abstract The frequency change in internal gravity waves upon scattering from a rough topography is investigated analytically. For this, sets of appropriate and tractable governing equations for various parameter regimes are derived using the method of multiple scales under the assumption that the amplitude of the bottom topography is small. A solution is shown for a simple case in which an incident internal wave is approximately linear and monochromatic. The solution has the following features: the intrinsic frequencies of the scattered waves are given as the sum and difference of the incident-wave frequency and the Doppler shift (or lee-wave frequency). This Doppler shift causes the change in the frequency. Hence, the assumption of frequency conservation is not valid if the Doppler shift is significant, that is, when the horizontal scale of the bottom roughness (or the length scale in the plane of the slope) is on the order of or much less than that of the incident-wave flow excursion. This condition can be satisfied in a realistic parameter range. The occurrence of such a frequency change has the following implications: first, it affects the estimate of the boundary mixing induced by the scattering because the energy redistribution in the vertical wavenumber space on scattering differs from that estimated using the assumption of frequency conservation. This effect happens because for a given horizontal wavenumber, the change in the frequency alters the vertical wavenumber of the scattered waves through the dispersion relation. Furthermore, if the incident waves are not monochromatic, even the leading-order scattered waves cannot be obtained by the superposition of the solutions for all the Fourier components of the incident waves because of the difference in the Doppler shift. Second, the effects of the background flow associated with the incident and primary reflected waves are significant when the frequency change occurs such that the background flow can create a critical level and/or advect scattered waves. The former causes mixing and background-flow acceleration, and the latter is favorable for the amplification of the scattered waves through superposition. Third, the resulting energy redistribution in frequency space could modify the spectrum shape of the oceanic internal waves, which is considered to affect both interior and boundary mixing.

scholarly journals Huge internal waves in the vicinity of the Spitsbergen Island (Barents Sea)

2011 ◽  
Vol 11 (3) ◽  
pp. 981-986 ◽  
Author(s):  
O. E. Kurkina ◽  
T. G. Talipova
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Internal Waves ◽  
Barents Sea ◽  
Stratified Fluid ◽  
High Latitudes ◽  
Barotropic Tide ◽  
Nonlinear Internal Waves ◽  
Total Height ◽  
The Barents Sea

Abstract. The generation of huge amplitude internal waves by the barotropic tide in the Barents Sea at high latitudes is examined using the numerical model of the Euler 2-D equations for incompressible stratified fluid. The area considered is located between the Spitsbergen (Svalbard) Island and the Franz-Victoria Trough with a cross-section of 350 km length. There are two underwater hills about 100–150 m high on the background depth of about 300 m. It is shown that intensive nonlinear internal waves with amplitudes up to 50 m and lengths of about 6–12 km are generated in this zone. The total height of such waves is huge and they must be considered as a significant factor of the environment in this basin.

Weakly nonlinear internal waves in a two-fluid system

1996 ◽  
Vol 313 ◽  
pp. 83-103 ◽  
Author(s):  
Wooyoung Choi ◽  
Roberto Camassa
Keyword(s):  
Internal Waves ◽  
Numerical Solutions ◽  
Lower Layer ◽  
Bottom Topography ◽  
Ocean Dynamics ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Characteristic Wavelength ◽  
Upper Boundary

We derive general evolution equations for two-dimensional weakly nonlinear waves at the free surface in a system of two fluids of different densities. The thickness of the upper fluid layer is assumed to be small compared with the characteristic wavelength, but no restrictions are imposed on the thickness of the lower layer. We consider the case of a free upper boundary for its relevance in applications to ocean dynamics problems and the case of a non-uniform rigid upper boundary for applications to atmospheric problems. For the special case of shallow water, the new set of equations reduces to the Boussinesq equations for two-dimensional internal waves, whilst, for great and infinite lower-layer depth, we can recover the well-known Intermediate Long Wave and Benjamin–Ono models, respectively, for one-dimensional uni-directional wave propagation. Some numerical solutions of the model for one-dimensional waves in deep water are presented and compared with the known solutions of the uni-directional model. Finally, the effects of finite-amplitude slowly varying bottom topography are included in a model appropriate to the situation when the dependence on one of the horizontal coordinates is weak.

Sign in / Sign up

Export Citation Format

Share Document