NP7.1

Extreme Internal Wave Events: Generation, Transformation, Breaking and Interaction with the Bottom Topography

This session welcomes contributions presenting advances in, and approaches to, the modelling, monitoring, and forecasting of internal waves in stratified estuaries, lakes and the coastal oсean.
Internal solitary waves (ISWs) and large-amplitude internal wave packets are a commonly observed event in oceans and lakes. In the oceans ISWs are mainly generated by the interaction of the barotropic tides with bottom topography. Large amplitude solitary waves are energetic events that generate strong currents. They can also trap fluid with larvae and sediments in the cores of waves and transport it a considerable distance. ISWs can cause hazards to marine engineering and submarine navigation, and significantly impact marine ecosystems and particle transport in the bottom layer of the ocean and stratified lakes. Contributions studying flows due to internal waves, their origin, propagation and influence on the surrounding environment are thus of broad scientific importance.
The scope of the session involves all aspects of ISWs generation, propagation, transformation and the interaction of internal waves with bottom topography and shelf zones, as well as an evaluation of the role of internal waves in sediment resuspension and transport. Breaking of internal-waves also drives turbulent mixing in the ocean interior that is important for climate ocean models. Discussion of parameterizations for internal-wave driven turbulent mixing in global ocean models is also invited.

Co-organized by OS2
Convener: Marek Stastna | Co-conveners: Kateryna Terletska, Zhenhua Xu, Tatiana Talipova
Presentations
| Thu, 26 May, 17:00–18:24 (CEST)
 
Room 0.94/95

Presentations: Thu, 26 May | Room 0.94/95

Chairperson: Marek Stastna
17:00–17:06
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EGU22-4274
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On-site presentation
Kateryna Terletska and Vladimir Maderich

Simulations of internal solitary waves (ISW) of the first mode over the isolated obstacles of various shapes:  triangles, semicircle and rectangles of different lengths are presented.  The influence of height, length and shape of the obstacle on the transformation of ISW and energy dissipation was investigated. A two-layer free surface water system with upper and bottom layer thicknesses h1 and h2 and densities ρ1 and ρ2, respectively, and water depth H was considered.  It was carried out set of 42 numerical experiments with both ISW of elevation and depression types. The results of simulation were compared with the results of laboratory experiments. It is shown that the blocking parameter B  [1] (that is a dimensionless parameter equal to the ratio of the lower layer above the obstacle to the wave amplitude) is useful for describing the type of interaction and estimation of energy loss.  The transformation of large amplitude ISW over a triangular obstacle differs from the corresponding interaction with the semicircle obstacle. Internal boluses formed in the case of semicircle or rectangle obstacle are 1.5 - 2 times larger than in the case of a triangular obstacle. As a result, energy dissipation and corresponding mixing in the case of ISW transformation over semicircle and a rectangular obstacle is greater than in the case of a triangular ones. Maximum energy losses can reach 42% in the case of a rectangular obstacle. Energy losses increase with increasing length of the obstacle. Thus, we can conclude that topographic effects, namely the influence of shape and geometric characteristics of underwater obstacles have a significant impact on the dissipation of mechanical energy. 

 

[1]  T. Talipova , K. Terletska, V. Maderich, I. Brovchenko, K. T. Jung, E. Pelinovsky and R. Grimshaw  Internal solitary wave transformation over the bottom step: loss of energy. // Phys. Fluids, 2013, 25, 032110

How to cite: Terletska, K. and Maderich, V.: Estimation of energy loss of internal solitary waves over an isolated obstacle, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-4274, https://doi.org/10.5194/egusphere-egu22-4274, 2022.

17:06–17:12
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EGU22-1228
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On-site presentation
Marek Stastna

In late winter/early spring temperate and northern lakes often experience a so-called weak, inverse stratification.  This occurs since: i) fresh water experiences a maximum density at around four degrees Centigrade, ii) the lake is iced over and thus mechanically isolated from the overlying atmosphere, iii) the increasing solar insolation heats the water column according to the Beer-Lambert-Bouguer law; thereby producing a region of instability that mixes a portion of the water column.  This classical scenario fits some lakes, but the small density differences due to the thermal forcing also imply that very small amounts of dissolved salts could create a more complex, combined solute-thermal stratification.  We explore the behaviour of nonlinear internal waves for one such measured stratification. For mode-1 we find well defined internal solitary waves. For mode-2 the coupling between pycnoclines is weaker leading to a more complex dynamics that we quantify in detail. 

How to cite: Stastna, M.: Mode-2 internal waves and inter-mode resonance in late winter lakes, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1228, https://doi.org/10.5194/egusphere-egu22-1228, 2022.

17:12–17:18
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EGU22-2365
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ECS
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Highlight
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On-site presentation
Sam Hartharn-Evans and Magda Carr

Internal Waves are commonly observed along density interfaces across the world’s oceans. In the Arctic Ocean, the internal wave field is much less energetic than at lower latitudes, but due to relative quiescence of the region, nonlinear internal waves are particularly important for mixing there. This mixing is responsible for bringing heat from warm Atlantic Water at intermediate depth towards the surface where it has ramifications for the formation and melt of sea ice, as well as the general circulation of the Arctic Ocean. In the rapidly changing Arctic Ocean, as sea ice extent declines, understanding how internal waves interact with sea ice, and how sea ice affects them is crucial, particularly in the marginal ice zone.

Using laboratory experiments of internal solitary waves (ISWs) propagating under model ice the interaction of ice and internal solitary waves is investigated. Specifically, (i) Particle Tracking Velocimetry is used to measure the motion of floating discs (with the same density as sea ice ρ = 910kg/m³), to determine how ice moves in response to the near-surface internal wave-induced flow using is quantified. Additionally, (ii) Particle Image Velocimetry is used to determine how the near-surface internal wave-induced flow dynamics are impacted by the presence and motion of the model sea-ice, which acts as a rough upper boundary condition and moves with the flow.

How to cite: Hartharn-Evans, S. and Carr, M.: The Interaction of Internal Solitary Waves and Sea Ice in the laboratory, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-2365, https://doi.org/10.5194/egusphere-egu22-2365, 2022.

17:18–17:24
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EGU22-5790
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On-site presentation
Tess Wegman, Julie Pietrzak, Wouter Kranenburg, Robert Jan Labeur, and Martin Verlaan

The Rotterdam Waterway is part of the Rhine-Meuse estuary, which is characterized a salt wedge estuary. Therefore, it is persistently strongly stratified. Field observations in the Rotterdam Waterway, described in earlier literature, reveal internal waves (IWs) generated by resonance over undular bottom topography. IWs are widely found in estuarine and coastal regions, and can contribute to mixing in stratified bodies of water. In this study we explore the generation of IWs over a series of sinusoidal bed forms and their potential of mixing.

An idealised 2D stretch of an estuary, containing sinusoidal bottom topography, is modelled in the non-hydrostatic finite element numerical model FINLAB. The effects of varying wavelength and wave height of the undular topographic features on internal wave generation and vertical mixing are evaluated.

From the model results we find that the generation of the resonant internal wave modes are in correspondence with an analytical analysis based on linear theory. Our results show that in the case of bed form induced internal waves, vertical mixing in the short 2D stretch increases, compared to a flat bed. This is predominantly caused by an increase in bottom friction. This suggests that the trapped internal waves only give a relatively small contribution to this increase in vertical mixing in the area of generation.

Further investigations are required to quantify the contribution from internal waves to vertical mixing, once the waves start to propagate through the domain. Furthermore, the model results will be compared to recent observations of internal waves in the Rotterdam Waterway. Internal wave characteristics and the generation mechanism will be compared to the model results.

How to cite: Wegman, T., Pietrzak, J., Kranenburg, W., Labeur, R. J., and Verlaan, M.: Mixing contributions from resonant trapped internal waves generated by bottom topography in an estuary, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-5790, https://doi.org/10.5194/egusphere-egu22-5790, 2022.

17:24–17:30
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EGU22-6793
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ECS
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Virtual presentation
Peiwen Zhang, zhenhua Xu, qun Li, jia You, baoshu Yin, robin Robertson, and quanan Zheng

The deformation and evolution of internal solitary waves (ISWs) beneath an ice keel can enable potential diapycnal mixing and facilitate upper ocean heat transport, despite a poor understanding of the underlying physics and energetics of ISWs in Polar environments. This study aims to understand the dynamic processes and mixing properties during the evolution of ISWs beneath ice keels (undersea portion of ice cover) in the Arctic Ocean using high-resolution, non-hydrostatic simulations. Ice keels can destabilize ISWs through overturning events. Consequently, the initial ISW disintegrates and transfers its energy into secondary smaller-scale waves. During the ISW-ice interaction, ISW-induced turbulent mixing can reach O(10-3) W/kg with a magnitude of resultant heat flux of O(10)W/m. Sensitivity experiments demonstrated that the ISW-ice interaction weakened as the ice keel depth decreased, and consequently, the resultant turbulent mixing and upward heat transfer also decreased. The ice keel depth was critical to the evolution and disintegration of an ISW beneath the ice keel, while the approximate ice keel shape had little effect. Our results provide an important but previously overlooked energy source for upper ocean heat transport in the Arctic Ocean.

How to cite: Zhang, P., Xu, Z., Li, Q., You, J., Yin, B., Robertson, R., and Zheng, Q.: Numerical simulations of an internal solitary wave evolution beneath an ice keel, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6793, https://doi.org/10.5194/egusphere-egu22-6793, 2022.

17:30–17:36
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EGU22-7582
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Virtual presentation
Subhajit Kar and Roy Barkan

Fronts and near-inertial waves (NIWs) are energetic motions in the upper ocean that are thought to interact and provide a possible route for kinetic energy dissipation of mesoscale balanced flows. To date, the theoretical explanations for such interactions rely on the fronts being geostrophic, with a weak ageostrophic secondary circulation (ASC) and a small Rossby number. We develop a quasilinear model to study the interactions between NIW vertical modes and a 2D front undergoing semigeostrophic frontogenesis. In our model, frontal sharpening is divided into two stages: an exponential stage, that is characterized by a low Rossby number and is driven by geostrophic strain; and a super-exponential stage, that is characterized by an O(1) Rossby number and is driven by the convergence of the ASC. We identify a new mechanism, the convergence production, through which NIWs can efficiently extract energy from the front during the super-exponential stage. It is shown that the convergence production can dominate the known mechanism of energy extraction during the exponential stage, the deformation shear production, for a relatively strong geostrophic strain field.

How to cite: Kar, S. and Barkan, R.: Energy exchanges between two-dimensional front and internal waves., EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7582, https://doi.org/10.5194/egusphere-egu22-7582, 2022.

17:36–17:42
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EGU22-3255
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Virtual presentation
Zhenhua Xu

Ocean circulation strongly influences how internal tides radiate and break and stimulates the spatial inhomogeneity and temporal variation of internal tidal mixing. Qualitative and quantitative characterizations of interactions between internal tides and general circulation are critical to multi-scale circulation dynamics. Based on significant progress in regional circulation simulation, we obtain an observation-supported internal tide energy field around Luzon Strait by deterministically resolving the dynamics of the radiating paths of the internal tide energy. These paths are created when the known most powerful internal tide of Luzon Strait interacts with the Kuroshio Current. We found that the radiating tidal pattern, local dissipation efficiency, and energy field respond differently to the leaping, looping, and leaking Kuroshio paths within Luzon Strait. Our new insights into the dynamics and our clarifying the controlling refraction mechanism within the general circulation create the potential for internal tides to be represented better in climate models. 

How to cite: Xu, Z.:  Dynamics Insight of  Internal Tide Radiation in the Kuroshio , EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3255, https://doi.org/10.5194/egusphere-egu22-3255, 2022.

17:42–17:48
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EGU22-8974
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ECS
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Virtual presentation
Seung-Woo Lee and SungHyun Nam

Oceanic nonlinear internal waves (NLIWs) play an important role in regional circulation, marine biogeochemistry, energetics, vertical mixing, underwater acoustics, marine engineering, and submarine navigation, most commonly generated by the interaction between barotropic tides and bathymetry. However, our understanding of their characteristics, generation, and propagation is still far from complete in many water bodies. Here, we present the characteristics of NLIWs observed from moored and underway observation in the northern East China Sea during May 15-28, 2015 and discuss their generation and propagation. The NLIWs observed during the experiment were characterized by an amplitude ranging from 4 to 16 m, width ranging from 380 to 600 m, and propagated southwestward at a speed of 0.64–0.72 m s−1. Groups of NLIWs were predominantly observed during, or a couple of days after, the period of spring tides, with a time interval 24–96 min shorter than the canonical semidiurnal period (12.42 h; M2); this is in contrast to those found in many other regions that have a phase-locking to the barotropic semidiurnal tides. The remote generation and propagation of the NLIWs from potential generation sites into the study area under time-varying stratification support the fact that the time interval departed from the semidiurnal period. Our results have substantial implications for turbulent mixing and ocean circulation in regions where the shelf is broad and shallow. The NLIWs generated from multiple sources propagate in multiple directions with propagating speeds varying over days depending on stratification. 

How to cite: Lee, S.-W. and Nam, S.: Characteristics, Generation, and Propagation of Nonlinear Internal Waves Observed in the Northern East China Sea, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8974, https://doi.org/10.5194/egusphere-egu22-8974, 2022.

17:48–17:54
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EGU22-3426
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Virtual presentation
Jia You, ZhenHua Xu, Robin Robertson, Qun Li, and BaoShu Yin

   Upper ocean mixing plays a key role in the atmosphere-ocean heat transfer and sea ice extent and thickness via modulating the upper ocean temperatures in the Arctic Ocean. Observations of diffusivities in the Arctic that directly indicate the ocean mixing properties are sparse. Therefore, the spatiotemporal pattern and magnitude of diapycnal diffusivities and kinetic energy dissipation rates in the upper Arctic Ocean are important for atmosphere-ocean heat transfers and sea ice changes. These were first estimated from the Ice-Tethered Profilers dataset (2005–2019) using a strain-based fine-scale parameterization. The resultant mixing properties showed significant geographical inhomogeneity and temporal variability. Diapycnal diffusivities and dissipation rates in the Atlantic sector of the Arctic Ocean were stronger than those on the Pacific side. Mixing in the Atlantic sector increased significantly during the observation period; whereas in the Pacific sector, it weakened before 2011 and then strengthened. Potential impact factors include wind, sea ice, near inertial waves, and stratification, while their relative contributions vary between the two sectors of the Arctic Ocean. In the Atlantic sector, turbulent mixing dominated, while in the Pacific sector, turbulent mixing was inhibited by strong stratification prior to 2011, and is able to overcome the stratification gradually after 2014. The vertical turbulent heat flux constantly increased in the Atlantic sector year by year, while it decreased in the Pacific sector post 2010. The estimated heat flux variability induced by enhanced turbulent mixing is expected to continue to diminish sea ice in the near future. 

How to cite: You, J., Xu, Z., Robertson, R., Li, Q., and Yin, B.: Geographical inhomogeneity and temporal variability in mixing property and driving mechanism in the Arctic Ocean, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3426, https://doi.org/10.5194/egusphere-egu22-3426, 2022.

17:54–18:00
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EGU22-3451
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Virtual presentation
Chen Zhao, Zhenhua Xu, Robin Robertson, Qun Li, Yang Wang, and Baoshu Yin

  Internal tides are energetic in the Mariana arc, but their three-dimensional radiation and dissipation remain unexplored, particularly the trench-arc-basin impacts. Here, the generation, propagation and dissipation of M2 internal tides over the Mariana area are examined using a series of observation-supported high-resolution simulations. The M2 barotropic to baroclinic conversion rate amounts to 8.35 GW, of which two arc-shaped ridges contribute ~81% of the generated energy. The contributions to generation by the Mariana basin and deep trench are weak. Nevertheless, they are important in modulating the energy radiation and dissipation, since tidal beams can spread to these areas. The Mariana ridges radiate the westward-focused and eastward-spreading tidal beams. This is very consistent with the altimetric measurements. The resonance in the ridge center enhances the westward converging beam, which can travel across the Palau Ridge, 800 km away. In contrast, the eastward beams propagate over a limited lateral range, but can radiate and dissipate significant energy in the deep water column, reaching even to the abyssal Mariana trench. The direct estimation from the model results reveals the dissipation’s multilayer vertical profile in the entire water column, and is well consistent with the finescale parameterization estimate based on vertical strain. However, the estimate of an oft-used energy balance method, which typically assumes an exponentially decaying vertical structure function for the dissipation rate based on distance above the seafloor, is largely inconsistent with the measurements. Our findings highlight the complexity of three-dimensional radiation paths and dissipation map of internal tides in the Mariana area.

How to cite: Zhao, C., Xu, Z., Robertson, R., Li, Q., Wang, Y., and Yin, B.: The Three-Dimensional Internal Tide Radiation andDissipation in the Mariana Arc-Trench System, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3451, https://doi.org/10.5194/egusphere-egu22-3451, 2022.

18:00–18:06
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EGU22-3460
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ECS
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Virtual presentation
Weidong Wang, Robin Robertson, Yang Wang, Chen Zhao, Jia You, Zhenhua Xu, and Baoshu Yin

Internal tide variations and mixing properties are important to shelf dynamics and mass exchange. In the present study, spatiotemporal variability of internal tides and their modulation factors on the southern East China Sea (ECS) shelf are examined using a three-month mooring observation. Semidiurnal and diurnal internal tides are found to exhibit distinct varying trends. Specifically, the semidiurnal internal tides are quite weak at the early stage, but greatly enhanced in the last three spring-neap cycles. In contrast, the diurnal internal tides follow quasi spring-neap variability except for the strengthening in two specific periods. The enhancement of semidiurnal internal tides in late July and August can be attributed to the strengthened stratifications shelf-slope area northeast of Taiwan Island, which is identified as the generation source. While the diurnal internal tides are modulated by background circulation through the effective critical latitude. The weak critical latitude effect corresponds to the intermittent enhancement of diurnal internal tides in two specific periods. In addition, the circulation also affects the vertical modal structures of the internal tides. The proportion of higher modes internal tides increases during robust eddy activities.  The high-frequency and high-mode internal tides are of crucial significance for turbulent mixing on the shelf region.

Key word: Internal Tides; Mooring Observation; Spatiotemporal variation; Shelf dynamics

How to cite: Wang, W., Robertson, R., Wang, Y., Zhao, C., You, J., Xu, Z., and Yin, B.: Temporal variability of Multimodal Internal Tides at the East China Sea Shelf, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3460, https://doi.org/10.5194/egusphere-egu22-3460, 2022.

18:06–18:12
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EGU22-8278
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ECS
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Virtual presentation
Yang Wang, Zhenhua Xu, Toshiyuki Hibiya, Baoshu Yin, and Fan Wang

The diurnal internal tides contribute nearly a quarter of global baroclinic tidal energy, while their roles in shaping spatiotemporal inhomogeneity of tidal energy field are not well known. Here, based on a combination of observation-supported numerical simulation and theoretical analyses, we clarify the combined and relative contributions of β refraction, subtidal circulation refraction and multi-wave interference to the long-range radiation and dissipation maps of diurnal internal tides in the northwestern Pacific. The diurnal tidal beams are primarily emanated from the Luzon Strait (LS) and Talaud-Halmahera Passage (THP). The β refraction effect, which is more pronounced at higher latitudes, refracts the mean path of LS tidal beam equatorward by ~40° when it arrives at the deep basin, consistent with previous altimeter observations. A second refraction effect by subtidal circulation with seasonal variability deflects the mean beam path by ~10°. Multi-wave interference of tidal beams from the LS and THP further enhances the inhomogeneous pattern, resulting in enhanced and reduced energy flux beam branches with distinct vertical structures in the west Mariana basin. A modified line-source model and theoretical ray-tracing analysis can well explain the effects of refraction and interference. Internal tidal dissipation map in the deep basin coincides well with the inhomogeneous and spreading radiation paths. The mechanism characterization of the world’s most energetic diurnal internal tides in the northwestern Pacific could improve our understanding of global baroclinic tidal energy redistribution and associated tidal mixing parameterization in climate-scale ocean models.

How to cite: Wang, Y., Xu, Z., Hibiya, T., Yin, B., and Wang, F.: Radiation Path of Diurnal Internal Tide in the Northwestern Pacific Controlled by Refraction and Interference, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8278, https://doi.org/10.5194/egusphere-egu22-8278, 2022.

18:12–18:18
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EGU22-59
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ECS
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Virtual presentation
Egor Svergun and Aleksey Zimin

The main source of generation of short-period internal waves (SIW’s) is the dissipation of the internal tide on the roughness of the bottom relief. Differences in the slope of the bottom and geographical latitude have an impact on the propagation of internal tide and on the generation of SIW’s. Based on the synthesis of the results of contact, remote observations, and modeling, the characteristics of the SIW’s in the Barents Sea on a wide shelf with small bottom slopes, and in the Avacha Bay with a narrow shelf and significant bottom slopes are considered.

In the Barents Sea, in situ observations were carried out in August 2016 near the Kharlov island. Measurements in the Avacha Bay were carried out in August – September 2018 near the Cape Shipunsky. The height and period of the SIW’s were estimated. The SIW’s spectrum was calculated and compared with the Garrett-Munk spectrum.

Sentinel-1A/B, ALOS-2 PALSAR-2, Sentinel-2A/B, and Landsat-8 images were used to analyze the manifestations of SIW’s. To identify the centers of internal tide generation, the tidal body force criterium for harmonics M2 and K1 was used, calculated using Copernicus reanalysis data and the OTIS tidal model.

On the records in the Avacha Bay, long-period fluctuations of isotherms due to semi-daily tidal dynamics are traced. Against the background of semi-daily fluctuations, SIW’s with a period of about 15 minutes and a height of up to 8 meters are distinguished. On the record, during the low tide period, a SIW’s train with heights of up to 15 meters was recorded. In the Barents Sea, the long-period variability of isotherms is less pronounced, short-period fluctuations with a period of about 10 minutes and a height of up to 5 meters are dominant.

The Ursell parameter demonstrates that waves about 8 meters high in the Barents Sea are weakly nonlinear, and waves about 15 meters high in the Avacha Bay are strongly nonlinear. Spectrum calculations show that the oscillation energy in the Barents Sea at all frequencies is lower than in the Avacha Bay, while it does not exceed the energy of the Garrett-Monk spectrum. In Avacha Bay, the oscillation energy at almost all frequencies is higher than the energy of the Garrett-Monk spectrum.

93 manifestations of SIW’s were detected in the Barents Sea, and 72 ones were detected in the Avacha Bay. Most of the manifestations are in the areas of high values of the tidal body force criterium, which may indicate the generation of SIW’s under the influence of the decay of the internal tide.

It was shown that both in the Barents Sea, close to the critical latitude for the semidiurnal tide, and in the Avacha Bay beyond the critical latitude for the diurnal tide, SIW’s are generated under the influence of an internal tide. However, the energy of short-period oscillations in the Avacha Bay is higher than in the Barents Sea.

The study was supported by RFBR grant No. 20-35-90054.

How to cite: Svergun, E. and Zimin, A.: Short-period internal waves in tidal seas on various types of shelf according to in situ and satellite observations, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-59, https://doi.org/10.5194/egusphere-egu22-59, 2022.

18:18–18:24
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EGU22-3184
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Presentation form not yet defined
Tatiana Talipova and Efim Pelinovsky

As it is known, the canonical Korteweg-de Vries equation is applied to describe nonlinear long internal waves in the first approximation on parameters of nonlinearity and dispersion. To compare with surface gravity waves, the coefficient of quadratic nonlinearity can have either sign and to be zero. In this case, the asymptotic procedure should take into account higher terms of nonlinearity. Generalized Korteweg-de Vries equation called the Gardner equation is now a popular model to analyze nonlinear internal waves in the ocean with complicated density and shear flow stratification. If the density stratification is almost linear, the number of nonlinear terms is increased. The family of the Korteweg-de Vries-like equations for internal waves in the form ut+ [F(u)]x + uxxx = 0 is discussed in this presentation. In leading order the nonlinear term is F(u) ~ qub  with b > 0. The steady-state travelling solitary waves is analyzed.

            For q > 0 and b > 1 the analysis re-confirmed that all travelling solitons have “light” exponentially decaying tails and propagate to the right. If q < 0 and b < 1, the travelling solitons (so called compactons) have a compact support (and thus vanishing tails) and propagate to the left. For more complicated F(u) and b > 1 (e.g., the Gardner equation and higher-order generalizations) standing algebraic solitons with “heavy” power-law tails may appear. If the leading term of F(u) is negative, the set of solutions may include wide or table-top solitons (similar to the solutions of the Gardner equation), including algebraic solitons and compactons with any of the three types of tails. The solutions usually have a single-hump structure but if F(u) represents a higher-order polynomial, the generalized KdV equation may support multi-humped pyramidal solitons.

Study is supported by RFBR Grant No 21-55-15008.

How to cite: Talipova, T. and Pelinovsky, E.: Korteweg-de Vries equation family in the theory of nonlinear internal waves, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3184, https://doi.org/10.5194/egusphere-egu22-3184, 2022.