scholarly journals Internal wave attractors in three-dimensional geometries: trapping by oblique reflection

2018 ◽  
Vol 845 ◽  
pp. 203-225 ◽  
Author(s):  
G. Pillet ◽  
E. V. Ermanyuk ◽  
L. R. M. Maas ◽  
I. N. Sibgatullin ◽  
T. Dauxois
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Energy ◽  
Transverse Direction ◽  
Three Dimensional ◽  
Direction Parallel ◽  
3D Geometry ◽  
Experimental Parameters ◽  
Set Up

We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.

Diapycnal diffusivity induced by the breaking of lee waves

2020 ◽  
Author(s):  
Thomas Eriksen ◽  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
Diapycnal Mixing ◽  
Overturning Circulation ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Energy Flux ◽  
Diapycnal Diffusivity

<p>A key component in setting the large scale ocean circulation is the process of diapycnal mixing, since this can drive the meridional overturning circulation. Diapycnal mixing in the interior ocean is predominantly associated with the breaking of internal waves. Traditionally, diapycnal mixing has been represented in ocean models by a diapycnal diffusivity either constant or exponentially decreasing with depth. This approach, however, does not take into account the actual physics behind the breaking of internal waves. The energetically consistent internal wave model IDEMIX (Internal wave Dissipation, Energetics and MIXing), on the other hand, computes diffusivities directly on the basis of internal wave energetics. One such type of internal waves are lee waves. These are generated and subsequently dissipated when geostrophic currents interact with bottom topography and are therefore believed to be a source of energy for deep ocean mixing. In this study IDEMIX is coupled to a 1/12<sup>th</sup> degree regional model of the Atlantic. The lee wave energy flux is calculated and used as a bottom flux at each time step effectively allowing lee waves to propagate, interact with mean flow and waves, and subsequently dissipate. This setup enables not only an estimate of the lee wave energy flux but also a direct investigation of the influence of lee waves on dissipation, stratification and horizontal and overturning circulation.</p>

scholarly journals Strong Internal Waves Generated by the Interaction of the Kuroshio and Tides over a Shallow Ridge

2019 ◽  
Vol 49 (11) ◽  
pp. 2917-2934 ◽  
Author(s):  
Eiji Masunaga ◽  
Yusuke Uchiyama ◽  
Hidekatsu Yamazaki
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
High Frequency ◽  
Deep Ocean ◽  
Internal Tides ◽  
Navier Stokes ◽  
Wave Energy Flux ◽  
The Kuroshio

AbstractThe Kuroshio and tides significantly influence the oceanic environment off the Japanese mainland and promote mass/heat transport. However, the interaction between the Kuroshio and tides/internal waves has not been examined in previous works. To investigate this phenomenon, the two-dimensional high-resolution nonhydrostatic oceanic Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) model was employed. The results show that strong internal tides propagating upstream in the Kuroshio are generated at a near-critical internal Froude number (Fri = 0.91). The upstream internal wave energy flux reaches a magnitude of 12 kW m−1, which is approximately 3 times higher than that of internal waves without the Kuroshio. On the other hand, under supercritical conditions, the Kuroshio suppresses the internal wave energy flux. The interaction of internal tides and the Kuroshio also generates upstream propagating high-frequency internal waves and solitary wave packets. The high-frequency internal waves contribute to the increase in the total internal wave energy flux up to 40% at the near-critical Fri value. The results of this study suggest that the interaction of internal tides and the Kuroshio enhances the upstream propagating internal tides under the specified conditions (Fri ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

scholarly journals Energetics of Seamount Wakes. Part II: Wave Fluxes

2020 ◽  
Vol 50 (5) ◽  
pp. 1383-1398 ◽  
Author(s):  
B. Perfect ◽  
N. Kumar ◽  
J. J. Riley
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Parameter Space ◽  
Energy Flux ◽  
Wave Energy ◽  
Wave Model ◽  
Barotropic Flow ◽  
Unsteady Wake ◽  
Lee Wave ◽  
Wave Energy Flux

AbstractSeamounts are thought to facilitate ocean mixing through unsteady wake processes, and through the generation of internal waves, which propagate away from the seamount and later break. The relative importance of these processes is examined for idealized, isolated seamounts (with characteristic width D and height H) in uniform barotropic flow U. A range of Coriolis parameters f and buoyancy frequencies N are used such that a broad parameter space of low Froude numbers (U/NH) and low Rossby numbers (U/fD) is considered. Results indicate that eddy processes energetically dominate the internal wave energy flux in this range of parameter space. The internal wave field is specifically examined and partitioned into steady lee waves and unsteady, wake-generated waves. It is found that the lee wave energy flux cannot be explained by existing analytical theories. A lee wave model by Smith is then extended into the low-Froude-number regime and the effect of rotation is included. While strongly stratified experiments have previously indicated that only the top U/N of an obstacle generates internal waves, the effect of rotation appears to modify this wavemaking height. Once the U/N height is revised to account for rotation, the lee wave energy flux can be reasonably accurately reproduced by the extended Smith model.

Analysis of Flexible Roller Parameters Influences on Roll Forming of Three-Dimensional Parts

2014 ◽  
Vol 875-877 ◽  
pp. 450-454
Author(s):  
Jiao Jiao Zhen ◽  
Zhi Qing Hu ◽  
Zeng Ming Feng ◽  
Jun Hui Cao
Keyword(s):  
Three Dimensional ◽  
Roll Forming ◽  
Forming Process ◽  
Bending Process ◽  
Experimental Parameters ◽  
Flexible Roll ◽  
Roll Velocity ◽  
Set Up ◽  
Roll Forming Process

Roll forming is a well known bending process and sheet metals can only be machined into two-dimensional surfaces in traditional roll forming. While with more and more personalized demands, three-dimensional surfaces are widely required. Thus, flexible rollers are used to achieve three-dimensional surfaces. And in order to optimize experimental parameters and to predict experimental results, finite element method (FEM) is developed. In this paper the set-up of flexible roll-forming is described and the process of roll forming is simulated. Then the influences of forming parameters, such as the thickness and the roll velocity, on forming quality of the sheet metal in roll forming process are discussed. The results show that the analysis of flexible roller parameters is practical for the continuous and efficient forming of three-dimensional surfaces.

scholarly journals Oblique internal-wave chain resonance over seabed corrugations

2017 ◽  
Vol 833 ◽  
pp. 538-562
Author(s):  
Louis-Alexandre Couston ◽  
Yong Liang ◽  
Mohammad-Reza Alam
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Resonance Condition ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Resonant Interactions ◽  
Near Resonance ◽  
Chain Resonance ◽  
Small Scales ◽  
A Chain

Here we show that monochromatic long-crested corrugations on an otherwise flat seafloor can coherently scatter the energy of an oblique incident internal wave to multiple multi-directional higher-mode internal waves via a series of resonant interactions. We demonstrate that a resonance between seabed corrugations and a normally or slightly oblique incident internal wave results in a series of follow-up resonant interactions, which take place between the same corrugations and successively resonated shorter waves. A chain resonance of internal waves that carries energy to small scales is thus obtained, and we find that the Richardson number decreases by several orders of magnitude over the corrugated patch. If the incidence angle is large, and the incident wave perfectly satisfies a resonance condition with the topography, it turns out that not many higher-mode resonance or near-resonance conditions can be satisfied, such that energy stays confined within the first few modes. Nevertheless, if the incident waves are sufficiently detuned from satisfying a perfect resonance condition with the seabed corrugations, then we show that this frequency detuning may balance off the large detuning due to oblique incidence, leading to a chain resonance that again carries energy to small scales. The evolution of the incident and resonated wave amplitudes is predicted from the envelope equation for internal waves over resonant seabed topography in a three-dimensional rotating fluid, which we derive considering the Boussinesq and $f$-plane approximations with $f$ the Coriolis frequency, linear density stratification and small-amplitude corrugations. Our results suggest that topographic features on the ocean floor with a well-defined dominant wavenumber vector, through the chain resonance mechanism elucidated here, may play a more important role than previously thought in the enhancement of diapycnal mixing and energy dissipation.

Mechanical Stress Analysis of Different Shapes Pillars with Cnoidal Internal Wave Action

2013 ◽  
Vol 732-733 ◽  
pp. 417-420
Author(s):  
Xiao Chao Fan ◽  
Rui Jing Shi ◽  
Feng Ting Li ◽  
Bo Wei ◽  
Yue Dang
Keyword(s):  
Internal Wave ◽  
Stress Analysis ◽  
Internal Waves ◽  
Three Dimensional ◽  
Wave Force ◽  
Viscous Force ◽  
Inertia Force ◽  
Converted Wave ◽  
Numerical Wave Flume ◽  
Wave Flume

The numerical simulations of the flow around different pillars acted by the cnoidal internal waves have been made by building numerical wave flume based on FLUENT software. The cnoidal internal wave was created by using the push-pedal method, and the free surface was tracked by using VOF (volume of fluid) method. The three-dimensional different amplitude and period cnoidal internal waves were simulated. The inertia force and viscous force trends were analyzed, and for different pillars the total wave force were compared. There were some significance for stress analysis of the offshore terminal pillars. The converted wave force could alternative and treatment problems about square columns.

Low-Frequency Acoustic Propagation Through Crossing Internal Waves in Shallow Water

2020 ◽  
Vol 28 (03) ◽  
pp. 1950013
Author(s):  
Alexey Shmelev ◽  
Ying-Tsong Lin ◽  
James Lynch
Keyword(s):  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Three Dimensional ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Full Field ◽  
Wave Trains ◽  
Acoustic Ducts ◽  
Numerical Approaches

Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.

scholarly journals Analytical and numerical investigation of nonlinear internal gravity waves

2001 ◽  
Vol 8 (1/2) ◽  
pp. 37-53 ◽  
Author(s):  
S. P. Kshevetskii
Keyword(s):  
Internal Wave ◽  
Analytical Model ◽  
Internal Waves ◽  
Numerical Models ◽  
Wave Mode ◽  
Vertical Acceleration ◽  
Quasistatic Problem ◽  
Wave Simulation ◽  
Non Linear

Abstract. The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration), we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory coincidence of simulation outcomes with analytical ones is revealed and some examples of numerical simulations illustrating wave disintegration into solitons are given. The phenomenon of internal wave mixing is considered and is explained from the point of view of the results obtained. The numerical methods for internal wave simulation are examined. In particular, the influence of difference interval finiteness on a numerical solution is investigated. It is revealed that a numerical viscosity and numerical dispersion can play the role of regularizators to a nonlinear quasistatic problem. To avoid this effect, the grid steps should be taken less than some threshold values found theoretically.

Observed seasonality in internal wave energy and associated mixing in a temperate shelf sea

2020 ◽  
Author(s):  
Juliane Wihsgott ◽  
Matthew Palmer ◽  
Jonathan Sharples ◽  
Jo Hopkins
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Energy ◽  
Seasonal Cycle ◽  
Strong Dependence ◽  
Marginal Stability ◽  
Buoyancy Frequency ◽  
North West ◽  
Internal Mixing ◽  
Continuous State

<p>Long-term observations (March’14 − July’15) of ocean density and velocity from the North West European shelf reveal a seasonality in internal wave energy linked to the seasonal cycle of stratification. Further, this seasonality extends to internal mixing associated with internal waves that can be effectively described by the buoyancy frequency (N<sup>2</sup>), with the strongest mixing associated with strongly stratified summer conditions. To better understand these results a model was used that employed three different, commonly used parameterisations of internal mixing. Each parameterisation produced some degree of seasonality in internal mixing. Contrary to observed results however, all three model scenarios produced a minimum in internal mixing during summer, with enhanced mixing observed during spring and autumn. This failure in each model was attributed to the lack of realistic levels of enhanced baroclinic energy and shear (S<sup>2</sup>) that is identified in observations to be attributable to internal waves. These observations reveal a close relationship between N<sup>2</sup>and S<sup>2</sup>, resulting in a near continuous state of marginal stability; where the gradient Richardson number is maintained at a near critical level. Due to the observed strong dependence of internal wave energy and internal mixing on stratification, a modified version of the MacKinnon and Gregg (2003a) turbulence scaling was employed. This modified parameterisation successfully replicated the observed seasonality in internal mixing. This important result implies that future parameterisations should aim to scale internal mixing on enhanced levels of S<sup>2</sup> from internal waves, which are shown here to be suitably predicted by the seasonal cycle of stratification (N<sup>2</sup>).</p>

scholarly journals Ultrasonography in the diagnosis of ovarian and endometrial carcinoma

2011 ◽  
Vol 152 (47) ◽  
pp. 1887-1893
Author(s):  
Sándor Valent ◽  
Orsolya Oláh ◽  
Levente Sára ◽  
Attila Pajor ◽  
Zoltán Langmár
Keyword(s):  
Endometrial Carcinoma ◽  
Significant Role ◽  
Transvaginal Ultrasound ◽  
Three Dimensional ◽  
Transvaginal Sonography ◽  
Gynecological Diseases ◽  
Set Up ◽  
Almost All ◽  
Crucial Part

Transvaginal sonography has become a crucial part of the routine gynecologic examination. It offers now a great help in the diagnosis of almost all gynecological diseases. Transvaginal ultrasound means the first step in the diagnosis of the first two most common gynecological malignancies, and in many cases we are able to set up a diagnosis of its own. The purpose of this article is to emphasize the significant role of transvaginal ultrasonography in the diagnosis of these two dieseases mentioned above, with summarizing the latest developments regarding the capabilities of sonography (Doppler-technique, three-dimensional ultrasonograpy). Orv. Hetil., 2011, 152, 1887–1893.

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