Generation Of Internal Solitary Waves Research Articles

Application of fluctuations in the sound field in inversion of internal solitary wave phase speed

Internal solitary waves propagation perturbing the sound velocity field, causes fluctuations in the sound field. This paper proposes to process the sound pressure data by the Product of the Slope and the even square of the Difference between two points of the acoustic parameter-time curve (PSD). The PSD processed data are processed to time-frequency analysis to extract the frequencies of the fluctuations in sound field. In this paper, numerical simulations and laboratory experiments are carried out on the process of internal solitary wave propagation in the sound field, and the characteristics of the sound field perturbation by internal solitary waves of different amplitudes are investigated. Results are both showing that the method can extract the dominant frequency of fluctuations in the sound field caused by internal solitary waves in real conditions. The method can be applied to the inversion of internal solitary wave phase speed which related to other parameters such as amplitude and characteristic width by theory. It is anticipated that this method can help realize the monitoring of internal solitary waves using acoustic paths.

Observations of anomalously strong mode-2 internal solitary waves in the central Andaman sea by a mooring system

During the period from July 2016 to July 2018, a mooring system deployed in the central Andaman Sea recorded a significant number of highly intense mode-2 internal solitary waves (ISWs), with wave-induced current strengths comparable to those of local mode-1 ISWs. Distinct propagation characteristics and seasonal variations are uncovered, with mode-2 ISWs being identified as primarily propagating eastward and exhibiting a notable frequency peak from November to March. A significant correlation is established between the occurrence of mode-2 ISWs and higher-mode internal tides (ITs), particularly characterized by a high correlation with the third Empirical Orthogonal Function (EOF) mode. Combined with satellite remote sensing images, it is further confirmed that mode-2 ISWs are generated by the nonlinear steepening of ITs and propagate over long distances through resonance with higher-mode ITs. In contrast, our findings suggest that mode-1 ISWs are predominantly generated by the Lee-wave mechanism, especially south of the Ten Degree Channel, and typically propagate northeastward. This study underscores the complex interplay of ocean stratification and seabed topography in the genesis and propagation of ISWs.

Construction of a wavefront model for internal solitary waves and its application in the Northern South China Sea

Internal solitary waves (ISWs) play a crucial role in the development of various physical and biological processes, and numerous high-precision two-dimensional or three-dimensional numerical models have been developed to simulate the generation and propagation processes of ISWs. However, these numerical models, especially when simulating the interaction between ISWs and ocean circulation, require substantial computational resources. This burden can make it challenging to apply them in real-time or short-term forecasting scenarios. In this study, we propose a new numerical model for ISWs by combining traditional one-dimensional ISW theory with wave refraction theory. The proposed model resolves the issues of ray crossing and divergence, which are commonly encountered in traditional refraction models, by employing equally spaced grids along the wave crest line. As a result, this model is capable of simulating the far-field propagation of ISWs. This model enables rapid prediction of the vertical structure and wave crest morphology of ISWs in specific current fields and at given time frames, and it is utilized to investigate the characteristics and propagation of ISWs generated by the nonlinear steepening of internal tide (IT) in the South China Sea. Comparative analysis with satellite imagery demonstrates the model's accurate representation of ISW processes and phenomena, such as wave crest line discontinuities, diffraction, and wave‒wave interactions when passing through Dongsha Island. Furthermore, propagation time estimates based on this model have errors of ±0.98 h (1σ) over which the ISWs are observed by a mooring system, and the average time difference is 0.81 h

Experimental investigation of propagation evolution characteristics of internal solitary waves passing through downslope topography

In contrast to the extensive research on the propagation evolution of internal solitary waves (ISWs) over continental shelf topography, few investigations have been conducted on the propagation evolution of ISWs over downslope topography. In this experiment, the characteristics of the ISWs passing over a downslope topography were investigated in an immiscible two-layer fluid system to clearly capture the waveform information. The main objective of this study was to analyze the propagation evolution of ISWs with different incident amplitudes passing through a downslope topography. Using the particle image velocimetry technique, the evolutionary characteristics of ISWs (such as waveform, wave height, energy budget, and flow field) are investigated. According to the flow field analysis results, the phase velocity near the downslope topography changes with the propagation of ISWs. Moreover, the gradient distribution of velocity progressively becomes perpendicular to the right surface of the topography. Furthermore, a counterclockwise vortex gradually forms at the right upper vertex of the topography. The propagation of ISWs is influenced by varying water depth and topography. The front waveform of ISWs is significantly flat, and the back is steeper than the original back waveform. Around the tail wave, an upward convex wave packet is generated. The trends of wave energy and wave height losses are broadly consistent. Furthermore, the energy loss is related to the incident wave height with a 20% higher loss rate for large-amplitude ISWs than small-amplitude ISWs at the inflection point of the topography.

Generation and Evolution of Internal Solitary Waves in a Coastal Plain Estuary

Abstract Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions. Significance Statement In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary.

Suspension and transportation of sediments in submarine canyon induced by internal solitary waves

The submarine canyon was the main channel for the transport of sediment to the deep sea, but the transport process in submarine canyon induced by internal solitary waves (ISWs) had not yet been conducted. Based on computational fluid dynamics, this study investigated sediment resuspension and transport induced by the interaction between ISWs and submarine canyon. The simulations showed that sediment particles near the canyon were resuspended due to the propagation of ISWs. The sediment of slope section experienced higher resuspension rates compared to the horizontal section. Sediments on the slope were suspended before the trough of ISW and then transported into the canyon. Sediment resuspension induced by ISWs was more significant in the slope section compared to the horizontal sections and contained 45% more sediment particles than the horizontal section within the canyon. The sediment concentration within the canyon gradually increased in both the horizontal and slope sections, with a particularly pronounced increase at the junction between the horizontal and slope section. The concentration of particles in the canyon was significantly higher than in the horizontal section, with an increase in 2.73 times. Furthermore, the sediment concentration within the canyon was 1.73 times higher than outside the canyon. A sediment water column with higher suspended matter concentration, known as the bottom nepheloid layer, was formed above the submarine canyon. However, these sediment particles could not cross the pycnocline and accumulated in the upper region of the lower water. The sediment distribution of the canyon was much greater than outside the canyon within the transverse section, with three times more sediment particles within the canyon compared to outside. The sediment distribution of slope section was significant more than the horizontal section. Sediment suspended above the canyon gradually moved downstream along the submarine canyon and primarily deposit at the junction between the horizontal and slope sections. Sediment movement also occurred along the submarine canyon in the horizontal section. The interaction between ISWs and submarine canyons intensified sediment resuspension and significantly affected the spatial distribution of sediment particles. This interaction could transport resuspended sediments from the continental shelf to the deep-sea basin, thereby influencing the deep-sea environment.

Characterization of solitary internal waves in the northern Bali waters

Internal solitary wave (ISW) is an underwater wave, formed due to the evolution of internal tides. The presence of breaking ISWs in coastal areas can potentially influence coastal ecosystems through cross-shelf exchange mechanisms. The southern waters of the Kangean Island and the eastern waters of the Madura Island, known also as part of the northern Bali waters, have been an active habitat for ISW propagation. This study aims to identify and characterize ISW which potentially breaking onshore the Southern Kangean Waters (SKW) and the Eastern Madura Waters (EMW) using Sentinel 1 SAR (Synthetic Aperture Radar) imagery. ISW characterization was carried out using the Korteweg-de Vries (KdV) model. The ISW amplitudes which propagate to EMW varies from 1 - 28 m with a propagation speed of 1.60 - 1.98 m/s, while the ISW which propagate to the SKW has an amplitude of 1 - 60 m with a propagation speed of 0.83 to 2.17 m/s. The results show that the ISW propagating to the SKW has stronger amplitude, phase velocity, and horizontal-vertical velocities than the ISW propagating to the EMW. The maximum speed of the horizontal current triggered by ISW leading to the EMW is 0.03 - 0.17 m/s and the vertical velocity 0.11 - 4.53 cm/s; the maximum speed of horizontal velocity leading to the SKW is 0.02 - 1.29 m/s and the maximum speed of the vertical velocity 0.04 - 19.03 cm/s.

Generation of internal solitary waves by the Mackenzie River plume in the coastal Arctic Ocean

High-resolution spaceborne synthetic aperture radar (SAR) images have verified the wide existence of internal solitary waves (ISWs) over the Chukchi and Beaufort Seas. A major ISW generation hotspot has been observed at the mouth of the Mackenzie River. Considering the weak tidal currents and relatively flat topography of the Mackenzie Shelf, such ISWs are unlikely to be generated by tide–topography interactions. However, this is more likely caused by the intrusion of river plumes. Therefore, the generation of ISWs by the Mackenzie River plume is investigated numerically. A series of numerical simulations are conducted to explore the influence of stratification, river plume strength, and Earth's rotation on the generation and evolution of ISWs. The results indicate that the Mackenzie River plume is an essential ISW source for the coastal Arctic Ocean. The amplitude of the ISWs is affected by the intrusion strength of the Mackenzie River plume. In addition to the direct observational evidence from summer, the numerical results show that the environmental conditions in winter are suitable for the generation of ISWs. Rotation affects the amplitude of the generated ISWs and the number of ISWs in an ISW packet by modulating the plume intrusion strength and dispersing the ISWs. This study highlights the crucial role of the river plume mechanism in exciting ISWs and emphasizes the importance of ISWs for vertical mixing in the Arctic Ocean.

Characteristics of Internal Solitary Waves near Its Generation Site in the Lombok Strait, Indonesia

Evidence of internal solitary waves (ISWs) formation through the Lee wave mechanism in the Lombok Strait was revealed from the echosounder measurements conducted in November 2017. This study is aimed to characterize the property of ISW packet formed around ~30 km away from the generation site, in the southern part of the strait above the Nusa Penida Sill (NPS), by employing Korteweg-de Vries (KdV) solution. The packet can be categorized as the early stage of ISW formation, consisting of two waves of depression, with typical amplitude of 30 m and 10 m, for the first and second wave, respectively. The waves propagated northward with a typical phase speed of ~1.2 m∙s -1. The waves drive a maximum horizontal velocity anomaly of ~0.8 m∙s - 1 and a vertical velocity anomaly of ~10 cm∙s -1. The amplitude of the ISW packet will be potentially amplified during their propagation away from the strait. This study provides an observational based understanding on the early stage of internal tides evolution in the Lombok Strait, particularly highlights the energy transfer of internal tides through the propagation of internal solitary waves.

Non-Boussinesq effect on the internal solitary wave propagation under a Lagrangian-like description for various pycnocline thickness conditions

The Dubreil–Jacotin–Long (DJL) equation is an exact model for the steady propagation of internal solitary waves (ISWs) under Boussinesq approximation. The aim of this study is to discuss the non-Boussinesq effect on ISWs initialized by DJL equation for various pycnocline thickness conditions. The simulated results show that the non-Boussinesq effect can indeed lead to instability of DJL equation, and the pycnocline thickness will affect the amplitude of re-stable ISWs and the separation process of tail waves. Moreover, in order to extract features of the non-Boussinesq instability and the location of the tail wave separation, we propose an effective analytical approach for the quasi-traveling wave problem inspired by the definition of classical Lagrangian coherent structure (LCS). The improved finite-time Lyapunov exponent with a moving window (FTLEmw) is a Lagrangian-like description with considering the prior information of physical phenomenon. For a steady ISW propagation in the Boussinesq system, the repelling and attracting FTLEmv fields are symmetrical and the field ridge behaves as a continuous spiral topology, which suggests that particles on different streamlines in the flow structure have different rotation periods, while the streamlines are not actually completely closed due to the forward propagation of the wave. During the main unstable stage of non-Boussinesq effect, the topology of separated tail wave which is disconnected from the ISW main part can be clearly distinguished. The tail wave separation locations identified by the improved FTLEmv field and the classical FTLE field are not the same, which illustrates the difference between the two perspectives of flow structure change and fluid particle motion. In addition, the leading edge, trailing edge and main part of ISWs will gradually be divided into three-part FTLEmv topologies in the thicker pycnocline conditions.

Higher-Order Benjamin–Ono Model for Ocean Internal Solitary Waves and Its Related Properties

In this study, the propagation of internal solitary waves in oceans at great depths was analyzed. Using multi-scale analysis and perturbation expansion, the basic equation is simplified to the classical Benjamin–Ono equation with variable coefficients. To better describe the propagation characteristics of solitary waves, we derived a higher-order variable-coefficient integral differential (Benjamin–Ono) equation. Subsequently, the bilinear form of the model was derived using Hirota’s bilinear method, and a multi-soliton solution was obtained. Based on the multi-soliton solution of the model, we further studied the interaction of the soliton, which led to the discovery of Mach reflection. Some conclusions were drawn, which are of potential value for further study of solitary waves in the ocean.

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghdi-type equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height.

Characteristics of Internal Solitary Waves in the Timor Sea Observed by SAR Satellite

Internal solitary waves (ISWs) with features such as large amplitude, short period, and fast speed have great influence on underwater thermohaline structure, nutrient transport, and acoustic signal propagation. The characteristics of ISWs in hotspot areas have been revealed by satellite images combined with mooring observation. However, the ISWs in the Timor Sea, which is located in the outflow of the ITF, have not been studied yet and the characteristics are unrevealed. In this study, by employing the Synthetic Aperture Radar (SAR) images taken by the Sentinel-1 satellite from 2017 to 2022, the temporal and spatial distribution characteristics of ISWs in the Timor Sea are analyzed. The results show that most of ISWs appear in Bonaparte basin and its vicinity. The average wavelength of the ISWs is 248 m, and most of the wave lengths are less than 400 m. The peak line of ISWs is longer in deeper water. The underwater structures of two typical ISWs are reconstructed based on the Korteweg–de Vries (KdV) equation combined with mooring observation. This shows that, compared with the two-layer model, the continuous layered model is more suitable for reconstructing the underwater structures of ISWs. Further analysis shows that both the rough topography and the spring-neap tides contribute to the generation of ISWs in the Timor Sea. This study fills a gap in knowledge of ISWs in regional seas, such as the Timor Sea.

Mechanical model and characteristics of deep-water drilling riser-wellhead system under internal solitary waves

Internal solitary waves with a huge amount of energy easily trigger the large dynamic responses of riser-wellhead system and threaten its structural safety. However, previous studies have only focused on the dynamic response of the riser under internal solitary waves. The riser may experience excessive traction from the platform, especially from the mooring platform, in response to the arrival of internal solitary waves. The bottom of the riser connects to the wellhead system, which in turn exerts a reaction force on the riser. To address this problem, a coupled dynamic model of deep-water drilling mooring platform-riser-wellhead system under internal solitary waves is developed in this paper. A dynamic response analysis method based on the fourth-order Runge-Kutta method and finite element method is also proposed for the mooring platform-riser-wellhead system. A dynamical solver for the coupled system is then developed using MATLAB. The dynamic response characteristics of the riser-wellhead system under internal solitary waves are calculated. Results show that the displacement and bending moment of the system initially increases and then decreases along with the propagation of internal solitary waves, and finally reach equilibrium position. The displacement and bending moment reach their peak before the trough of internal solitary waves passes through the riser-wellhead system. The dynamic responses of the riser-wellhead system under the influence of internal solitary wave loads are much larger than those without the effect of internal solitary wave loads. The riser system experiences shearing loads at the interface of internal solitary waves, which trigger a step-like bending moment variation. The bending moment of the conductor under the mudline is greatly increased by the internal solitary waves.

A study of internal solitary waves in the Northern South China Sea using the Geo High-Speed Imager of the FY-4B satellite

ABSTRACT The FY-4B satellite is the first operational satellite of China’s new generation of geostationary-orbit meteorological satellites in the Fengyun-4 series. This study is the first to analyse the changes in the dynamic processes of internal solitary waves (ISWs) in the northern South China Sea using FY-4B Geo High-Speed Imager (GHI) data with a 250 m spatial resolution. By calculating the propagation direction, wave crest line length, distance between ISW packets and other characteristics of ISWs and comparing them with FY-3D and MODIS optical images, the feasibility and reliability of using the FY-4B GHI to observe ISWs are verified. This study analyses the dynamic processes of ISW propagation at a high temporal resolution of up to 1 minute and observes ISW propagation processes at different sea depths, ISW evolution dynamics, ISW interaction processes, and the change processes of ISWs as they pass islands and reefs. A comparison between these results and in situ measurements obtained in the northern South China Sea demonstrates that the FY-4B GHI has the unique advantage of continuously tracking and observing ISWs in the northern South China Sea and can provide new tracking observations for the study of ISWs in the South China Sea.

Analysis of Internal Solitary Waves in the Gulf of Oman and Sources Responsible for Their Generation

A combination of multiple data sources has been used to study the characteristics of internal solitary waves (ISWs) in the Gulf of Oman (GoO). Water column stratification in the Gulf has been examined using field observations and World Ocean Atlas 2018 datasets. The spatiotemporal distribution of ISWs has been obtained from satellite images obtained by means of Synthetic Aperture Radar (SAR) and optical sensors taken from 2018 to 2020. The mechanisms of ISW generation in the GoO have been studied using the data revealed from different available sources. The results show that there are annually two major typical stratifications in the GoO throughout the year, strong stratification in May through September and weak stratification during other months. Dispersion relations corresponding to these types of stratification have been obtained with acceptable accuracy for both deep and shallow regions. The spatiotemporal distribution of ISWs demonstrates that the western and southern regions of the GoO are the hotspots for generation of ISWs in this basin. Several mechanisms of ISW generation in the GoO are discussed including tide, eddies, lee waves, and atmospheric perturbation; the latter one is, apparently, responsible for the appearance of large-amplitude ISWs.

Analisis Kecepatan Perambatan Gelombang Internal Soliter di Selat Lombok dengan Citra Himawari-8

Internal waves are phenomena that occur below sea surface. One of the most observed types of internal waves was called a solitary wave or soliton so it is often known as an internal solitary wave (ISW). Lombok Strait was one of the straits located in the southern part of the Indonesian archipelago which has the characteristics of intensive ISW generation because this strait has complex waters characteristics. This study aim to analyzed in detail the changes in the ISW propagation speed at the first crest soliton every 10 minutes using Himawari-8 data. The detected ISW pattern is then extracted at the first crest of the soliton as a reference to measure the distance between the detected soliton every 10 minutes as input in estimating the propagation speed. The Himawari-8 image which was in this study detected 2 ISW packets in the Lombok strait area. Packet 1 which was detected in the northern part of the Lombok strait approaching Kangean island had a group speed of 2.22 m/s and Packet 2 which was detected in the area around the Lombok strait had a group speed of 2.78 m/s. The difference in group velocity of the two packets is due to the variation in depth along the ISW propagation. The analysis results of changes in ISW propagation speed in this study indicate that Himawari-8 imagery is a very effective instrument for analysing changes in ISW propagation speed in detail every 10 minutes which is difficult for satellite imagery which usually has low temporal resolution.

Effect of internal solitary wave on the dynamic response of a flexible riser

Dynamic responses can arise when a flexible riser encounters the internal solitary wave (ISW) in the ocean. It is, thus, necessary to explore its dynamical behaviors induced by ISW. First, the governing equations of the flexible riser, ISW, and hydrodynamic force are introduced and interpreted. The accordant validations are performed so as to examine the accuracy of the applied models. Then, the dynamic response of the flexible riser is studied with the increase of the nondimensional ISW amplitude. Representative characteristics, such as vortex-induced vibration (VIV), top tension, and stress along the flexible riser, are mainly analyzed and discussed. The results prove that with the propagation of ISW, VIV in both inline (IL) and crossflow (CF) directions can be incurred. The maximum values of IL and CF oscillation frequencies, top tension, inline deflection, as well as riser stress can be detected while the ISW trough reaches to the flexible riser. Furthermore, all these four dynamic characteristics show an increasing trend with the increase of the nondimensional ISW amplitude. Note that the maximum values of oscillation frequencies, inline deflection, and stress on the upper section of the flexible riser tend to be larger compared with those on the lower section. In addition, the maximum inline deflection, top tension, and stress along the flexible riser can be affected by VIV responses.

Numerical Simulation on Free Motion Response of a Submarine Induced by Internal Solitary Wave

Abstract：The internal solitary waves (ISWs) in the ocean carry huge energy and pose a serious threat to the safety of underwater vehicle. In order to obtain the dynamic response of the submarine under the action of ISWs, the amplified SUBOFF model was placed in a large numerical water tank with a length of 5000m, a width of 200m and a depth of 500m. The Korteweg-de Vries (KdV) theory was adopted to simulate the generation of ISWs in the two-layer flow, and overset grid technology was used to ensure the grid quality during the submarine movement. The results show that before the ISWs peak reaches the position of the submarine, the submarine will move, which causes the submarine to sink, move laterally and pitch. The longitudinal velocity is obviously greater than the lateral velocity, and the submarine finally hits the water tank bottom. With the increase of the ISWs amplitude, the time needed for submarine to reach the bottom increases, and the pitching angle increases greatly. The ISWs amplitude has no effect on the motion trajectory of the submarine's center of gravity, and has little effect on the lateral and longitudinal velocity. With the decrease of submergence depth of the submarine, the time required for submarine to reach the bottom will also increase, and the motion trajectory will change, but the trend of change is basically the same. The submergence depth has little influence on the variation range of lateral velocity, longitudinal velocity and pitching angle.

Inversion models of internal solitary wave propagation speed in ocean based on least squares method and support vector machine

The propagation speed is one of the important parameters of the internal solitary wave (ISW). How to obtain the ISW speed through optical remote sensing images accurately and quickly is an important problem to be solved. In this paper, we simulate ISW optical remote sensing imaging, obtain an experimental database, and build the ISW speed inversion model based on a single-scene optical remote sensing image by using the least squares method and the support vector machine. The accuracy of the ISW speed inversion model is tested by using MODIS Image and GF-4 image data of the South China Sea. The study results are shown below. The least squares ISW speed inversion model can give the regression equation, which is more intuitive and has less accuracy in the water depth ranging from 300 m to 399 m, while the support vector machine ISW speed inversion model has high accuracy in the water depth ranging from 400 m to 1200 m and from 83 m to 299 m. Therefore, the two kinds of ISW speed inversion models have different advantages, and can be applied to the inversion of the ISW speed in the real ocean.