Generation Of Nonlinear Internal Waves Research Articles

Impact of Typhoon Nanmadol (2011) on the propagation of nonlinear internal waves in the South China Sea

In situ measurements from an array of pressure-equipped inverted echo sounders (PIESs), numerical simulation results using a non-hydrostatic model (SUNTANS) that does not account for mesoscale variability, and a ray-tracing method are used to investigate the behavior of nonlinear internal waves (NLIWs) in the South China Sea, focusing on period of Typhoon Nanmadol passage. Unusual significant differences in NLIWs arrival time occur between the PIES observation and SUNTANS simulation results after Typhoon Nanmadol passage; i.e., the observed NLIWs show a delay of 0.5–1.5 h at the westernmost PIES sites compared to the simulated ones in the SUNTANS. A data-assimilated ocean model outputs in addition to satellite altimetry reveal that the passage of Typhoon Nanmadol alters the oceanic environments remarkably, creating thermocline shoaling of ~80 m, which can slow down the wave propagation speed. We account for the delay of NLIWs using ray-tracing simulations. Our results demonstrate that typhoon-induced changes in mesoscale structure can significantly impact the fate of NLIWs in the South China Sea, which have potential on ocean mixing and biogeochemical systems.

Generation of nonlinear internal waves on the northern continental shelf south of Hainan Island

Nonlinear internal waves (NLIWs) are prevalent on the northern continental shelf south of Hainan Island in the South China Sea. However, our understanding of these NLIWs is still in a preliminary state. In the study, we take a step toward fully elucidating the generation and propagation process of the NLIWs on the northern continental shelf south of Hainan Island through a synergistic analysis of satellite observations, in situ measurements, and numerical simulations. Both mooring and satellite observations suggest that the Xisha Islands remotely generate the NLIWs on the northern continental shelf south of Hainan Island; moreover, more than one source exists in the Xisha Islands. Based on the realistic topography, stratification, and tidal forcing, two-dimensional numerical simulations using the MITgcm reveal that the NLIWs observed on the continental shelf can be generated from the Xisha Islands through the internal tidal beam regime. Furthermore, the internal tide energy flux estimation shows that the locally generated internal tides that arise from the continental shelf break mostly carry their energy toward the deep water and have little effect on the generation of NLIWs on the shelf.

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.

A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry

A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non-hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier–Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

A nonlinear equation of the Korteweg–de Vries equation usually describes internal solitary waves in the coastal ocean that lead to an exact solitary wave solution. However, in any real application, there exists the Earth’s rotation. Thus, an additional term is required, and consequently, the Ostrovsky equation is developed. This additional term is believed to destroy the solitary wave solution and form a nonlinear envelope wave packet instead. In addition, an internal solitary wave is commonly disseminated over the variable topography in the ocean. Because of these effects, the Ostrovsky equation is retrieved by a variable-coefficient Ostrovsky equation. In this study, the combined effects of both background rotation and variable topography on a solitary wave in a two-layer fluid is studied since internal waves typically happen here. A numerical simulation for the variable-coefficient Ostrovsky equation with a variable topography is presented. Two basic examples of the depth profile are considered in detail and sustained by numerical results. The first one is the constant-slope bottom, and the second one is the specific bottom profile following the previous studies. These indicate that the combination of variable topography and rotation induces a secondary trailing wave packet.

The derivation of an isotropic model for internal waves and its application to wave generation

In contrast to two-dimensional oceanic internal waves which have been extensively investigated, there are relatively few theoretical studies on three-dimensional internal waves. The most remarkable theory describing three-dimensional internal waves is the Kadomtsev–Petviashvili (KP) equation. Nevertheless, two shortcomings – unidirectional propagation and anisotropy – limit its application in some general cases. In the current paper, via an asymptotic analysis, we derive an isotropic and bidirectional model, the modified Benney–Luke equation, for a two-layer fluid with bottom topography which can vary both in time and space, therefore tides and currents can be incorporated into the internal wave problem due to the relative motion. In the derivation, the assumption of incompressibility and long waves are invoked and the effects of the Earth’s rotation and dissipation are ignored. Based on this model, the generation of nonlinear internal waves by background currents and barotropic tides flowing over topography are investigated. The resulting equation aims to facilitate dynamical analyses, as well as the interpretation of in-situ observational data and laboratory experimental results.

Generation of nonlinear internal waves by flow over topography: Rotational effects.

We use the forced Ostrovsky equation to investigate the generation of internal waves excited by a constant background current flowing over localized topography in the presence of background rotation. As is now well known in the absence of background rotation, the evolution scenarios fall into three cases, namely subcritical, transcritical, and supercritical. Here an analysis of the linearized response divides the waves into steady and unsteady waves. In all three cases, steady waves occur downstream but no steady waves can occur upstream, while unsteady waves can arise upstream only when there is a negative minimum of the group velocity. The regions occupied by the steady and unsteady waves are determined by their respective group velocities. When the background current is increased, the wave number of the steady waves decreases. In addition, the concavity (canyon or sill), the topographic width, and the relative strength of the rotation play an important role in the generation mechanism. Nonlinear effects modulate the wave amplitude and lead to the emergence of coherent wave packets. All these findings are confirmed by numerical simulations.

The Generation of Nonlinear Internal Waves in the South China Sea: A Three‐Dimensional, Nonhydrostatic Numerical Study

AbstractThe generation of nonlinear internal waves (NLIWs) by stratified tidal flow over an isolated topography has been a subject of research for many years. However, the enhanced complexity of the dynamics as a consequence of flow over two topographical features has been less studied and understood. Here, we report results of the generation of type‐A and type‐B NLIWs in the South China Sea that originate from a double‐ridge system. Based on a realistic three‐dimensional nonhydrostatic simulation, it is found that type‐A NLIWs are generated at the western ridge through the mechanism of internal tide release, while the generation of type‐B NLIWs occurs at the eastern ridge as a consequence of internal wave interaction. Associated with the ridge height, separation distance, and modulated tidal forcing, the generation of type‐B NLIWs is strongly modified by the resonant process between the two ridges. As a result, type‐A and type‐B NLIWs appear in the observations with alternating large and small amplitudes. In addition, with a detailed knowledge of the generation, it is also found that the different arrival time of these waves could be due to their different generation times. Finally, the reflection/transmission of type‐B NLIWs at the subcritical western ridge is suggested as a key feature of resonance. However, it is governed by hydraulically controlled flow instead of the ratio of the local topographic slope to the internal wave beam angle.

Generation and Propagation of Nonlinear Internal Waves in Sheared Currents Over the Washington Continental Shelf

AbstractThe generation, propagation, and dissipation of nonlinear internal waves (NLIW) in sheared background currents is examined using 7 days of shipboard microstructure surveys and two moorings on the continental shelf offshore of Washington state. Surveys near the hypothesized generation region show semi‐diurnal (D2) energy flux is onshore and that the ratio of energy flux to group speed times energy ( ) increases sharply at the shelf break, suggesting that the incident D2 internal tide is partially reflected and partially transmitted. NLIW appear at an inshore mooring at the leading edge of the onshore phase of the baroclinic tide, consistent with nonlinear transformation of the shoaling internal tide as their generation mechanism. Of the D2 energy flux observed at the eastern extent of the generation region (133 ± 18 Wm−1), approximately 30% goes into the NLIW observed inshore (36 ± 11 Wm−1). Inshore of the moorings, 7 waves are tracked into shallow (30‐40 m) water, where a vertically sheared, southward current becomes strong. As train‐like waves propagate onshore, wave amplitudes of 25‐30 m and energies of 5 MJ decrease to 12 m and 10 kJ, respectively. The observed direction of propagation rotates from N of E to S of E in the strongly sheared region. Linear ray tracing using the Taylor‐Goldstein equation to incorporate parallel shear effects accounts for only a small portion of the observed rotation, suggesting that three‐dimensionality of the wave crests and the background currents is important here.

A Coupled-Mode Shallow-Water Model for Tidal Analysis: Internal Tide Reflection and Refraction by the Gulf Stream

AbstractA hydrostatic, coupled-mode, shallow-water model (CSW) is described and used to diagnose and simulate tidal dynamics in the greater Mid-Atlantic Bight region. The reduced-physics model incorporates realistic stratification and topography, internal tide forcing from a priori estimates of the surface tide, and advection terms that describe first-order interactions of internal tides with slowly varying mean flow and mean buoyancy fields and their respective shear. The model is validated via comparisons with semianalytic models and nonlinear primitive equation models in several idealized and realistic simulations that include internal tide interactions with topography and mean flows. Then, 24 simulations of internal tide generation and propagation in the greater Mid-Atlantic Bight region are used to diagnose significant internal tide interactions with the Gulf Stream. The simulations indicate that locally generated mode-one internal tides refract and/or reflect at the Gulf Stream. The redirected internal tides often reappear at the shelf break, where their onshore energy fluxes are intermittent (i.e., noncoherent with surface tide) because meanders in the Gulf Stream alter their precise location, phase, and amplitude. These results provide an explanation for anomalous onshore energy fluxes that were previously observed at the New Jersey shelf break and linked to the irregular generation of nonlinear internal waves.

Three-Dimensional Numerical Simulation of Nonlinear Internal Waves in the St. Lawrence Estuary, Canada

Nguyen, V. T., 2016. Three-Dimensional Numerical Simulation of Nonlinear Internal Waves in the St. Lawrence Estuary, Canada. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 902–906. Coconut Creek (Florida), ISSN 0749-0208.The existence of nonlinear internal waves (NIWs) running up a sloping boundary of the Ile-aux-Lievres Island in the St. Lawrence Estuary, Canada has been revealed by the researchers at Memorial and Dalhousie Universities of Canada. Unfortunately, there is no direct field observation of the generation of the NIWs in this region in order to determine where these waves be generated and emanated from. In this paper, a nonhydrostatic three-dimensional model, MITgcm model, is modified and applied to investigate the generation and propagation of NIWs by tidal forcing over an idealized depression simplified from the topography of the North Channel in the St. Lawrence Estuary. A comparison between the numerical results and the observations shows very good qualitative agreements. The results of the simulation is not only to explain above phenomenon, but also to show the mechanism of the NIWs in this region.

Characteristics, generation and mass transport of nonlinear internal waves on theWashington continental shelf

AbstractAs a step toward better understanding the generation of nonlinear internal waves (NLIWs) on continental shelves and the factors determining their morphology, amplitude and propagation, we analyze more than 1500 NLIWs detected on the Washington (WA) continental shelf using four summer/fall time series of temperature and velocity measurements from a surface mooring deployed in 100 m of water. Propagating onshore toward the northeast, these NLIWs take a variety of forms, including internal solitary waves, solitary wave trains and bores. Nearly all are mode‐1 depression waves that arrive semidiurnally along with the internal tide. The NLIW energy flux is correlated with the internal tide energy flux but not the local barotropic forcing, implying that the observed NLIWs arise primarily from shoaling remotely generated internal tides rather than local generation. Estimated onshore transport by the waves can equal or exceed offshore Ekman transport, suggesting the waves may play an important role in the mass balance on the continental shelf.

Transcritical generation of nonlinear internal waves in the presence of background shear flow

While the occurrence of large amplitude internal waves in the Earth's natural bodies of water is widely documented, the generation of these waves remains an active area of exploration. We discuss numerical simulations of transcritical flows of a density stratified fluid with a dual focus on the role of a background shear current and transitions of the background current from super to subcritical. We demonstrate that the presence of a background shear can lead to the formation of large quasi-trapped regions of high vorticity over the downstream slope of the topography, but that this vorticity leads to only moderate perturbations of the underlying pycnocline, and hence that a wave and instability can co-exist for long times. Subsequently, we demonstrate the existence of hysteresis in the wave amplitude when the current is accelerated to supercritical then decelerated to subcritical, as opposed to accelerated to the subcritical value from rest. Finally, we explore situations in which the background shear is strong enough to preclude the formation of solitary-like waves, and discuss possible implications for the coastal ocean.

The Generation of Nonlinear Internal Waves

The Generation of Nonlinear Internal Waves

Impacts of tidal currents and Kuroshio intrusion on the generation of nonlinear internal waves in Luzon Strait

The analysis of remotely sensed images shows that two kinds of nonlinear internal solitary waves (ISWs) in the forms of single ISW and groups of ISWs are commonly seen in Luzon Strait (LS), with larger occurrence during spring tides. A 2‐D numerical model with idealized topography is then used to investigate the generation processes of ISWs in LS. The model results confirm that the ISWs are likely generated during spring tides with strong tidal currents. The results further suggest that the ISWs can be generated by two mechanisms: the evolution of depression and the internal mixing disturbance. Our simulations also show that the Kuroshio intrusion to LS or South China Sea through LS increases the occurrence of generating internal mixing and groups of ISWs. Both remotely sensed images and numerical simulations suggest the existence of a distance between the actual locations where ISWs are generated and where the strongest flow occurs.

Generation and propagation of nonlinear internal waves in Massachusetts Bay

During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.

Generation and propagation of nonlinear internal waves in Massachusetts Bay

Generation and propagation of nonlinear internal waves in Massachusetts Bay

Stratified flow over topography: upstream influence and generation of nonlinear internal waves

Results are presented from a recent experiment in Knight Inlet, British Columbia, focusing on the generation and propagation of nonlinear internal waves near the sill during ebb tide. High–quality echo–sounder and velocity measurements were obtained in a novel fashion, using instrumentation carried aboard a small inflatable boat. Complementing these data, a set of photographic images of the surface signature of the internal waves was acquired from both a fixed mountainside location and a helicopter. These photographs situate the observations within the larger–scale structure of the internal response found in the inlet. The observations reveal the development of strongly nonlinear internal waves on a bore occurring upstream of the sill crest. As the tidal flow relaxes, these waves propagate upstream, at first slowly, and later rapidly against the gradually waning flow. A simulation of wave generation with a fully nonlinear numerical model is discussed. The simulation shows that upstream influence, associated with the rapidly increasing tidal forcing, leads to formation of an undular bore upstream of the sill crest. As the tidal flow relaxes, the bore subsequently evolves into a group of upstream–propagating solitary–like internal waves. Taken together, the observations and numerical simulation describe a process for the generation of nonlinear internal waves involving upstream influence, which likely has application in other environments for stratified flow over topography.

The generation of non-linear internal waves in the Gulf of Oman

The generation of non-linear internal waves evident in two Synthetic Aperture Radar (SAR) images of the Gulf of Oman has been studied. The internal waves form packets, propagating towards the Musandam Peninsula from the eastern shelf-edge, travelling right up to the coast. The internal waves on the shelf have the classic appearance of rank ordered non-linear waves that depress the pycnocline. The images suggest a tidal generation mechanism. Under this assumption, estimates of the phase speeds of the waves were derived and found to vary from 0.5 m s −1 near the coast to 0.7 m s −1 on the shelf. The possible generation of the internal waves at the Gulf of Oman shelf-break has been investigated using numerical models. A 2D barotropic tidal model has been used to assess the tidal flux across the continental slope in the region of interest. The model indicates that tidal flow at the shelf-edge is mainly across-slope. The tidal flux information is used to drive a two-layer non-linear internal tide model, which simulates the internal tide along a vertical slice perpendicular to the shelf-edge. Numerical results for a tidal flux corresponding to the spring tide (corresponding to one of the SAR images) indicate that this is strong enough to produce high-frequency waves for all layer depths considered. It is found that for the weaker modelled value of tidal flux corresponding to the time of the other SAR image, using two-layer parameters derived from a climatological density profile, the forcing is just too weak to force high-frequency internal waves. However, a sensitivity study investigating the effects of different layer depths suggests that a reduction in the top layer thickness by 10 m is sufficient to produce waves similar to those observed. The model predicts internal waves of depression with peak to trough amplitudes up to 25 m, surface currents up to 0.6 m s −1, and strain rates of O(10 −3 s −1). The phase speeds of the internal waves from the model (0.9 m s −1) are slightly higher than those observed, possibly due to approximations of smooth bathymetry and climatological density profiles used in the model, or due to the approximate nature of inferring observed phase speeds from two SAR images from different years. As the qualitative features of the observed internal waves are reproduced by the internal tide model, it is concluded that tidal flow over the shelf-edge is the likely generation mechanism for the internal waves imaged by SAR.

The generation of non-linear internal waves by a barotropic tide in the area of a solitary bottom elevation

A mathematical model is suggested for calculating current, density, and pressure fields in the area of a solitary bottom rise (seamount). The model is based on a set of non-linear differential equations governing the motion of an inviscid continuously stratified fluid. The algorithm for solving the equations is based on the splitting technique. The model has been used to compute non-linear baroclinic waves generated by a barotropic tide in the seamount area.