A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅱ. Simulation of SAR signatures of internal solitary waves

A new model developed from the full-spectrum model of Lyzenga and Bennett （ 1988 ） is built up by us preliminarily through considering the impact of the ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves. In the partial differential equation of the action spectral density of the surface gravity-capillary waves the source function representing the contribution of the turbulence is added besides the usual source function representing the contribution of the wind. The source function is determined by applying the κ - ε model and adopting the Nasmyth spectrum of oceanic turbulence （ Nasmyth, 1970; Oakey, 1982; Fan, 2002） on the basis of the previous simulation results of internal tide transformation obtained in the companion paper （Fan et al. ,2008）. Either under relatively high wind speed, or under low wind speed, our model predicts significant large modulations of radar backscatter at all three bands （ L, C and X bands） for both VV and HH polarization. These results prove that considering the impact of ocean surface mixed layer turbulence on SAR remote sensing of internal solitary waves is reasonable and appropriate for settlement of the well-known problem of contemporary radar imaging models.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅰ. Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

Penetration of internal waves into the ocean’s thickness

The data of beam propagation of internal waves into the ocean are confirmed by several analytical solutions of the linear long wave theory. The obtained solutions are applied to calculate the mode of the internal waves.     

Infragravity waves with internal wave characteristics in the south of the Bohai Sea of China

The measurements by using ADCP (500 KH) and CTD were made during August 2000 in the south (37°55''N, 120°25''E) of the Bohai Sea, where the water depth was about 16.5m. The data of horizontal velocity with sampling interval of 2 min in 7 layers were obtained. The power spec-trum analysis of these data indicates that there are very energetic infragrvity waves with a period of about 6 min. The coherence spetrum analysis and the analysis of temporal variation of shear show that these infragravity waves are mainly the free wave model (properties of edge waves), in the meantimethey possess some characteristics of internal waves, which are likely due to the distinctive marine environment in this area. It is speculated on that the instability processes (chiefly shear instability) of sheared stratified tidal flow owing to the effect of sea-floor slope in the coastal area might be the main mechanism generating these infragravity waves.     

Optical remote sensing image characteristics of large amplitude convex mode-2 internal solitary waves: an experimental study

A series of experiments are designed to propose a new method to study the characteristics of convex mode-2internal solitary waves(ISWs) in optical remote sensing images using a laboratory-based optical remote sensing simulation platform. The corresponding wave parameters of large-amplitude convex mode-2 ISWs under smooth surfaces are investigated along with the optical remote sensing characteristic parameters. The mode-2 ISWs in the experimentally obtained optical remote sensing image are produc...     

Numerical modeling on the interaction of internal solitary wave with slope-shelf and modal analysis

On the basis of a nonhydrostatic numerical model,the interaction of internal solitary wave with slope-shelf was studied.The breaking and polarity transformation were analyzed.A "kink" structure,due to shoaling topography and higher nonlinear effect,was found to be generated by the leading wave before breaking.Coherent vortex shedding behind the leading wave was presented.The evolution characteristics of the modal structure were analyzed based on the empirical orthogonal function method.The modal structure was complicated due to the effect of the variable topography,especially when breaking occurred.In the performed experiments,the contributions to the total variance from higher mode jumped from no more than 20% to over 40%.     

On the run-up and back-wash processes of single and double solitary waves — An experimental study

The run-up and back-wash processes of single and double solitary waves on a slope were studied experimentally. Experiments were conducted in three different wave flumes with four different slopes. For single solitary wave, new experimental data were acquired and, based on the theoretical breaking criterion, a new surf parameter specifically for breaking solitary waves was proposed. An equation to estimate maximum fractional run-up height on a given slope was also proposed. For double solitary waves, new experiments were performed by using two successive solitary waves with equal wave heights; these waves were separated by various durations. The run-up heights of the second wave were found to vary with respect to the separation time. Particle image velocimetry measurements revealed that the intensity of the back-wash flow generated by the first wave strongly affected the run-up height of the second wave. Showing trends similar to that of the second wave run-up heights, both the back-wash breaking process of the first wave and the reflected waves were strongly affected by the wave–wave interaction. Empirical run-up formula for the second solitary wave was also introduced.     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

The mixing mechanism in the formation of ocean shear waves

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The grouping characteristics of sea waves in the Shijiu Port

A review concerning the methods of studying and describing wave groups is presented in this paper. After analysing 78 field records collected in the Shijiu Port, China, the measured parameters of wave groups and some factors describing wave groupness and their variations are given. Moreover, these results are compared with those of theory.     

An investigation of the morphodynamic change of reef islands under monochromatic waves

The persistence and habitability of coral reef islands in future extreme oceanographic conditions has received increasing attention in the recent decade, concerning that the sea level rise(SLR) and more frequent and intense storms in the context of global climate change are expected to destabilize those islands. Here, we conduct a set of wave-flume laboratory experiments focusing on the morphodynamic change of reef islands to varying ocean forcing conditions(wave height and SLR). Subsequently, a...     

The effect of internal tides on the vertical structure of tidal current in the North Huanghai Sea

The tidal current is generally predominant in China's offshore areas. The vertical structure of the observedtidal current is quite complicated with the presence of seasonal thermocline. The observed tidal current may be divided into two parts, an averaged barotropic tide current and a variation tide current. A method for studying the vertical structure of tidal current is developed from the constitution and distribution of energy, and the vertical structure of the observed tide current in the North Huanghai Sea is studied on the basis of the method. The result shows that the reason why the energy of the tidal current is concentrated on the neighbourhood of the thermocline mainly lies in the internal tides i under certain conditions, the fact that the direction of the internal tide current above the thermocline is opposite to the one below the thermocline will be able to cause the rotary directions of the observed tidal current above and below the thermocline to be in opposite. The interaction between th     

A study on dynamical features of air-sea coupling waves in the tropics

The dynamical features of air-sea coupling waves and their stabilities in a simple coupled air-sea model in the tropics have been studied with respect to interaction occurring among different types of the free waves in the o-cean and in the atmosphere. It is pointed out that there exist a stable and an unstable air-sea interaction modes in the tropical coupled system , respectively. The propagation of the unstable mode relies greatly on the zonal space scale, i. e. only for wave length ranging from 5 000 km to 10 000 km can the disturbance unstably move slowly eastward. The waves that slowly propagate unstably eastward agree well with the observational facts. Finally,it is also proposed that the interaction between Kelvin wave in one medium and Rossby wave in another medium is a necessary condition for the occurrence of destabilization of the coupled air-sea system in the tropics.     

A method for detecting the breaking of wind-generated waves in deep water

The breaking of wind-generated waves is an important phenomenon in the ocean, having close relation to many aspects of the ocean, such as air-sea interaction, ocean wave dynamics, oceanic remote sensing and ocean engineering. The first problem encountered in both its theoretical study and practical measurement is how to detect the breaking of waves.     

An experimental study of the relations between bispectra and nonlinear apparent features of wind waves

To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the nonlin-earity of wind waves are studied by using bispectral and statistical analysis of surface elevations. The relations between bispectra and nonlinear apparent characteristics of wind waves are established and confirmed.     

On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract

The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poisson's ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbers, i.e., the ratio of water‐wave speed to shear‐wave speed in soil and the ratio of water‐wave speed to compressional‐wave speed in soil. Most of the water‐wave propagation problems fall into the subsonic flow condition, where elastic waves in the bed travel faster than water waves.

For sandy beds, generally the speeds of compressional and shear waves are much higher than the phase velocity of the water wave. For this case, the solution of the Coulomb‐damped poroelastic bed response presented in this paper approaches the solution of the massless poroelastic bed response in Yamamoto et al. (1978 [Jour. Fluid Mech., 87(1): 193–206]). The damping of water waves due to internal grain‐to‐grain friction is equally or more significant than the damping due to percolation in sand beds.

For clay beds, the speed of the shear wave in soil becomes low and comparable to the phase speed of the water wave. The bed motion for this case is considerably amplified due to the near‐resonance vibration of shear mode of bed vibration. The water wavelength on a clay bed is significantly shortened compared to the water wavelength over a rigid bed. The water wave damping due to internal grain‐to‐grain friction in soil becomes much larger compared to the water wave damping due to percolation in clay beds. Long water waves over a soft clayey bed attenuate within several wavelengths of travel distance.     

Instability analysis of three-dimensional ocean shear waves

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Regeneration and anti-migration of sand waves associated with sand mining in the Taiwan Shoal

Sand waves in the Taiwan Shoal are characterized by two distinct spatial scales. Giant sand waves have a length of2 kilometers with height between 5 m and 25 m, whilst small sand waves is less than 100-m long with height less than 5 m between giant sand wave peaks(crests). A series of five high-resolution multi-beam echo-sounding surveys between 2012 and 2020 in the middle of Taiwan Shoal indicated that artificial dredging on the giant sand waves had caused sand wave reform and evolution. Overal...     

Modelling of the temporal and spatial evolutions of weakly nonlinear random directional waves with the modified nonlinear Schrödinger equations

The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are theoretically studied under the governing of MNLS equations, demonstrating that the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the presence of strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical model, are systematically compared to mechanically generated waves with different initial directional spreading and Benjamin–Feir Index, mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. On the whole, it can be argued that the statistical properties of both numerically simulated wave fields are basically consistent with the laboratory observations.