Numerical investigation of wake-collapse internal waves generated by a submerged moving body

The state-of-the-art OpenFOAM technology is used to develop a numerical model that can be devoted to numerically investigating wake-collapse internal waves generated by a submerged moving body.The model incorporates body geometry,propeller forcing,and stratification magnitude of seawater.The generation mechanism and wave properties are discussed based on model results.It was found that the generation of the wave and its properties depend greatly on the body speed.Only when that speed exceeds some critical value,between 1.5 and 4.5 m/s,can the moving body generate wake-collapse internal waves,and with increases of this speed,the time of generation advances and wave amplitude increases.The generated wake-collapse internal waves are confirmed to have characteristics of the second baroclinic mode.As the body speed increases,wave amplitude and length increase and its waveform tends to take on a regular sinusoidal shape.For three linearly temperature-stratified profiles examined,the weaker the stratification,the stronger the wake-collapse internal wave.     

Effects of tidal currents on nonlinear internal solitary waves in the South China Sea

The propagation and fission process of internal solitary waves (ISWs) with amplitudes of about 170 m are simulated in the northeast of the South China Sea (NSCS) by using the generalized Korteweg-de Vries (KdV) equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons (defined as the distance between two neighboring peaks of ISWs). The difference in nonlinearity coefficient α between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.     

On the nonlinear waves in a developing process

Based on the discrete form of the main governing equation derived, a single wave as the main motion of the instability analysis was found. This solution gives the whole process from the initial stage to the nonlinear equilibrium state. Next we examined the instability of the main motion above-mentioned in the initial stage and showed the instability properties of a developing process. Contribution No. 987 from the Institute of Oceanology, Academia Sinica.     

Ocean mixing with lead-dependent subgrid scale brine rejection parameterization in a climate model

Sea ice thickness is highly spatially variable and can cause uneven ocean heat and salt flux on subgrid scales in climate models.Previous studies have demonstrated improvements in ocean mixing simulation using parameterization schemes that distribute brine rejection directly in the upper ocean mixed layer.In this study,idealized ocean model experiments were conducted to examine modeled ocean mixing errors as a function of the lead fraction in a climate model grid.When the lead is resolved by the grid,the added salt at the sea surface will sink to the base of the mixed layer and then spread horizontally.When averaged at a climate-model grid size,this vertical distribution of added salt is lead-fraction dependent.When the lead is unresolved,the model errors were systematic leading to greater surface salinity and deeper mixed-layer depth(MLD).An empirical function was developed to revise the added-salt-related parameter n from being fixed to lead-fraction dependent.Application of this new scheme in a climate model showed significant improvement in modeled wintertime salinity and MLD as compared to series of CTD data sets in 1997/1998 and 2006/2007.The results showed the most evident improvement in modeled MLD in the Arctic Basin,similar to that using a fixed n=5,as recommended by the previous Arctic regional model study,in which the parameter n obtained is close to 5 due to the small lead fraction in the Arctic Basin in winter.     

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19°35′N, 112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.     

A wave modulation model of ripples over long surface waves

A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modulation model is proposed. In this model, the wind surface stress modulation is related to the modulation of ripple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the ripple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves.     

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow. One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained. The model simulations describe the generation and propagation of internal waves well. When the strength of imposed barotropic tides and the water stratification stay unchanged, the steepness of the sill slope can control both (a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves, and (b) the amplitude of the internal solitary waves generated. If the steepness of the sill is asymmetric, the nonlinear internal solitary waves may be induced on the steeper side of the sill. These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.     

The dispersion relation for nonlinear waves in a developing process

We derived the dispersion relation (correct to the second order in wave slope) of nonlinear waves in a developing process, proved that there are mainly three time scales in a developing process of nonlinear waves governed by coupling mechanisms. The three time scales are oscillation, evolution and developing time scales. We also proved that even in the developing process of nonlinear waves, there is no term in dispersion relation in proportion to the first order of wave slope. In a stationary case our results agreed with the discrete form obtained by Weber in 1977. Our computed results of wave speed in the wallops spectrum were in good agreement with the laboratory measurements made by Ramamonjiarisoa (1976) in energy-containing range.     

The investigation of internal solitary waves over a continental shelf-slope

Internal solitary waves (ISWs) always happen in marginal seas, where stable stratification exists. ISWs may carry large energy when they propagate and affect marine engineering constructions such as marine drilling platforms. Previous studies, including a large number of mooring observations and laboratory experiments, show the speed of ISWs will change when they pass by shelf slopes. Korteweg-de Vries (KdV) theory explain this phenomenon. In the paper, we use a laboratory experiment and a numerical model experiment to verify this theory. In the laboratory experiment, we injected two layers of water of different densities in a tank to simulate marine stratification and make ISWs. We use a CCD camera to record the whole process. The camera can take 16 photos per second. In the numerical experiment, we input the same original conditions as the laboratory one. The results of 18 different original conditions show the dimensionless factor d plays a key role in deciding the amplitudes and shapes of ISWs. The main conclusion also contains that small-amplitude waves match well with KdV theory while mKdV is better for largeamplitude waves. Whether the laboratory experiment or numerical experiment shows results with a high agreement. In future studies, we may use a numerical model with higher resolution to get analysis about phase speed and energy of ISWs.     

一类非线性系统的定性分析研究

应用H.Poincaré定性理论与Liapunov,稳定性理论,讨论了一类含参非线性系统随参数变化在有限远奇点的性质.通过用计算机软件Maple进行图形绘制,能清晰了解轨线的走向和趋势,从而证明了该微分动力系统理论分析的正确性.     

Numerical analysis of the flow field in a sloshing tank with a horizontal perforated plate

Liquid sloshing is a type of free surface flow inside a partially filled water tank. Sloshing exerts a significant effect on the safety of liquid transport systems; in particular, it may cause large hydrodynamic loads when the frequency of the tank motion is close to the natural frequency of the tank. Perforated plates have recently been used to suppress the violent movement of liquids in a sloshing tank at resonant conditions. In this study, a numerical model based on OpenFOAM (Open Source Field Operation and Manipulation), an open source computed fluid dynamic code, is used to investigate resonant sloshing in a swaying tank with a submerged horizontal perforated plate. The numerical results of the free surface elevations are first verified using experimental data, and then the flow characteristics around the perforated plate and the fluid velocity distribution in the entire tank are examined using numerical examples. The results clearly show differences in sloshing motions under first-order and third-order resonant frequencies. This study provides a better understanding of the energy dissipation mechanism of a horizontal perforated plate in a swaying tank.     

Characteristics of nonlinear internal waves observed in the northern South China Sea

The South China Sea (SCS) is one of the most active areas of internal waves. We undertook a program of physical oceanography in the northern South China Sea from June to July of 2009, and conducted a 1-day observation from 15:40 of June 24 to 16:40 of June 25 using a chain of instruments, including temperature sensors, pressure sensors and temperature-pressure meters at a site (117.5°E, 21°N) northeast of the Dongsha Islands. We measured fluctuating tidal and subtidal properties with the thermistor-chain and a ship-mounted Acoustic Doppler Current Profiler, and observed a large-amplitude nonlinear internal wave passing the site followed by a number of small ones. To further investigate this phenomenon, we collected the tidal constituents from the TPXO7.1 dataset to evaluate the tidal characteristics at and around the recording site, from which we knew that the amplitude of the nonlinear internal wave was about 120 m and the period about 20 min. The horizontal and vertical velocities induced by the soliton were approximately 2 m/s and 0.5 m/s, respectively. This soliton occurred 2–3 days after a spring tide.     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study, typhoon waves generated during three typhoons(Damrey(1210), Fung-wong(1416), and Chan-hom(1509)) in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN) model, and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model. Various parameters, such as the Holland fitting parameter(B) and the maximum wind radius(R), were investigated in sensitivity experiments in the Holland model that affect the wind field construction. Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements. The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied, including wind input, whitecapping, and bottom friction. Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation) and the JONSWAP scheme(dissipation of bottom friction) resulted in good reproduction of the significant wave height of typhoon waves. A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon, while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves. The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.     

Investigation of wave characteristics in a semi-enclosed bay based on SWAN model validated with buoys and ADP-observed currents

In this study, the simulating waves nearshore(SWAN) model with a locally refined curvilinear grid system was constructed to simulate waves in Jervis Bay and the neighbouring ocean of Australia, with the aim of examining the wave characteristics in an area with special topography and practical importance.This model was verified by field observations from buoys and acoustic Doppler profilers(ADPs). The model precisions were validated for both wind-generated waves and open-ocean swells. We present an approach with which to convert ADP-observed current data from near the bottom into the significant wave height. Our approach is deduced from the Fourier transform technique and the linear wave theory. The results illustrate that the location of the bay entrance is important because it allows the swells in the dominant direction to propagate into the bay despite the narrowness of the bay entrance. The wave period T p is also strongly related to the wave direction in the semi-enclosed bay. The T p is great enough along the entire propagating direction from the bay entrance to the top of the bay, and the largest T p appears along the north-west coast,which is the end tip of the swells' propagation.     

A numerical model for tidal currents in the Changjiang River estuary

A generalized finite difference scheme is presented for the solution of two-dimensioned tidal current equations (averaged over the depth of water). This method has been used to simulate the tidal currents in the Changjiang River estuary, with computed results being in good agreement with the field observations. The two-dimensional domain consists of triangular elements with acute angles. First- and second-order partial derivatives are defined at nodal points. In addition, the basic tidal current equations contain an extra term to account for horizontal eddy viscosity. The method has the great advantage of allowing a wide flexibility in configuration simulation, thereby exhibiting the capability to arbitrarily subdivide the region of interest as well as to provide a more accurate boundary shape, and what is more, it offers savings in computing costs. This paper was published in Chinese in the Ocean. et Limn. Sinica.16(1):18–27, 1985