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.     

Cause and countermeasure of long-period oscillations of moored ships and the quantification of surge and heave amplitudes

Long-period oscillations of moored ships whose periods are about 1 or 2 min cause many troubles in many ports and harbours. It is necessary to investigate these phenomena and verify their causes and countermeasures in each case because they are strongly dependent on the environment of each port and harbour. From this point of view, long-period oscillations of moored ships in the Port of Shibushi in Japan were investigated by means of wave observations, the image processing of moored ship motions using the video camera and motion-capture software and numerical simulations. From observation results, the relationship between offshore long-period waves and long-period oscillations of moored ships was recognized and surge and heave amplitudes were quantified by using wave data in order to forecast moored ship motions. Furthermore, from observation and numerical results, it was revealed that long-period waves with the peak period of 120 s from the offshore typhoon kept or exaggerated the local harbour oscillation of 60–70 s and it caused long-period oscillations of moored ships. Numerical results in case of reducing the reflection coefficient of the target berth implied that it ceased the local harbour oscillation and it would give an effective countermeasure to reduce long-period oscillations of moored ships in the Port of Shibushi.     

Exploration of the wind-induced drift characteristics of typical Chinese offshore fishing vessels

The drift motion of a maritime distress target is the collective result of the balance of forces that comes from wind, currents and waves. The drift properties vary from one type of object to another. The objective of this paper is to explore the leeway drift characteristics of typical Chinese offshore fishing vessels as well as evaluate the leeway drift model. First, a series of field experiments were conducted in South China Sea to provide data source. Next, nine leeway coefficients in AP98 leeway model were derived by the least square fitting based on the experimental data. Furthermore, another drifting dynamics model based on a balance of forces on the drifting vessel due to wind and currents, was also calibrated for comparison. Finally, two cases of drift trajectory and searching areas were simulated by the two different models through Lagrangian particle tracking and Monte Carlo techniques. Results indicate that the AP98 leeway model is in better accordance with the observation compared with the drifting dynamics model. Additionally, the simulation accuracy of AP98 leeway model can be improved to some extent especially when the probability of positive crosswind (POPC) is considered. Considering the large number of the typical offshore fishing vessels in South China Sea, and their high accident rate, the model coefficients for this type of vessels are expected to be implemented into more search and rescue (SAR) models by SAR organizations.     

Modeling of iceberg drift in the marginal ice zone of the Barents Sea

The paper is focused on the analysis of the drift of tabular iceberg observed in 2009 in the marginal ice zone of the North-West Barents Sea. Momentum balance equations are derived from the Kirchhoff equations describing plane motion of solid body in an ideal fluid. Field works performed on the drift iceberg and on the drift icenear the iceberg are described. Results of the field works and numerical simulations of the iceberg drift and rotation are performed and discussed. It is shown that acceleration of water flow around the iceberg has visible influence on the iceberg drift. Kinetic energy balance of drift iceberg is used to estimate the forces applied to the iceberg by the drift ice.     

Cyclostrophic adjustment and nonlinear oscillations in the core of an intense atmospheric vortex

Intense atmospheric vortices are characterized by a regime of cyclostrophic balance, i.e., the balance between the pressure gradient and centrifugal force. To describe motions in the core of an axisymmetrical vortex, a class of exact solutions to the equations of gas dynamics with a linear dependence on radius is derived for the velocity components and with a quadratic dependence for temperature. It is shown that small deviations from the balance state give rise to oscillations of the hydrothermodynamic fields in the vortex core with a frequency proportional to the angular velocity of the rotation of the core. For fairly large initial deviations, oscillations are clearly anharmonic and, under the conditions of the prevailing centrifugal force, result in a significant temperature decrease on the vortex axis. The application of this class of solutions to describing the Ranque vortex effect (the intense cooling of gas during rapid rotations) and the acoustic radiation from tornadoes is discussed.     

Identification of the excitation and reaction forces on offshore platforms using the random decrement technique

This paper describes a method to identify the parameters of the dynamic model of a fixed offshore platform subjected to wind-generated random waves using its stationary response. The structure is modeled as a single degree of freedom system. The parameters identified are the damping coefficient, the natural frequency, and the excitation. In addition, the moment and force acting on the foundation are also identified. The method uses the random decrement signature as a tool to identify the parameters in the equation of motion. Excellent agreements were obtained between the predicted and actual values of the parameters as well as for the reaction and moment at the platform's foundation. The method can be applied without any interruption to the operation of the offshore structure. The method is easy to apply, and uses inexpensive motion measurement instruments. The estimated force and moment can be used as a tool for an on-line foundation check.     

Thermohydrodynamics of the ocean decay of nonlinear oscillations in a bounded basin of variable depth

We study the time decay of surges of a liquid in a round shallow-water basin of variable depth. The dependence of the logarithmic decrement of oscillations on the bottom topography and wind velocity is analyzed. The role of convective acceleration and bottom friction in the formation of both the level of vertical displacement of the surface of the basin and the velocity field of horizontal wave currents is estimated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 3–11, March–April, 2006.     

Application of leeway drift data to predict the drift of panga skiffs: Case study of maritime search and rescue in the tropical pacific

The use of Search and Rescue (SAR) drift forecasting in an operational capacity is demonstrated through two SAR case studies, each predicting the drift of a panga skiff for 120 h (Case 1) and 72 h (Case 2). The leeway characteristics of panga skiffs were previously unknown, until a leeway field study was undertaken in mid-2012 to empirically determine the influence of wind and waves on their drift. As part of the two case studies described herein, four ocean models were used as environmental forcing for a stochastic particle trajectory model, to forecast the drift and resulting search areas for the panga skiffs. Each of the four ocean models were tested individually, and then combined into a consensus forecast to ascertain which ocean model was the most accurate in terms of distance error of modelled positions compared to actual panga skiff locations. Additionally, a hit analysis was undertaken to determine whether the panga skiff was located within the forecast search areas for each ocean model, and for consensus search areas. Finally, an assessment of the search area sizes was carried out to assess the single ocean model forecast search area sizes, and how they compared with the consensus search area size. In both of the case studies, all four ocean model forecast search areas contained the panga skiff at the time intervals tested, indicating a 100% hit rate and general consensus between the ocean models. The consensus search area, where all four ocean models overlapped, was approximately one third the size of the average single model search area. This demonstrates that the consensus search areas provide a more efficient search area compared to individual ocean model search area forecasts.     

Application of a nonlinear frequency domain wave–current interaction model to shallow water recurrence effects in random waves

The effect of ambient currents on nearshore nonlinear wave–wave energy transfer in random waves is studied with the use of a nonlinear frequency domain wave–current interaction model. We focus on the phenomenon of wave recurrence as a classical nonlinear phenomenon whose characteristics are well established for systems truncated to small numbers of frequency modes. The model used for this study is first extended to enhance accuracy; comparisons of permanent form solutions to analytical forms confirm the model accuracy. Application of the model to a highly truncated system confirmed the model’s consistency with published results for both positive (following) and negative (adverse) currents. Propagation of random wave spectra over a flat bottom was performed with the model, with the intent of determining the prevalence of recurrence between the spectral peak and its harmonics. For spectra of moderate Ursell number, it was found that positive currents extended the length scale of recurrence relative to the case with no currents; conversely, negative currents reduced the recurrence lengths. However, beyond a propagation distance of ≈40 wavelengths of the spectral peak, recurrence becomes almost completely damped as the spectra becomes broad and the spectral energies equilibrate. For spectra of high Ursell number, in contrast, recurrence is almost immediately damped, suggesting that the nonlinearity is sufficient to allow immediate spectral broadening and equilibration and overwhelming any preferential interactions among the spectral peak and its harmonics, regardless of current magnitude or direction.     

Measures to diminish the parameter drift in the modeling of ship manoeuvring using system identification

System identification provides an effective way to predict the ship manoeuvrability. In this paper several measures are proposed to diminish the parameter drift in the parametric identification of ship manoeuvring models. The drift of linear hydrodynamic coefficients can be accounted for from the point of view of dynamic cancellation, while the drift of nonlinear hydrodynamic coefficients is explained from the point of view of regression analysis. To diminish the parameter drift, reconstruction of the samples and modification of the mathematical model of ship manoeuvring motion are carried out. Difference method and the method of additional excitation are proposed to reconstruct the samples. Using correlation analysis, the structure of a manoeuvring model is simplified. Combined with the measures proposed, support vector machines based identification is employed to determine the hydrodynamic coefficients in a modified Abkowitz model. Experimental data from the free-running model tests of a KVLCC2 ship are analyzed and the hydrodynamic coefficients are identified. Based on the regressive model, simulation of manoeuvres is conducted. Comparison between the simulation results and the experimental results demonstrates the validity of the proposed measures.     

An analysis of horizontal dispersion due to the drift current with an Ekman layer

An analytical method for describing horizontal matter dispersion in shear currents is presented using a tensor expression from the point of view that matter dispersion due to the shear effect should be one of the principal mixing dilution processes. Although the behavior of horizontal dispersion is considerably more complicated than common longitudinal dispersion, the present study elucidates the vertical structure of dispersion and the dispersing process from the initial to the stationary stage, besides the usual depth-averaged dispersion coefficient at the stationary stage. As one of the typical applications of horizontal dispersion, dispersion due to the pure drift current with an Ekman layer is examined theoretically using the present method. This examination reveals that the displacement of the centroid and the major axis of dispersion are twisted in the vertical direction more than the direction of the current vector forming the Ekman spiral; that the variance increases in proportion to the third power of the elapsed time; and that the dispersion coefficient at the stationary stage remains constant, independent of the depth normalized by an Ekman layer thickness. Such dependence of the dispersion coefficient in the steady current is shown to be different from that in the oscillatory current, which is inversely proportional to the depth normalized by a Stokes layer thickness. This is considered to be induced by the difference of the vertical profiles of the first order moment in both currents, that is, the shear region of the first order moment is restricted around the floor by the alternation of the current shear in the oscillatory current while it is diffused in the whole depth in the steady current.     

Transient fluid motion due to the forced horizontal oscillations of a vertical cylinder

The problem of the forced horizontal oscillations of a vertical cylinder extending throughout the fluid depth is considered on the basis of the linearised theory of water waves. A new integral form is given for the frequency-domain solution and the procedure is then used to obtain an explicit time-domain solution.     

An explicit approximation to the wavelength of nonlinear waves

An explicit and concise approximation to the wavelength in which the effect of nonlinearity is involved and presented in terms of wave height, wave period, water depth and gravitational acceleration. The present approximation is in a rational form of which Fenton and Mckee's (1990, Coastal Engng 14, 499–513) approximation is reserved in the numerator and the wave steepness is involved in the denominator. The rational form of this approximation can be converted to an alternative form of a power-series polynomial which indicates that the wavelength increases with wave height and decreases with water depth. If the determined coefficients in the present approximation are fixed, the approximating formula can provide a good agreement with the wavelengths numerically obtained by Rienecker and Fenton's (1981, J. Fluid Mech. 104, 119–137) Fourier series method, but has large deviations when waves of small amplitude are in deep water or all waves are in shallow water. The present approximation with variable coefficients can provide excellent predictions of the wavelengths for both long and short waves even, for high waves.     

A second approximation to the time-mean lagrangian drift beneath a series of progressive gravity waves

A fourth-order solution is derived for the mean drift induced by a steady train of waves in water of constant depth. New measurements are carried out of the drift in the body of the fluid and the drift velocity gradient at the free surface. Comparison of theory and experiment shows significantly better agreement with the present fourth-order solution than with the previous second-order solution of Longuet-Higgins, M.S., 1953 [Phil. Trans. R. Soc.245, 535–581]. In particular, the present solution reproduces the observed tendency of the surface drift velocity to rise in shallow water and to level-off in very deep water.     

An explicit approximation to the wavelength of nonlinear waves

An explicit and concise approximation to the wavelength in which the effect of nonlinearity is involved and presented in terms of wave height, wave period, water depth and gravitational acceleration. The present approximation is in a rational form of which Fenton and Mckee's (1990, Coastal Engng 14, 499–513) approximation is reserved in the numerator and the wave steepness is involved in the denominator. The rational form of this approximation can be converted to an alternative form of a power-series polynomial which indicates that the wavelength increases with wave height and decreases with water depth. If the determined coefficients in the present approximation are fixed, the approximating formula can provide a good agreement with the wavelengths numerically obtained by Rienecker and Fenton's (1981, J. Fluid Mech. 104, 119–137) Fourier series method, but has large deviations when waves of small amplitude are in deep water or all waves are in shallow water. The present approximation with variable coefficients can provide excellent predictions of the wavelengths for both long and short waves even, for high waves.