Witold Cieślikiewicz

Mass transport within the free surface zone of water waves

Abstract The mean velocities within both deterministic and random waves are examined in the Eulerian frame. The total mean flux on the basis of linear wave theory, with emergence effect taken into account, is derived. It is shown that the approximation of the total mean flux for random waves leads to the result obtained by Phillips (1960) and is equal to the joint statistical moment of second order for surface elevation and horizontal velocity taken at the mean water level. The same approach adapted to regular small-amplitude waves gives in approximation the well-known formula usually derived in the Lagrangian frame. Referring the theoretical predictions to the measured kinematics allows the estimation of the return flow in the wave flume. In the vicinity of the mean water level the currents in opposite directions to each other have been noticed. Firstly, the emergence effect gives rise to a current at the mean water level in the direction of the wave advance. Secondly, a flow in the opposite direction, interpreted as a return current in the wave flume, is noticed just below that level.

Stochastic characteristics of wave kinematics in laboratory-scale random waves

Abstract This paper presents the results of analysis of wave kinematics data of Skjelbreia et al. taken in a wave flume using Laser Doppler Velocimetry. This data set is unique with respect to accuracy and amount of data in the vicinity of the mean water level. The present publication of the statistical and spectral characteristics of these data sheds further insight into wave kinematics mechanism in the free surface zone where measurement points are not continuously submerged and when the so called “emergence effect” should be taken into account. Stochastic characteristics estimated from measurements are compared with known theoretical predictions applying the not commonly used approach presented by Tung. Furthermore, the theoretical spectral density of particle velocities, modified by emergence effect, obtained by taking the Fourier transform of the covariance function as derived by Pajouhi and Tung, is compared with measured values. Such a comparison has previously been made by Anastasiou et al. for a data set with limited amount of data above the free surface elevation. Anastasiou et al. have used an approximate formula for the modified covariance function. In this paper, however, the exact modified covariance function is for the first time used for statistical analysis and comparison with measurements of wave kinematics in a wave flume.

Spatial variability of long-term trends in significant wave height over the Gulf of Gdańsk using System Identification techniques

Abstract The significant wave height field over the Gulf of Gdańsk in the Baltic Sea is simulated back to the late 19th century using selected data-driven System Identification techniques (Takagi-Sugeno-Kang neuro-fuzzy system and non-linear optimization methods) and the NOAA/OAR/ESRL PSD Reanalysis 2 wind fields. Spatial variability of trends in the simulated dataset is briefly presented to show a cumulative “storminess” increase in the open, eastern part of the Gulf of Gdańsk and a decrease in the sheltered, western part of the Gulf.

System Identification Techniques for the Modelling of Irregular Wave Kinematics

This paper presents the development of a parametric model linking the free-surface elevations with the orbital velocities field under an irregular wave. The system identification procedures are applied to estimate the parameters of the model based on data recorded in the wave tank. The free-surface time series are taken as input data and the output data are components of the particle velocity vector. A linear time-invariant model with the static nonlinearities at the input side incorporated is assumed. In the study different system identification procedures are applied for two cases—firstly when orbital velocities are modelled at points that are always submerged in the water and, secondly, in the surface zone where measurement points are not continuously submerged. This paper demonstrates the results of modelling the horizontal component of the orbital velocity in comparison with wave kinematics data taken in a wave flume using Laser Doppler Velocimetry specifically designed to give accurate measurements also in the vicinity of the mean water level. Comparison between the modelled and observed velocity time series presents a sufficiently good agreement to prove the effectiveness of the applied approach. The SI techniques applied to determine from the free-surface records the orbital velocities as well as other hydrodynamic parameters such as particle acceleration and forces may be very important and useful in engineering and oceanography.