20 June 2022, 14:00 - 15:00 
פקולטה להנדסה 
Department Seminar of Rotem Sofer



School of Mechanical Engineering Seminar
Monday, June 20, 2022, at 14:00
Wolfson Building of Mechanical Engineering, Room 206


Rotem Sofer

PhD Yaron Toledo


Field measurements of waves and currents, conducted by an Acoustic Doppler Current Profile (ADCP) instrument mounted in the sea environment, were conducted and processed in this work. The data processing was compared to corresponding theoretical models, and advanced to account for waves in the presence of shearing currents.

Tel-Aviv University Marine Engineering and Physics laboratory (MEPlab), and the author of this thesis, were part of an inter-universities team establishing the "Deep Levantine" (DeepLev), a monitoring mooring station, the first of its kind in the Eastern Mediterranean Sea (EM) region, anchored at a depth of $\sim1470m$. The station contains a large number of state-of-the-art measuring instruments, including ADCPs, velocimeters, sediment traps, and CTDs, enabling continuous study of the physical and ecological system in the EM. The first part of this work deals with the deployment of the upper ADCP on DeepLev's mooring system and its data processing providing waves and currents for the first time in the deep waters of the EM.

Wind waves are of great importance in various fields of oceanography and engineering. They are essential for the design of maritime structures, such as breakwaters, ports, desalination plants, offshore platforms and marine pipelines, etc. Although they propagate along entire seas and oceans, they are mostly measured in nearshore regions due to the complexity and high costs in setting deep water measurements. The connection between deep sea wave conditions and nearshore ones is commonly done by using wave propagation models, and employing the Wave Action Equation (WAE). Available coastal measurements are back scattered to the deep sea, and are propagated to other locations of interest in the coastal waters. Nevertheless, due to the scarcity of deep water measurements, the validity of this process is seldomly tested.

The second part of this work tested this process of field comparing data. Wave evolution from the deep sea measured in DeepLev to intermediate coastal waters was investigated. Another ADCP was deployed on the sea bed (26m depth) two kilometers offshore. During this campaign, a substantial storm (Hm0=6m) was recorded simultaneously by both ADCPs. Significant differences between the two measurements were found. A wave evolution model accounting for triad and quartet interactions was employed for connecting the two measurements. A new methodology was developed for resolving spatial variability in the deep sea conditions by assimilating the deep water data into the output of an operational wave model for the Mediterranean Sea. This allowed forming appropriate boundary conditions for propagation of the wave field from deep to coastal waters. Model results show an importance of accounting for inhomogeneity of the wave field in deep water. Nevertheless, the measurements indicate

that one cannot expect to fully resolve the exact wave spectra only by applying wave modeling. This emphasizes the importance of conducting such deep wave measurements, and pointing out that backward propagation of nearshore measurements to the deep sea, and then propagating it to another coastal location, would not yield the same results as the propagation of deep sea measurements to the same location of interest.

An additional observation in the above campaign was that the ambient current is not necessarily aligned with the wave propagation direction or with the winds. It also had a vertically shearing profile, which cannot be modelled using the common potential theory. This raised a question about the influence of shearing currents on the wave directions. Rotational wave theory can address that question and find the wave properties in the presence of shearing currents via the Rayleigh equation. However, there is no

methodology for wave data processing accounting for such currents, even though instruments such as ADCPs can provide the current profile. The common data processing is done by employing cross-spectra calculations of the sea elevation and the oscillatory velocities, non-rotationally transferred to the sea elevation according to transfer functions derived from the potential theory.

The third part of this work tests accuracy of the common data processing approach on simulations of waves propagating over shearing currents. The potential approach inherent assumption that the current profile can be either constant in depth or more common, there is no current at all.  The goal of those simulations was to generate realistic datasets of sea elevations, and the horizontal velocities, as could have been obtained by an ADCP for a known predetermined sea state. Simulations of two predetermined wave directional spectra in the presence of shearing currents were conducted, and several case studies of different inclinations between ambient shearing current and the waves were investigated.  The Rayleigh equation was employed to derive the horizontal oscillatory wave velocities per predetermined discrete wave amplitudes in the presence of a given ambient current profile. The Rayleigh equation is a first order perturbation of Euler equations where the zero order components are related to the ambient current profile, and the first order components are the oscillatory wave's flow. It was solved for each of the spectra's frequencies and directions, and all the amplitudes were transferred to the time domain by applying uniformly distributed phases. The results of the simulation showed that there are great deviations between the predetermined wave spectra and those that were processed according to the potential theory, and as the inclination between the waves and the current is greater, so is the error in the directional spectral estimation.  Hence, potential data processing is not appropriate for wave spectra calculations in the presence of shearing currents.

The last part of this work was dedicated for filling this gap and developing a new non-potential data processing methodology that would be able to accurately estimate directional wave spectra in the presence of shearing currents profile. New numerical transfer functions and a new methodology for the estimation of the directional spread function Fourier coefficients were derived. In same manner as in the simulation part, three data-sets of sea elevation and horizontal velocities time series were prepared, accounting for the same shearing currents case studies. To simplify the simulations, the effects of shearing currents on the behavior of wave directions was studied using monochromatic waves instead of full spectrum. Potential methodology data processing and the newly derived rotational data processing were applied to the data sets to generate spread functions.  The new rotational data processing methodology was found to be superior compared to the potential one, significantly yielding more accurate results.

The findings that the commonly used potential data processing methodology has such significant errors (up to 30°) in such common scenarios is of great importance. Realistic current in seas and oceans are almost always changing in depth. The newly developed rotational methodology overcomes large discrepancies and hence has the potential to become the leading approach in wave data analysis.



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