The analytical solutions and deep learning assessment of long waves over linear and nonlinear breadth and depth profiles: 30 October 2020 İzmir tsunami case

Abstract

Long waves in harbor engineering present some difficulties, such as preventing harbor resonance. Understanding and forecasting their dynamics is essential due to similar issues. The nonlinear geometries with power-law forms are not well explored, despite the fact that their dynamics have been thoroughly examined in the literature for a wide range of geometries. A recent paper by the advisor of this thesis describes the analytical solutions of the long-wave equation over nonlinear depth and breadth profiles with power-law forms as h(x)=(c_1)(x^a) and b(x)=(c_2)(x^c), where the parameters c_1, c_2, a, and c are some constants. Motivated by this, we expand on our previous work in this thesis and derive the precise analytical solutions of the long-wave equation across both linear and nonlinear in the power-law form depth and breadth geometries in which a solid vertical or inclined wall exists. This thesis consists of 5 chapters. In Chapter 1 within the frame of Introduction, we discuss the known solutions of long waves over different variations in breadth and depth. The solutions for the Bessel Function are expressed. Free Oscillation Period examples are presented. We refer to Laguerre Polynomials and Gauss Hypergeometric Series. Lastly, we introduce the Power-Law form solution to the Long Wave equation. In Chapter 2 within the frame of Publication Number 1, in the presence of the solid vertical wall, we demonstrate that for these specific power-law forms of depth and breadth profiles, the long-wave equation admits solutions in terms of Bessel-Z functions and the Cauchy-Euler series. Analytical solutions' singular points are removed from the domain when the origin of the harbor/bay geometry contains a solid vertical wall. Consequently, the solutions produced exhibit both the first and second kind of the Bessel functions. Our findings pertain to the overall category of geometries that we examine that have solid vertical or inclined walls. Furthermore, six other instances for the above geometries with the presence of a solid vertical wall are analyzed. Water surface fluctuation functions are obtained in terms of Bessel-Z functions for each of the six different cases. These obtained functions are displayed graphically along with the relevant geometry drawing. Afterward, these graphics are interpreted regarding areas such as in-harbor resonance and wave energy converter. In Chapter 3 within the frame of Publication Number 2, the work on the exact analytical solutions of the long-wave equation with vertical wall case, which we had previously completed in Chapter 2 within the frame of Publication Number 1, is repeated, but for the case with inclined walls. First, we provide a general overview of partial reflection and its constituent parts—the slope angle, phase lag, reflection coefficient, and Iribarren number—which we have to consider because of the inclined wall, in addition to the preceding chapter on this subject. On the other hand, we discover that the solutions to the long wave equations are given by Bessel-Z functions; nevertheless, when accounting for a parabolic depth variation, these solutions assume the form of the Cauchy-Euler series. Once more, we present our findings and provide the analytical solution for long waves in different configurations. As in the previous section, water surface fluctuation functions are obtained in terms of Bessel-Z functions for each of the six different cases. These obtained functions are displayed graphically along with the relevant geometry drawing. Afterward, these graphs are compared with the graphs of the vertical wall situation in the previous chapter, and interpretations are made regarding areas such as in-harbor resonance and wave energy converter. After completing the analytical solutions of long waves containing vertical and inclined wall situations, in Chapter 4 within the frame of Publication Number 3, we move on to the study of the 30 October 2020 İzmir Tsunami, which is the special case of our thesis. In the nearshore environment, tsunamis can be exceedingly deadly even if they happen less frequently than certain other natural disasters. Around 23 km south of Turkey's İzmir province, off the Greek island of Samos, an earthquake with a magnitude of 6.9 Mw struck on October 30, 2020, at 12:51 p.m. UTC (2:51 p.m. GMT+03:00). The tsunami event generated by this earthquake is known as the 30 October 2020 İzmir-Samos (Aegean) tsunami, and in this thesis, we examine the hydrodynamics of this tsunami using some of artificial intelligence (AI) approaches applied to observational data. Comprehensive information is given about the history, structure, content, and working principle of the LSTM deep learning algorithm. We explain that data flow is made possible by the forget, input, and output gates as well as a memory cell outside the input that determines whether the information will be transferred, retained, or forgotten. More precisely, we make use of the tsunami time series that we obtained at various sites in Bodrum, Syros, Kos, and Kos Marina from the UNESCO data portal. Next, the application and limitations of the Long Short Term Memory (LSTM) DL approach for the Fourier spectrum and time series prediction of tsunamis are examined. More specifically, we investigate the predictability of the dynamics of offshore water surface elevation, their spectral frequency and amplitude properties, potential success factors for predictions, and the improvement of the precise early prediction time scales. To do this, the data utilized in this study is de-tided using a spectral technique to eliminate the astronomical tidal influence. An FFT-IFFT technique is employed for this. It is shown that LSTM with updates is more successful in predicting the lower frequency components for the tsunami time series. Potential study options are also explored, along with the applications and use of our results. In Chapter 5, within the frame of Conclusion, we report our findings. Our findings can be used in the study of long wave resonance and runup in bays and harbors, as well as wave energy focusers and resonators. It is also possible to investigate the effects on long-wave hydrodynamics of wall building, dredging, and geometry changes generated by landslides within the framework of the conclusions reached in this thesis. Moreover, performance gains in tsunami early warning systems and numerous investigations on tsunami characteristics, such as run-up time series and horizontal and excursion velocities, can be pioneered by utilizing the findings of this thesis study. We propose to use our work to obtain the solutions of the long wave equation for additional geometries with different shapes, such as a vertical or inclined wall, in terms of Laguerre, Chebyshev, Hermite, or Legendre polynomials. Likewise, we state that all these parameters can be studied in 2D instead of 1D as well. Finally, we state in detail the studies we plan to do in the future using the findings of our thesis studies and how we will do them in the Conclusion section.