Μελέτη της εντατικοποίησης των κυματικών μεγεθών κατάντη κυματοθραύστη και εκτός της σκιάς του

Abstract

Αντικείμενο της παρούσας μεταπτυχιακής εργασίας είναι η μελέτη της επίδρασης της περίθλασης και της διάθλασης κατάντη του κυματοθραύστη στην περιοχή εκτός της σκιάς του, με τη χρήση του υπολογιστικού μοντέλου ΜΙΚΕ 21 και συγκεκριμένα της υπορουτίνας ΜΙΚΕ 21 BW. Μελετάται η επιρροή στην προαναφερθείσα περιοχή της γωνίας πρόσπτωσης α του εισερχόμενου κυματισμού, της μέγιστης γωνίας κατευθυντικότητας θ και της μη γραμμικότητας. Γίνεται επεξεργασία των κυματικών χαρακτηριστικών στην περιοχή μελέτης χωρίς την παρουσία κυματοθραύστη και η διαδικασία επαναλαμβάνεται με την παρουσία του. Τα εξαγόμενα αποτελέσματα συγκρίνονται και οπτικοποιούνται κατάλληλα για την καλύτερη κατανόηση από τον αναγνώστη. Παρουσιάζεται συμπερασματικά η επιρροή των παραπάνω χαρακτηριστικών στην περιοχή ενδιαφέροντος. Αρχικά γίνεται μια παρουσίαση των γενικών χαρακτηριστικών των λιμενικών εγκαταστάσεων καθώς και πειραματικών παρατηρήσεων για το φαινόμενο της κυματικής ενίσχυσης στα κατάντη του κυματοθραύστη και στην περιοχή της σκιάς του. Ακολούθως αναλύεται το φαινόμενο της περίθλασης αλλά και αυτό της διάθλασης. Στη συνέχεια γίνεται η παρουσίαση των γενικών και των ειδικών χαρακτηριστικών του αριθμητικού μοντέλου MIKE 21 BW που χρησιμοποιήθηκε για την επεξεργασία. Αναλύεται ο καθορισμός των παραμέτρων που επιλέχθηκαν. Ακολουθεί η παρουσίαση της επιρροής της γωνίας πρόσπτωσης του εισερχόμενου κυματισμού, της μέγιστης γωνίας κατευθυντικότητας και της μη γραμμικότητας στην ενίσχυση της κυματικής δράσης στην περιοχή ενδιαφέροντος με την ανάλυση των αποτελεσμάτων και τον σχολιασμό που τα συνοδεύει. Παρατίθενται κατάλληλα οπτικοποιημένες εικόνες για την καλύτερη κατανόηση των αποτελεσμάτων και του σχολιασμού από τον αναγνώστη. Η εργασία αυτή ολοκληρώνεται με τη σύνοψη των συμπερασμάτων για την επιρροή της παρουσίας του κυματοθραύστη και των παραπάνω μεταβαλλόμενων χαρακτηριστικών στην περιοχή που έγινε η μελέτη.

Wind waves are one of the most important phenomena in the marine environment. Understanding wave hydrodynamics and their effects is important for designing marine structures and planning of coastal management. Transformation of wave profile is induced by complex phenomena due to the presence of solid boundaries (e.g. sea bottom, coastal structures). Such physical processes are shoaling, diffraction, refraction, wave breaking, wave-wave interactions, reflection etc. Wiegel studied the effect of diffraction inside the port basin, for different incident wave directions. However, this study did not include random sea bottom and assumed a constant water depth, ignoring refraction and shoaling. In this research we study the effect of combined diffraction and refraction downstream of the breakwater in the region outside the shadow (area A) as shown in the Figure 1, considering a uniformly mild sloping bottom. Numerical model MIKE 21 is used and specifically BW module, based on the Boussinesq equations in order to describe the sea state in the area of interest. The effect of strengthening of wave characteristics is investigated paying attention to the following: • The angle of incident wave, α • The wave directional distribution, θ • The nonlinearity, ε Figure 1 – Grid divided in three sub areas

Theoretical background

In the last 20 years a significant effort was undertaken by various researchers to accurately simulate wave conditions in the offshore region as well as in shallower waters and the surf zone. The Boussinesq-type wave models have proven to be the most accurate ones, especially when dealing with relatively shallow water regions. The most recent of these incorporate highly non-linear wave characteristics and can simulate fully dispersive conditions with great accuracy MIKE 21 BW includes nonlinearity as well as frequency dispersion. Basically, the frequency dispersion is introduced in the momentum equations by taking into account the effect of vertical accelerations on the pressure distribution. The module solves the Boussinesq type equations using a flux-formulation with improved linear dispersion characteristics. These enhanced Boussinesq type equations (originally derived by Madsen et al, 1991, and Madsen and Sørensen, 1992) make the module suitable for simulation of the propagation of directional wave trains travelling from deep to shallow water. The maximum depth to deep-water wave length is h/L0 ≈ 0.5. For the classical Boussinesq equations the maximum depth to deep-water wave length is h/L0 ≈ 0.22. The model has been extended into the surf zone by inclusion of wave breaking and moving shoreline as described in Madsen et al (1997a,b), Sørensen and Sørensen (2001) and Sørensen et al (1998, 2004). The numerical model solves the equations in two horizontal dimensions calculating the surface elevation (ξ) and the depth integrated velocity components (P) and (Q) at each note of the grid. Continuity equation: (1) Momentum equation in x-dimension: (2) (3) Momentum equation in y-dimension: (4) (5) Where the dispersive terms Ψ1 and Ψ2 are given by: (6) (7) Results and analysis The goal of the present study is to examine the influence of the presence of a breakwater under miscellaneous wave scenarios in the area of interest. In Figure 2 and Figure 3 the special distribution of wave heights is depicted without and with the breakwater respectively. All figures presented in this thesis arise by the combination of the previous two, giving Hbw/H. A resulting figure is illustrated in Figure 4. Figure 2 – Wave height Η Figure 3 – Wave height Hbw Figure 4 – Wave height’s ratio Hbw/H A number of cases were tested for simulation of wave propagation. The chosen wave climate refers to regular waves as well as irregular waves for a better representation of real life. Different types of wave characteristics were examined, linear and non-linear, unidirectional and multidirectional with different incident wave angle relative to the coast line. In Figures 5, 6 and 7 representative results are shown for incident wave angle, directionality and non-linearity. Figure 5 – T=7sec, H=0.5m, α=100o, θ=0 9% 16,5% Figure 6 – T=7sec, H=0.5m, α=90ο, θ=30ο Figure 7 – T=7sec, H=1.2m, α=90ο, θ=0 In Figure 5 an incident wave with characteristics T=7sec, H=0.5m, α=100o, θ=0 results to an increase of 17% in the region A, though it doesn’t spread far away from the basin. In the next Figure 6 a wave with almost the same characteristics (a slight difference in wave direction) but with a strong difference in directionality (θ=30ο), gives a peak of 9% increase in the same area followed by a greater spread downstream. Finally, in Figure 7 an initial non-linear incident wave (T=7sec, H=1.2m, α=90ο, θ=0) affects almost the whole downstream numerical domain.

Conclusions

This thesis focuses on the combined effect of diffraction and refraction downstream of the breakwater and outside of its shadow. Numerical simulations have been done considering a number of wave scenarios for two cases of bathymetry (with and without breakwater presence). Afterwards, the ratio Hbw/H is illustrated in the whole grid and for a better inspection of wave conditions the wave steepness (H/L) and the relative water depth (H/d) were calculated. As the angle (α) of the incident wave increases (90o120o) the ratio Hbw/H decreases but remains greater than unity. In contrast with the previous behavior the increase of non-linearity results to greater wave heights downstream in both A and B areas. Finally, the change of directionality seems to behave similar to the change of incident wave’s angle, but with slight differences in ratio Hbw/H.