MATHEMATICAL MODEL OF NON-LINER DISPERSIVE WAVE PROPAGATION IN THE ONSHORE ZONE

A NUMERICAL SOLUTION OF BOUSSINESQ TYPE OF EQUATIONS IS PROPOSED, BASED ON A CENTRAL FINITE DIFFERENCES SCHEME, WITH THIRD ORDER ACCURACY. THE CORRECTION TERMS, FROM TRUNCATION ERRORS, ARE INCLUDED IN THE F.D. INTEGRATION. BY INTRODUCINGA DIFFUSION TERM, TO SIMULATE TURBULENCE, WE PROPOSE AN EXTENSION OF THE BOUSSINESQ EQUATIONS IN THE SURF ZONE. THE EDDY VISCOSITY COEFFICIENT IS CALCULATED FROM THE SOLUTION OF THE TURBULENCE TRANSPORT EQUATION (K-MODEL). BASED ON A POWER SERIES EXPANSION FOR THE DISTRIBUTION OVER THE DEPTH OF THE VERTICAL VELOCITY WE PROPOSE AN EXTENSION OF THE EQUATIONS IN DEEPER WATERS. THE MODEL IS TESTED AGAINST EXPERIMENTAL DATA AND ANALYTICAL SOLUTIONS.Η ΑΡΙΘΜΗΤΙΚΗ ΕΠΙΛΥΣΗ ΤΩΝ ΕΞ BOUSSINESQ, ΠΡΟΤΕΙΝΕΤΑΙ ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ, ΒΑΣΙΣΜΕΝΗ ΣΕ ΕΝΑ ΣΧΗΜΑ ΚΕΝΤΡΙΚΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΔΙΑΦΟΡΩΝ, ΜΕ ΤΡΙΤΗΣ ΤΑΞΕΩΣ ΑΚΡΙΒΕΙΑ. ΣΤΗΝΑΡΙΘΜΗΤΙΚΗ ΟΛΟΚΛΗΡΩΣΗ ΣΥΜΠΕΡΙΛΑΜΒΑΝΟΝΤΑΙ ΚΑΙ ΔΙΟΡΘΩΤΙΚΟΙ ΟΡΟΙ, ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΤΑ ΣΦΑΛΜΑΤΑ ΑΠΟΚΟΠΗΣ. ΕΙΣΑΓΟΝΤΑΣ ΕΝΑΝ ΟΡΟ ΔΙΑΧΥΣΗΣ, ΓΙΑ ΤΗΝ ΠΡΟΣΟΜΟΙΩΣΗ ΤΩΝΤΑΣΕΩΝ REYNOLDS (ΤΥΡΒΗ) ΠΡΟΤΕΙΝΕΤΑΙ Η ΕΠΕΚΤΑΣΗ ΤΟΥ ΜΟΝΤΕΛΟΥ ΣΤΗ ΖΩΝΗ ΘΡΑΥΣΗΣ. Ο ΤΥΡΒΩΔΗΣ ΣΥΝΤΕΛΕΣΤΗΣ ΙΞΩΔΟΥΣ ΥΠΟΛΟΓΙΖΕΤΑΙ ΑΠΟ ΤΗΝ ΕΞΙΣΩΣΗ ΜΕΤΑΦΟΡΑΣ ΤΗΣ ΤΥΡΒΩΔΟΥΣ ΚΙΝΗΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ. ΒΑΣΙΖΟΜΕΝΟΙ ΣΤΗΝ ΑΝΑΠΤΥΞΗ ΣΕ ΣΕΙΡΕΣ ΔΥΝΑΜΕΩΝ ΤΗΣ ΚΑΤΑΝΟΜΗΣ ΩΣ ΠΡΟΣ ΤΟ ΒΑΘΟΣ ΤΗΣ ΚΑΤΑΚΟΡΥΦΗΣ ΤΑΧΥΤΗΤΑΣ ΠΡΟΤΕΙΝΕΤΑΙ Η ΕΠΕΚΤΑΣΗ ΤΩΝ ΕΞΙΣΩΣΕΩΝ ΣΕ ΒΑΘΥΤΕΡΑ ΝΕΡΑ. ΤΟ ΜΟΝΤΕΛΟ ΕΛΕΓΧΕΤΑΙ ΜΕ ΤΗΝ ΣΥΓΚΡΙΣΗ ΜΕ ΠΕΙΡΑΜΑΤΙΚΑ ΔΕΔΟΜΕΝΑ ΚΑΙ ΑΝΑΛΥΤΙΚΕΣ ΛΥΣΕΙΣ

Soft shore protection methods: The use of advanced numerical models in the evaluation of beach nourishment

Beach nourishment is one of the worldwide most common soft shore protection methods. However, the design of these projects is usually based on empirical equations and rules, leaving large margins of error regarding their expected efficiency. In the present work, an advanced wave and sediment transport numerical model is developed and tested in the evaluation of beach nourishment. Non-linear wave transformation in the surf and swash zone is computed by a non-linear breaking wave model based on the higher order Boussinesq equations, for breaking and non-breaking waves. The new Camenen and Larson (2007), transport rate formula for non-cohesive sediments (involving unsteady aspects of the sand transport phenomenon) is adopted for estimating the sheet flow sediment transport rates, as well as the bed load and suspended load over ripples. Suspended sediment transport rate is incorporated by solving the 2DH depth-integrated transport equation. Model results are compared with experimental data of both profile (cross-shore) and planform morphology evolution; the agreement between the two is considered to be quite satisfactory

Assessment of the Role of Nearshore Marine Ecosystems to Mitigate Beach Erosion: The Case of Negril (Jamaica)

Coastal and marine ecosystems are supplying a wide range of services. With accelerated Sea Level Rise, intensification of waves and storm surge severity and increasing anthropogenic pressures, these areas are under multiple threats and society may not receive the same level of ecosystems services. This study aims at measuring the trend of beach erosion and at identifying and quantifying the role of some coastal and marine ecosystems in mitigating beach erosion in the region of Negril (Jamaica). In this location, the tourism industry provides the main source of economic revenue. Even at the national level, the two beaches are important assets linked with 5% of the national revenue as 25% of the hotel rooms are located around Negril. In Jamaica, the tourism industry is a significant component of national GDP. 25% of hotel rooms are located around the two beaches of Negril, which have lost an average of 23.4 m of width since 1968. Given the importance of Negril’s beaches to their economy, the Government of Jamaica asked UNEP to conduct a study to identify causes of beach erosion in Negril and potential solutions to address trends of beach erosion, in the context of future sea level rise scenarios induced by climate change. This paper addresses the current beach erosion status and future trends under different climate scenarios. We explain how, by using remote sensing, GIS, wave modelling and multiple regressions analysis associated with national, local and community consultations, we were able to identify and quantify the role of ecosystems for mitigating beach erosion. We show that larger widths of coral and seagrass meadows reduce beach erosion.</p

Coral reef structural complexity loss exposes coastlines to waves

Coral reefs offer natural coastal protection by attenuating incoming waves. Here we combine unique coral disturbance-recovery observations with hydrodynamic models to quantify how structural complexity dissipates incoming wave energy. We find that if the structural complexity of healthy coral reefs conditions is halved, extreme wave run-up heights that occur once in a 100-years will become 50 times more frequent, threatening reef-backed coastal communities with increased waves, erosion, and flooding

Coral reef structural complexity loss exposes coastlines to waves

Abstract Coral reefs offer natural coastal protection by attenuating incoming waves. Here we combine unique coral disturbance-recovery observations with hydrodynamic models to quantify how structural complexity dissipates incoming wave energy. We find that if the structural complexity of healthy coral reefs conditions is halved, extreme wave run-up heights that occur once in a 100-years will become 50 times more frequent, threatening reef-backed coastal communities with increased waves, erosion, and flooding

Coral reef structural complexity loss exposes coastlines to waves

Coral reefs offer natural coastal protection by attenuating incoming waves. Here we combine unique coral disturbance-recovery observations with hydrodynamic models to quantify how structural complexity dissipates incoming wave energy. We find that if the structural complexity of healthy coral reefs conditions is halved, extreme wave run-up heights that occur once in a 100-years will become 50 times more frequent, threatening reef-backed coastal communities with increased waves, erosion, and flooding