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**10**

*Portugal* 

**Turbulent Boundary Layer Models:** 

Shallow coastal areas are extremely dynamic regions where the fluid motions associated with both surface waves and currents interact with the bottom sediments. The prediction of the wave effects on sediment transport in shallow water conditions and in intermediate depth is still frequently restricted to monochromatic and unidirectional wave models. However, in real shallow water conditions, the nonlinear process of sediment transport responds in a rather different way to the idealized regular wave case. Therefore, in these regions, both the wave non-linearity and the wave-current interaction become important factors to be considered. Forecasts of morphological changes are invariably dependent on the correct prediction of the sand transport rate under the action of waves and currents, which requires accurate estimation of the friction at bed level, considering all resulting complex interactions effects in its entirety. A major consequence of the fluid dynamics resulting from the combined wave and current motions is the response of the movable seabed, which is significantly altered from that expected for a linear superposition of a pure wave motion with a pure current. In recent years, various attempts have been made to improve the state of knowledge of the flow in the bottom boundary layer regarding the wave non-linearity and complex wave-current effects on the sand-transport rate, using theoretical models. The erosion and sediment transport estimation around usual structures in the fluvial and coastal environment, like bridge piers, groynes and breakwaters, are of a major concern for designing these structures and for considering preventive measures. After a brief discussion on turbulence, the following sections present mathematical and numerical approaches of different complexity. Starting by the fundamental equations of the Fluid Mechanics, a complex unresolved formulation without further assumptions is obtained. Afterwards, considering some physical hypotheses, practical models of different complexity

are shown, followed by simple parametric approaches and applications.

Turbulence has been a long standing challenge for human mind. Five centuries after the first studies of Leonardo da Vinci, understanding turbulence continues to attract a great deal of attention. This may be due to its fascinating complexity and ubiquitous presence in a variety of flows in nature and engineering. The first turbulence references by Leonardo da Vinci are based on visual observations. In 1883, Osborne Reynolds introduced the concept of

**1. Introduction** 

**2. Turbulence** 

 **Theory and Applications** 

José Simão Antunes do Carmo

*University of Coimbra* 

