An inverse energy cascade in two-dimensional low Reynolds number bubbly flows

Abstract

The correct representation of depth-induced wave breaking is important for understanding coastal morphology and for design and management in the coastal zone. Although numerous studies have demonstrated the applicability of a constant scaling of the Battjes and Janssen (1978) dissipation model for depth-induced breaking, recent studies have shown its inability to sufficiently reproduce wave dissipation over complex field cases. In the present study, we contrast the application of such a constant scaling to two alternative wave breaking parameterizations with a variable scaling based on either the wave nonlinearity (the φ parameterization) or on both bottom slope and normalized wavelength supplemented with wave directionality (the β−kd parameterization). We consider three field data sets characteristic of a simple beach-bar profile, a bay partially protected by a shoal and a complex intertidal region. We demonstrate that in these cases the β−kd parameterization provides a better alternative to the use of a constant scaling or the φ parameterization. To illustrate the operational consequences, we up-scale the conditions over the case of the intertidal region to correspond to design conditions for the Dutch coast (storm conditions with a 4000 year return period). Under these extreme conditions, for locally generated waves both the β−kd and φ parameterizations predict qualitatively similar increased significant wave heights but the β−kd parameterization increased the waves twice as much as the φ parameterization. Under other conditions, when non-locally generated waves (swell) dissipates over a gently sloping bottom, the β−kd parameterization predicts lower significant wave heights compared to either the constant scaling or φ parameterization.