Waves and currents over a fixed rippled bed: 3. Bottom and apparent roughness for spectral waves and currents

Abstract

Abstract. This paper is the third in a series of three that presents the results of experiments designed to verify the use of a single bottom roughness length scale for waves and currents over a rough bed. While the first two papers concentrated on the bottom roughnesses experienced by monochromatic wave and current boundary layer flows, this paper presents the results of additional experiments that investigate the use of an equivalent wave representation to extend these results to spectral wave and current boundary layer flows. Spectral waves, simulated by five components, and currents were generated in a 20-m-long wave flume with a fixed rippled bottom. Attenuation due to bottom friction is determined from total attenuation measurements for individual wave components by removing the effects of sidewall dissipation and wave-wave interactions. These attenuation estimates are used to establish representative friction factors, which are used in conjunction with an existing eddy viscosity model to determine bottom roughnesses. The bottom roughnesses experienced by spectral waves (in the presence and absence of a current) match the bottom roughnesses for monochromatic waves. When these experimentally determined bottom roughnesses are used in conjunction with the eddy viscosity model, predictions of attenuation for individual wave components closely match measurements. When the wave boundary layer thickness is defined to be the height at which the predicted velocity deficit in the wave boundary layer is within 5% of the free stream velocity, excellent agreement is obtained between predicted and measured velocity profiles for currents in the presence of codirectional waves. Therefore these experiments show that a single bottom roughness, when used in conjunction with an equivalent wave representation, adequately characterizes both monochromatic and spectral wave-current boundary layer flows over a fixed rippled bed. IntroductionFluid velocities in bottom boundary layers play a significant role in defining circulation and sediment transport in coastal regions. Accordingly, numerous investigators have developed models to predict velocity distributions in bottom boundary layers for waves and currents. The most widely used models achieve turbulence closure using an eddy viscosity because of the simplicity and utility of this approach. To scale the eddy viscosity near the bottom, most eddy viscosity models use a time-invariant shear velocity for a velocity scale and the distance from the bed for the length scale. Examples of these eddy viscosity models include the models of Lundgren [1972] [1985], and Grant and Madsen [1979, 1986]. In particular, the model of Grant and Madsen [1979, 1986]

Spatial and seasonal variation in wave attenuation overZostera noltii

“…Moreover, Madsen's [1994] relationship between friction factor and bed roughness is based on the assumption that k N is independent of ambient hydrodynamic conditions. This assumption has been validated for fixed beds in laboratory studies [Mathisen and Madsen, 1999 [Méndez and Losada, 2004;Méndez et al, 1999]. To reduce the impact of this effect on the present analysis, all instruments were placed inside the meadow, at least 100 m away from its leading and trailing edge.…”

“…While a current is likely to cause bending of the flexible vegetation leaves, it is not known in detail how the current affects sea grass. Additionally, experiments over fixed beds showed that k N is bed specific and is not affected by changing hydrodynamic conditions [Mathisen and Madsen, 1999]. Equation (18) should therefore yield a good first approximation, especially as values of C m are generally close to unity [Madsen, 1994].…”

Bottom friction and bedload sediment transport caused by boundary layer streaming beneath random waves

“…Previous studies of bottom friction beneath random waves have been undertaken by Madsen [10][11][12][13][14][15][16][17][18][19] as well as Myrhaug and Holmedal [20][21][22]. Madsen [10] gave explicit wave friction factor formulas for spectral wave-current boundary layer flow.…”

Structure of the Wave Bottom Boundary Layer over Smooth and Rough Bottoms

“…Mathisen and Madsen [31][32][33] presented some results of the experimental investigation of the WBBL in the presence and in the absence of a constant current. It was shown that a sole scale of bottom irregularities can be used to characterize the state of the boundary layer and, moreover, that this scale remains invariable both in the presence and in the absence of a constant current.…”

“…The results of laboratory and in-situ experiments carried out with an aim of investigation of the structure of nonstationary (fluctuating and wave) bottom boundary layers over smooth and rough bottoms are described in [15,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Numerous works are devoted to the analysis of the conditions of development of turbulence and its characteristics in bottom boundary layers (see, e.g., [18,36]).…”