Turbulent Currents in the Presence of Waves

Several theoretical models have been advanced for turbulent boundary layers associated with wave and current flows over a rough bed. Although these models differ, particularly in the sophistication with which turbulence is modeled, they all share one common feature: the bottom roughness is characterized by a single roughness length scale kn. However, no experimental data have been presented which accurately characterize the bottom roughnesses for wave and current boundary layers such that this basic assumption can be considered verified. This paper and a companion paper [Mathisen and Madsen, this issue] present results of an experimental study to verify this basic assumption. In this paper, wave roughnesses (i.e., bottom roughnesses experienced by pure waves and waves in the presence of a current) are compared with the roughness experienced by a pure current. The roughnesses for pure currents and pure waves are shown to be the same if determination of the pure wave roughness from measurements of wave energy dissipation includes the phase difference between the near-bottom horizontal orbital velocity and bottom shear stress. When these analysis procedures are extended to combined wavecurrent flows, the roughness experienced by waves in the presence of a current is shown to be that obtained for pure waves. 16,533 16,534 MATHISEN AND MADSEN: BOTTOM ROUGHNESS FOR WAVES

Section: Bottom Boundary Layers For Waves and Currentsmentioning

confidence: 99%

Waves and currents over a fixed rippled bed: 1. Bottom roughness experienced by waves in the presence and absence of currents

Mathisen¹,

Madsen²

1996

“…Temporal variation of the eddy viscosity also has possible importance in the related problem of interaction between a turbulent wave boundary layer and a steady turbulent current driven, for example, by an imposed pressure gradient or wind stress at the water surface. The case in which wave nonlinearity can be neglected was treated theoretically, based on time-invariant eddy viscosity models, by Lundgren [1972] and then in a more consistent manner by Smith [1977] and Grant and Madsen [1979]. If the steady component of the bed shear stress is regarded as given, these studies show that the effect of the turbulent wave boundary layer is to retard the near-bottom steady current.…”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

Turbulent wave boundary layers: 2. Second‐order theory and mass transport

Trowbridge¹,

Madsen²

1984

131

104

The solution for the turbulent near‐bottom boundary layer produced by a progressive wave train is advanced to second order in wave steepness. As in the first‐order analysis (part 1) the effective viscosity is assumed to be the product of a vertical length scale and the first few Fourier components of a shear velocity based on the instantaneous, local bed shear stress. An analytical solution for the second‐order flow field is obtained, with attention directed primarily toward the second‐order, wave‐induced steady current or mass transport. The mass transport is found to depend critically on temporal variation of the effective viscosity. The most dramatic result of the analysis is a predicted reversal of the mass transport produced by relatively long waves. This result, for which supporting experimental evidence is presented, has not been predicted previously and cannot be obtained by a time‐invariant eddy viscosity model. Implications of the present results for related problems are discussed.

“…The change of mean current velocity profile due to the superposition of waves has been theoretically investigated over the last two decades, and several models have been presented [Lundgren, 1972;Smith, 1977 …”

Section: Apparent Roughness Heightmentioning

confidence: 99%

Vertical profiles of longshore currents and related bed shear stress and bottom roughness

Faria¹,

Thornton²,

Stanton³

et al. 1998

115

Abstract. The vertical structure of the mean wave-driven longshore current over a barred beach is examined on three strong current days during the DUCK94 experiment, and it is found that the bottom boundary layer is well described by a logarithmic profile (mean correlation coefficient for all 22 profiles, 0.98). The logarithmic profile fits better in the trough, where turbulent bottom boundary layer processes predominate, than over the bar, where breaking-wave-induced turbulence generated at the surface modifies the profile. The surface layer in the presence of waves is well described by adjusting the logarithmic profile for the intermittent presence of water and adding the alongshore component of the mass transport velocity (slope of the least squares linear regression between model predictions and observations, 1.005 and root-mean-square (rms) error of 7%). Bed shear stresses calculated from logarithmic velocity profiles are equated to a quadratic bottom shear stress formulation. The associated bed shear stress coefficients vary by more than an order of magnitude across the surf zone (0.0006-0.012). Bottom roughness was measured throughout the nearshore using a sonic altimeter mounted on a moving platform. The bed shear stress coefficients are positively correlated with bottom roughness (linear correlation coefficient, 0.6). A higher linear correlation coefficient (0.8) is obtained by subtracting skin friction from the total bed shear stress.