Logarithmic velocity structure in the deep hypolimnetic waters of Lake Michigan

Abstract

The characteristics of the bottom boundary layer are reported from a Lake Michigan field study carried out in deep hypolimnetic waters (55 m depth) during the stratified period (June-September 2012). The sandy substrate at the measurement site was densely covered with invasive quagga mussels (mean size: 1.6 cm; mean density: 10,000 mussels m-2). The measurements reveal a sluggish, compact bottom boundary layer, with flow speeds at 1 mab less than 5 cm s-1 for most of the period, and a dominance of subinertial energy. A downwelling event caused the largest currents observed during the deployment (10 cm s-1 at 1 mab) and a logarithmic layer thickness of 15 m. In spite of the weak flow, logarithmic profile fitting carried out on high-resolution, near-bed velocity profiles show consistent logarithmic structure (90% of profiles). Flow was dominated by subinertial energy but strong modified by near-inertial waves. Fitted drag coefficients and roughness values are = 0.004 and = 0.12 cm, respectively. These values increase with decreasing flow speed, but approach canonical values for 1 mab flow speeds exceeding 4 cm s-1. The estimated vertical extent of the logarithmic region was compact, with a mean value of 1.2 m and temporal variation that is reasonably described by Ekman scaling, 0.07/, and the estimated overall Ekman layer thickness was generally less than 10 m. Near-bed dissipation rates inferred from the law of the wall were 10-8-10-7 W kg-1 and turbulent diffusivities were 10-4-10-3 m2s-1. Key Points: Over 90% of near-bottom velocity profiles are logarithmic with median 1 m flow speed of 2.7 cm/s Fitted 1 m drag coefficient is 0.004 with hydrodynamic roughness of 0.12 cm The logarithmic layer thickness agrees with Ekman scaling and is found to be 0.07 u/f.