Determination of Stresses at the Bed of a Shallow River

Advances in satellite remote sensing of rivers have made it possible to obtain detailed geometric variations of the riverbed. Such details are important for the study of near-bed flow. This paper uses a 200-m reach of the Nicolet River in Quebec, Canada as an example to demonstrate the usefulness of remote sensing data to the study of near-bed flow. For this river, there has been a threat of declining biodiversity and fish population. Also, floods are frequent, especially during the spring. The focus of this paper is on determining form drag and skin stress at a locally uneven riverbed. The drag plays a significant role in the prediction of sediment transport, channel erosion, and morphological change. The specific objectives of this paper are: (a) to develop an analytical function that describes the local variations in bed level along the thalweg, using satellite images as input, and (b) to calculate the form drag and surface drag. This paper uses multispectral WorldView-3 (WV-3) satellite images of 1.2 × 1.2 m pixel resolution to derive the local protrusions of bed level. These protrusions are considered as macro-scale bed roughness elements. The calculation methods divide the stresses on an element into surface and form components. The results show 73 roughness elements in the 200-m river reach. Although they differ in size, they can be fitted to a Gaussian function. The drag coefficient, CD, for each of the Gaussian elements is only dependent on shape parameters. Values of CD for roughness elements range from nearly zero to 0.6. A criterion is proposed to exclude small (or smooth) elements in drag calculations. For flow over roughness elements, there is a distinction between an internal boundary layer, a wake, and an outer boundary layer. Calculations of the total boundary shear stress over roughness elements require total roughness heights. The total boundary shear stress along the river reaches a maximum value of 55 N/m2. The results from this study are useful for a further investigation of sediment transport and erosion. The methods discussed are new contributions, more efficient and less expensive than field measurements of flow velocities for estimates of riverbed shear stress.