Evaluating the von K?rm?n Constant in Sediment-laden Air Flow

Abstract

Shear velocity is a critical variable used in many hydrodynamic and aeolian applications. The Law of the Wall is commonly used to derive shear velocity as the product of the slope of a measured velocity profile and the von K?rm?n constant, ? = 0.4. However, a number of hydrodynamic experiments show that there is a substantial apparent decrease of ? in sediment-laden flow, which was explained by: 1) The energy loss to support the sediment particle suspension in the fluid and 2) The buoyancy effect due to stratification. The energy loss is associated with sediment concentration and grain size, and the stratification can be characterized by sedimentological flux Richardson number or gradient Richardson number. Since there is an apparent change of ?, the term ?apparent von K?rm?n parameter?, or ?a, was adopted from Wright and Parker to replace ? in sediment-laden flow. There has been no study to attempt to detect and to evaluate the variability of ?a during aeolian saltation, which is the purpose of this dissertation research. Two ?clear air? runs and fifteen ?sediment-laden? runs were conducted at the northeast coast of Brazil. Wind profile data were collected by a stack of cup anemometers; ?true? shear velocity was estimated by an ultrasonic anemometer; and sediment mass flux profile and grain size were estimated from the sand samples collected in a stack of vertical hose-style traps. With these estimates, ?a, sediment concentration and sedimentlogical Richardson numbers were derived. Regression analysis indicates that there is a statistically insignificant relationship between ?a and grain size, which may be caused by small range of grain size in the study site. However, there is strong statistical relationship between ?a and bulk, volumetric concentration below 25 mm, S25, and between ?a and sediment transport rate Q (kg/m/s) as: ka = -2088.4S25 0.3964 and ka = -3.134Q 0.4011 A strong relationship was also found between ?a and sedimentological Richardson numbers in the lower saltation layer, which can be well explained by the stratification theory.