MEGHANISM OF RIPPLE FORMATION ON GRANULAR BED

Abstract

The plane granular bed when subjected to shear under fluid flow, usually starts moulding in statistically regular bed formations generally called 'ripples'. However, there are certain flow conditions in which it remains plane and does not deform. The mechanics of such ripple formation has been studied by a number of workers, usually varying grain properties and flow conditions. The effect of variation of liquid properties has not received much attention so far. In the present study different bed materials and liquids of different viscosities were used to explore and answer the following two basic questions:- 1, 'What physical factors cause a mobile plane bed to become unstable for certain grain sizes while a flat bed remains stable under similar flow conditions for grains above a certain size? 2. For the same granular material, v/hat are the flow conditions under which ripples form and under 'what conditions can a flat bed remain stable? What are the phyeioal factors causing instability of flow? In the present series of experiments five different sands were used. All sands except No.2 sand were of uniform size. The median diameter, d50, varied from 0.25 mm to 1 mm. Water, glycerine-water mixtures and lubricating oil-kerosine mixtures v/ere used to get a wide range of viscosity. The viscosity was varied upto 6 times that of water by proper proportioning of the mixtures. Each run was continued till steady state was reached and relevant data was collected. It was observed during the course of experimentation that viscosity Inhibits .rippling for smaller grain size material whereas it promotes rippling for bigger grains. Under liquids more viscous than v/ater, bed consisting of 0.72 and 1 mm grain size was found to ripple prominently and the pattern was quite similar to that of finer material under water. This phenomenon j does not seem to have been reported earlier in literature on the subject. In the light of this data, the causes of rippling given by earlier workers were examined. It is shown in Chapter V that neither Bagnold's nor Liu's criterion for rippling holds good. The Froude number appears to be an important parameter to separate rippling and non-rippling zones. It was further observed from the data that the shear stress at the bed does not have a significant influence on rippling, except in so far as it initiates the grain movement. Rippling was found to depend upon the properties of bed material and liquid besides flow conditions. Hence by dimensional 1/2 3/2 analysis a parameter, I i.— , depending upon the properties of bed material and liquid was obtained. The whole data was plotted l/2 "^/p on •Fr» g a plane0 It was found to separate out the rippling and non-rippling zones remarkably well. Kennedy has theoretically shown that rippling should depend upon Froude number and a dimensionless parameter j. He arbitrarily defines j as a function of depth, velocity of flow and properties of sand and fluid. He did not however give a precise combination of these variables to define j, nor did he indicate actual values of j in term of these variables. The author has correlated g1/^5/2 to Kennedy's j by the following equation; ' , 1/2 d3/2 3 = - 3.7 log ( fa f ) + 6#4 y With this correlation, the initiation of rippling is explainable in terms of Kennedy's theory. The present study provides a criterion which separates out rippling and non-rippling zones for the author's as well as earlier data. This work is a step forward towards the solution of the problem of 'Mechanism of ripple formation on granular bed' and suggests a new approach for further research in the field.