Diffusion Model of Sedimentation from Turbulent Flow
Most interpretations on the origin of sedimentary rocks are based on the calculation of a few distribution moments of grain- size measurements. All information about the sedimentary environment contained in the granulometric spectrum is not completely used. Utilization of all information is possible only with a model describing grain-size distribution in the formation mechanism. The problem of construction of an adequate sedimentation model is separated into three principal parts: erosion, transportation and sediment deposition. Turbulent flow theory, flume experiments and river hydrologic data permit the creation of a corresponding mathematical model.
The erosion of bottom material by flow with normally distributed instantaneous velocities and pressures corresponds to the point-source diffusion scheme. Particle fall velocity of suspended material is in proportion to the probability of the moment velocities to exceed the turbulent intensity.
All three types of the particle transportation (rolling, saltation and moving in suspended state) are the result of the single chance-wanderment mechanism and are described by the limit form of diffusion in the gravity field.
The fall-velocities distribution obtained coincides with the A. Einstein’s “sedimentary distribution”. The particle leap height distribution is obtained in the same manner. Settling of suspended sediment is determined by the law of turbulent intensity change. Sediment particle fall-velocity distribution is determined by the form of this law and parameters of “sedimentary distribution”.
A general model operator transforming the particle fall-velocity distribution of the material washed into the distribution of the settled particles has a composite form even for the simple example. So the parameter estimation is accomplished by minimizing the mean square difference using any suitable method.
The suggested model is in good agreement with the vertical particle distribution observed in flume experiments and natural rivers. Settled sediment in the flows investigated has the same concordance. Thus, the approach may give a new tool for the re-construction of some depositional environment characteristics.
KeywordsSuspended Material Sedimentary Distribution Fall Velocity Flume Experiment Turbulent Diffusion Coefficient
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