Double-diffusive Sedimentation

Dr. Eckart Meiburg
Professor
Department of Mechanical Engineering
UC Santa Barbara

When a layer of particle-laden fresh water is placed above clear, saline water, both double-diffusive and Rayleigh-Taylor  instabilities may arise.  We investigate the nonlinear dynamics of  these  processes  by  means of two- and  three-dimensional  direct  numerical  simulations.

The  simulations  show  that  the  presence  of  particles  with  a  Stokes  settling  velocity  modifies  the traditional double-diffusive fingering by creating an unstable `nose region' in the horizontally averaged profiles,  located  between  the  upward  moving  salinity  and  the  downward  moving  sediment  interface. The ratio of nose height to salinity interface thickness initially grows and then  plateaus, at a  value that is    determined  by  the  balance    between  the  flux  of  sediment  into  the  rose  region  from  above,  the double-diffusive/Rayleigh-Taylor  flux  out  of  the  nose  region  below,  and  the  rate  of  sediment accumulation  within  the  nose  region.  For  small  values  of  this  ratio,  double-diffusive  fingering dominates, while for larger values the sediment and salinity  interfaces become  increasingly separated in space  and the dominant instability mode becomes Rayleigh-Taylor-like. A scaling analysis based on the results of a parametric study indicates  that the ratio  is a linear  function of a single  dimensionless grouping. The  simulation  results  furthermore  indicate  that   double-diffusive and  Rayleigh-Taylor instability  mechanisms cause the effective  settling velocity of the sediment to scale with the overall buoyancy  velocity  of the  system,    which  can  be  orders   of  magnitude  larger   than the  Stokes  settling velocity.

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