text: In addition to the filtered mass and momentum equations, filtering the kinetic energy equation can provide additional insight.  The kinetic energy field can be filtered to yield the total filtered kinetic energy:
  and the total filtered kinetic energy can be decomposed into two terms: the kinetic energy of the filtered velocity field ,
  and the residual kinetic energy ,
  such that .
  The conservation equation for  can be obtained by multiplying the filtered momentum transport equation by  to yield:
  where  is the dissipation of kinetic energy of the filtered velocity field by viscous stress, and  represents the sub-filter scale (SFS) dissipation of kinetic energy.
  The terms on the left-hand side represent transport, and the terms on the right-hand side are sink terms that dissipate kinetic energy.
  The  SFS dissipation term is of particular interest, since it represents the transfer of energy from large resolved scales to small unresolved scales.  On average,  transfers energy from large to small scales.  However, instantaneously  can be positive or negative, meaning it can also act as a source term for , the kinetic energy of the filtered velocity field.  The transfer of energy from unresolved to resolved scales is called backscatter (and likewise the transfer of energy from resolved to unresolved scales is called forward-scatter).