A new class of forced, self-similar turbulence is proposed. This class is simply related to all other known self-similar turbulent flows. In unforced turbulence, the large-scale vortex rotation period is essentially equal to the vortex age, a direct consequence of dimensional analysis. As the vortex ages, it entrains irrotational fluid or fluid of opposite sign vorticity and hence rotates more slowly. For exponentially forced turbulence, with a constant e-folding time, the rotation period of the vortex is a constant, the imposed e-folding time. The entrainment rate is correspondingly reduced. A third case is called super-exponential forcing, where the e-folding time is itself a function of time. If the e-folding time declines linearly with time, then a self-similar flow is achieved, in which the vortex rotation period declines by a constant fraction at each rotation. This super-exponential flow is the mirror image of unforced turbulence, where the rotation period increases by a constant fraction at each rotation. As a consequence, it is predicted to have special characteristics, such as a small entrainment rate. This flow may be important in geo- and astrophysics as well as in inertial-confinement fusion.
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