We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes