Forced-dissipative two-dimensional turbulence: A scaling regime controlled by drag

YK Tsang, WR Young - Physical Review E—Statistical, Nonlinear, and Soft …, 2009 - APS
Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 2009APS
We consider two-dimensional turbulence driven by a steady prescribed sinusoidal body
force working at an average rate ε. Energy dissipation is due mainly to drag, which damps all
wave number at a rate μ. Simulations at statistical equilibrium reveal a scaling regime in
which ε∝ μ 1/3, with no significant dependence of ε on hyperviscosity, domain size, or
numerical resolution. This power-law scaling is explained by a crude closure argument that
identifies advection by the energetic large-scale eddies as the crucial process that limits ε by …
We consider two-dimensional turbulence driven by a steady prescribed sinusoidal body force working at an average rate . Energy dissipation is due mainly to drag, which damps all wave number at a rate . Simulations at statistical equilibrium reveal a scaling regime in which , with no significant dependence of on hyperviscosity, domain size, or numerical resolution. This power-law scaling is explained by a crude closure argument that identifies advection by the energetic large-scale eddies as the crucial process that limits by disrupting the phase relation between the body force and fluid velocity. The average input is due mainly to spatial regions in which the large-scale velocity is much less than the root-mean-square velocity. We argue that characterizes energy injection by a steady or slowly changing spectrally confined body force.
American Physical Society
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