Compressor Cascade Optimization based on Inverse Boundary Layer Method and Inverse Cascade Method : 1st Report, An Inverse Cascade Method for Incompressible Two-dimensional Potential Flow

On the edge of an inverse cascade.

We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the comput...

The Inverse Energy Cascade of Two-Dimensional Turbulence

Inverse cascade regime in shell models of two-dimensional turbulence.

We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium st...

Nonrobustness of the two-dimensional turbulent inverse cascade.

The inverse energy cascade in two-dimensional Navier-Stokes turbulence is examined in the quasisteady regime, with small-scale, band-limited forcing at scale kf-1, with particular attention to the influence of forcing Reynolds number Re on the energy distribution at large scales. The strength of the inverse energy cascade, or fraction of energy input that is transferred to larger scales, increa...

Field theory of the inverse cascade in two-dimensional turbulence.

A two-dimensional fluid, stirred at high wave numbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid's long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wave numbers, one expects a stationary invers...