Strain-coupled one-dimensional turbulence for rapid distortion

Abstract

The distortion of turbulence by mean strain - through component amplification, pressure-mediated redistribution and spectral rescaling - is central to flows ranging from wind-tunnel contractions to stagnation regions near lifting surfaces. Capturing this process economically remains difficult: scale-resolving simulation is expensive, linear rapid-distortion theory omits nonlinear relaxation over finite strain, and second-moment closures discard spectral information. We present a strain-coupled formulation of one-dimensional turbulence (ODT) that evolves strained turbulence with one-dimensional scale resolution at low computational cost. Mean-strain production is imposed as a continuous forcing of the line velocity, the rapid pressure-strain contribution is introduced as an energy-conserving redistribution operator consistent with homogeneous rapid-distortion theory, and scale compression is represented by dilatation of the ODT domain. The model predicts a broadband distorted spectrum that departs from the rigid spectral translation of linear theory at a strain-to-turbulence ratio of approximately 0.8, where rapid distortion and nonlinear eddy dynamics are both active. Under axisymmetry of the undistorted turbulence about the ODT line, the nonlocal three-dimensional rapid pressure-strain integral reduces to a closed single-line functional. The formulation reproduces rapid-distortion theory at onset and quantitatively captures the Reynolds-stress anisotropy trends of Lee and Reynolds (1985).