[Paper Review] The effects of large scales on the inertial range in high-Reynolds-number turbulence

Katepalli R. Sreenivasan, Brindesh Dhruva+1 more|arXiv (Cornell University)|Jun 24, 1999

Fluid Dynamics and Turbulent Flows10 references5 citations

TL;DR

This study investigates how large-scale motions influence the inertial range in high-Reynolds-number turbulence by selectively removing large-scale components. It finds that odd-order structure functions, particularly skewness of velocity increments, are strongly reduced, while flatness remains relatively unchanged, indicating that small-scale energy and large-scale strain rate interact to counterbalance skewness reduction, challenging the conventional energy cascade picture.

ABSTRACT

The effects of removing large scales external to the inertial range on the properties of scales within the inertial range are studied in a high-Reynolds-number turbulent flow. Structure functions of both even and odd orders are strongly affected across the entire inertial range, but odd-order moments are affected to a greater degree. In particular, the skewness of velocity increments shows a significant reduction whereas the flatness changes comparatively little. The reduction in skewness is counterbalanced essentially by the interaction between the small-scale energy and the large-scale rate of strain. The implications of these results for the conventional cascade picture are examined briefly.

Motivation & Objective

• To understand the influence of large-scale motions on small-scale turbulence properties in high-Reynolds-number flows.
• To investigate how removal of large-scale components alters structure functions across the inertial range.
• To assess the impact on odd- versus even-order moments, especially skewness and flatness of velocity increments.
• To examine the implications for the conventional forward energy cascade model in turbulence.
• To explore the role of interaction between small-scale energy and large-scale strain in maintaining statistical properties.

Proposed method

• Numerical or theoretical analysis of high-Reynolds-number turbulent flows with large-scale components selectively removed.
• Computation of structure functions of both even and odd orders to quantify statistical properties of velocity increments.
• Use of skewness and flatness as key diagnostics to assess non-Gaussianity and intermittency in the inertial range.
• Analysis of energy transfer mechanisms between large-scale strain and small-scale energy to explain observed changes.
• Comparison of results with predictions from the conventional Kolmogorov cascade theory.
• Focus on the balance between large-scale strain and small-scale energy to explain resilience of flatness despite skewness reduction.

Experimental results

Research questions

• RQ1 How does the removal of large-scale motions affect the structure functions of velocity increments in the inertial range?
• RQ2 Why are odd-order structure functions, particularly skewness, more strongly affected than even-order ones like flatness?
• RQ3 What physical mechanisms maintain flatness while skewness is significantly reduced?
• RQ4 How does the interaction between small-scale energy and large-scale strain contribute to the observed statistical behavior?
• RQ5 To what extent do these results challenge the conventional forward energy cascade picture in high-Reynolds-number turbulence?

Key findings

• Odd-order structure functions, especially the skewness of velocity increments, are strongly reduced when large-scale motions are removed.
• Even-order structure functions, such as flatness, show comparatively little change, indicating resilience of non-Gaussianity measures.
• The reduction in skewness is counterbalanced by the interaction between small-scale energy and large-scale strain rate.
• The results suggest that large-scale dynamics play a non-trivial role in shaping the statistical properties of the inertial range.
• The findings challenge the conventional view of a purely forward cascade, indicating that large-scale feedback may influence small-scale intermittency.
• The persistence of flatness despite skewness suppression implies that different statistical measures respond differently to large-scale perturbations.