Overview
This research examines turbulent dissipation within a von Karman flow, differentiating between bulk and wall dynamics. The investigation employs both Particle Image Velocimetry (PIV) and Diffusing Wave Spectroscopy measurements to provide a direct comparison of these two regions. A key focus is on the excess dissipation observed at the wall and its statistical properties, particularly its departure from log-normality, in contrast to the bulk's behavior.
Research Context
The study addresses the dissipative characteristics of turbulent flows, specifically within a von Karman geometry. This type of flow is a canonical system for studying turbulence. The concept of dissipative anomaly, where energy dissipation remains finite even as viscosity tends to zero, is a central theme for bulk dynamics. For wall dynamics, the research explores the implications of velocity-gradient dominated scaling on dissipation. Statistical descriptions of turbulence, such as log-normality and its variance (e.g., in the context of K62 refined similarity), provide a framework for analyzing the distribution of turbulent dissipation events.
Approach
The research utilized two primary experimental techniques: PIV (Particle Image Velocimetry) and Diffusing Wave Spectroscopy. These methods allowed for the direct measurement of turbulent dissipation in both the bulk and wall regions of a von Karman flow. The study characterized dissipation by analyzing its intensity bands, particularly focusing on events exceeding 10 times the mean intensity. The skin-friction coefficient was inferred from these measurements. Statistical analysis of the dissipation data focused on assessing log-normality and its variance across different Reynolds numbers (Re).
Findings
- Bulk dissipation in the von Karman flow conforms to the dissipative anomaly.
- Wall dissipation exhibits a clear excess compared to bulk dissipation. This excess increases with the Reynolds number (Re).
- The observed excess in wall dissipation is consistent with velocity-gradient dominated scaling.
- Decomposition of dissipation into intensity bands revealed that the wall dissipation excess is primarily driven by a progressive redistribution towards high-intensity events, specifically those larger than 10 times the mean. This redistribution intensifies as Re increases.
- The inferred skin-friction coefficient exhibited a decreasing trend with Re, which is fairly consistent with classical power-law behavior, despite the observed increase in dissipation.
- Statistically, the wall region showed strong departures from log-normality at low Re. This departure diminished as Re increased.
- The diminishing departure from log-normality at the wall with increasing Re reflects an increase in the effective dimensionality of the near-wall gradient field.
- In contrast, the bulk dissipation remained near log-normal across all investigated Re.
- The log-dissipation variance in the bulk showed a slow growth across the range of Re studies, consistent with K62 refined similarity.
- These results suggest distinct origins for log-normal behavior: multiplicative cascade dynamics in the bulk versus a combined effect of persistent shear and a superposition of an increasing number of independent gradient contributions at the wall.
Why This Matters
The differentiation between bulk and wall dissipation mechanisms and their distinct statistical behaviors contributes to a more nuanced understanding of turbulence. Recognizing that wall dissipation is increasingly dominated by spatially localized, high-intensity events as Reynolds number rises, while bulk dissipation maintains log-normality, provides insight into the complex nature of energy transfer in boundary layers. This distinction informs theoretical models aiming to describe the statistical properties of turbulent flows more accurately.