Turbulence Structure and Energy Transfer Below a Free Surface in Homogeneous Flows

Основные понятия

The free surface profoundly transforms the nature of the turbulence in its immediate proximity, altering the inter-scale energy transfer and the structure of upwellings and downwellings.

Аннотация

The study investigates the turbulence structure and energy transport in space and across scales below a quasi-flat free surface. The authors leverage a large zero-mean-flow tank where homogeneous turbulence is generated by randomly actuated jets, spanning a wide range of Reynolds numbers.
Key findings:

As the Reynolds number increases, the contributions to turbulent kinetic energy from both vertical and horizontal velocity components approach the predictions of rapid distortion theory.
However, the integral scale of the horizontal fluctuations grows as the surface is approached, contrary to the theory's predictions. This is attributed to the profound influence of the surface on the inter-scale energy transfer.
Along horizontal separations, the direct cascade of energy in horizontal fluctuations is hindered, while an inverse cascade of energy in vertical fluctuations is established.
Upwellings, characterized by larger spatial extent and stronger intensity, are associated with extensional surface-parallel motions and transfer energy to larger horizontal scales, prevailing over downwellings which favor the compression and vertical stretching of eddies.
Both upwellings and downwellings extend to depths between the integral and Taylor microscales.

Статистика

The turbulent kinetic energy in the bulk is approximately 0.5(u'_x^2 + 2u'_z^2).
The longitudinal and transverse integral length scales in the bulk range from 7.3 cm to 11.6 cm and 6.9 mm to 10.3 mm, respectively, as the Reynolds number increases from 3000 to 22800.
The Kolmogorov length scale in the bulk ranges from 0.35 mm to 0.12 mm as the Reynolds number increases.

Цитаты

"The free surface modifies the velocity gradients due to both the kinematic and the dynamic boundary conditions."
"The amplification of horizontal energy at the large scales results in a significant increase in surface-parallel footprint of the near-surface u_x structures."
"The profound influence exerted by the surface on the inter-scale energy transfer: along horizontal separations, the direct cascade of energy in horizontal fluctuations is hindered, while an inverse cascade of that in vertical fluctuations is established."

Ключевые выводы из

Structure and energy transfer in homogeneous turbulence below a free surface

by Daniel J. Ru... в arxiv.org 10-02-2024

https://arxiv.org/pdf/2406.05889.pdf

Дополнительные вопросы

How do the characteristics of upwellings and downwellings, such as their spatial extent and intensity, vary with the Reynolds number?

The characteristics of upwellings and downwellings in homogeneous turbulence below a free surface exhibit significant dependence on the Reynolds number (ReT). As the Reynolds number increases, the intensity of upwellings tends to be greater than that of downwellings, which is consistent with previous studies indicating that upwellings are more energetic. This disparity in intensity is crucial as it influences the overall energy transfer dynamics within the turbulent flow.
In terms of spatial extent, the study reveals that both upwellings and downwellings extend to depths between the integral scale and the Taylor microscales. However, as ReT increases, the spatial extent of upwellings becomes more pronounced, characterized by larger scales and stronger intensity. This is attributed to the enhanced turbulence intensity at higher Reynolds numbers, which allows for more vigorous vertical motions. Conversely, downwellings, which are associated with compressive motions, do not exhibit the same growth in spatial extent, indicating a fundamental asymmetry in the behavior of these structures as the turbulence becomes more intense.

What are the implications of the observed changes in the inter-scale energy transfer on the surface renewal and gas exchange processes?

The observed changes in inter-scale energy transfer have significant implications for surface renewal and gas exchange processes. The study highlights that as turbulence approaches the free surface, the direct cascade of energy in horizontal fluctuations is hindered, while an inverse cascade of energy in vertical fluctuations is established. This alteration in energy transfer dynamics affects the efficiency of surface renewal, as the upwellings, which are more energetic and have a larger spatial extent, contribute to the upward transport of water and associated substances, enhancing the renewal of the surface layer.
Moreover, the balance between upwellings and downwellings plays a critical role in gas exchange processes. Upwellings facilitate the upward movement of water, which can bring dissolved gases to the surface, promoting gas transfer rates. The study connects this to the surface divergence, indicating that the state of the sub-surface flow directly influences the gas exchange efficiency. As turbulence intensity increases, the enhanced upwelling activity can lead to improved gas exchange rates, which is particularly relevant in environmental contexts such as ocean-atmosphere interactions and industrial processes involving liquid surfaces.

How can the insights from this study on homogeneous turbulence be extended to more complex free-surface flows, such as those encountered in environmental and industrial settings?

The insights gained from this study on homogeneous turbulence can be effectively extended to more complex free-surface flows encountered in environmental and industrial settings by considering the fundamental principles of turbulence dynamics and energy transfer mechanisms. The findings regarding the behavior of upwellings and downwellings, particularly their intensity and spatial characteristics, provide a framework for understanding how turbulence interacts with free surfaces in various contexts.
In environmental settings, such as oceanic and atmospheric interactions, the principles of energy transfer and the role of turbulence in surface renewal can inform models of gas exchange and nutrient transport. For instance, the enhanced upwelling dynamics observed at higher Reynolds numbers can be applied to predict how turbulent flows influence the distribution of nutrients and gases in the upper ocean layers, thereby affecting biological productivity.
In industrial applications, such as mixing processes in liquid vessels, the study's insights can guide the design of systems that optimize turbulence characteristics to enhance mixing efficiency and surface interactions. Understanding how turbulence affects surface dynamics can lead to improved processes in chemical reactors, wastewater treatment, and other applications where surface renewal and gas exchange are critical.
Overall, the study provides a foundational understanding of turbulence dynamics that can be adapted to address the complexities of real-world free-surface flows, enhancing both theoretical models and practical applications in various fields.