arXiv subjects

Daniel J. Ruth

Publications and source records attributed to Daniel J. Ruth.

3 recordsLinked to original sources

arXiv2026

Free-surface curvature and its relation to subsurface turbulence

The free surface atop a turbulent liquid flow is deformed by the underlying fluid motion, with the turbulence imprinting its geometry on the surface. Here we develop a theoretical framework to model such deformations based on the Euler equation with gravity and surface tension, and evaluate it against simultaneous high-resolution measurements of surface topography and subsurface velocity fields in a zero-mean-flow turbulent water tank. We consider a range of Reynolds and Froude numbers, focusing on regimes in which the surface is unbroken. Over a range of spatial and temporal scales, we find close quantitative agreement between the measured surface curvature and that which is modeled based on the velocity field a few millimeters beneath the surface, both from the statistical and the local/instantaneous standpoints. Importantly, we verify a strong correlation between the magnitudes of the surface curvature and the divergence of the near-surface horizontal velocity, which in turn is directly related to gas and heat transfer at the air-water interface. We discuss how the sub-surface motion at increasing depths decorrelates from the surface shape, and does so more rapidly at smaller spatial scales. These findings demonstrate that measurements of surface deformations may be used to sense the state of the flow beneath the surface and provide a foundation to make optically-based inferences of processes controlled by near-surface turbulence.

physics.flu-dyn↗

arXiv2024

Structure and energy transfer in homogeneous turbulence below a free surface

We investigate the turbulence below a quasi-flat free surface, focusing on the energy transport in space and across scales. We leverage a large zero-mean-flow tank where homogeneous turbulence is generated by randomly actuated jets. A wide range of Reynolds number is spanned, reaching sufficient scale separation for the emergence of an inertial sub-range. Unlike previous studies, the forcing extends through the source layer, though the surface deformation remains millimetric. Particle image velocimetry along a surface-normal plane resolves from the dissipative to the integral scales. The contributions to turbulent kinetic energy from both vertical and horizontal components of velocity approach the prediction based on rapid distortion theory as the Reynolds number is increased, indicating that discrepancies among previous studies are likely due to differences in the forcing. At odds with the theory, however, the integral scale of the horizontal fluctuations grows as the surface is approached. This is rooted in 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. This is connected to the structure of upwellings and downwellings. The former, characterized by somewhat larger spatial extent and stronger intensity, are associated to extensional surface-parallel motions. They thus transfer energy to the larger horizontal scales, prevailing over downwellings which favour the compression (and concurrent vertical stretching) of the eddies. Both types of structures extend to depths between the integral and Taylor microscales.

physics.flu-dyn↗

arXiv2022

Experimental observations and modeling of sub-Hinze bubble production by turbulent bubble break-up

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale $d_\mathrm{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes $d_0$ much larger than $d_\mathrm{H}$ (probing up to $d_0 / d_\mathrm{H} = 8.3$), the size distribution of bubbles smaller than $d_\mathrm{H}$ follows $N(d) \propto d^{-3/2}$, with $d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small ones. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of $d_0 / d_\mathrm{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

physics.flu-dyn↗