Turbulence modulation in buoyancy-driven bubbly flows

We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large-scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

Thorpe turbulence scaling in night time convective surface layers in the North Indian Ocean

We use profiles from a Lagrangian Float in the North Indian Ocean to explore the usefulness of Thorpe analysis methods to measure vertical scales and dissipation rates in the ocean surface boundary layer. An rms Thorpe length scale LT and an energy dissipation rate εT were computed by resorting the measured density profiles. These are compared to the mixed layer depth (MLD) computed with different density thresholds, the Monin-Obukhov (MO) length LMO computed from the ERA5 reanalysis values of wind stress and buoyancy flux B0 and dissipation rates ε from historical microstructure data. LT is found to accurately match MLD for small (<0.005 kgm-3) density thresholds, but not for larger thresholds, because these do not detect the warm diurnal layers. We use ξ = LT/|LMO| to classify the boundary layer turbulence during night-time convection. In our data, 90% of points from the Bay of Bengal (Arabian Sea) satisfy ξ < 1 (1 < ξ < 10), indicating that wind forcing is (both wind forcing and convection are) driving the turbulence. Over the measured range of ξ, εT decreases with decreasing ξ, i.e. more wind forcing, while ε increases, clearly showing that ε/εT decreases with increasing ξ. This is explained by a new scaling for ξ ≪ 1, εT = 1.15 B0ξ0.5 compared to the historical scaling ε = 0.64 B0 + 1.76ξ−1. For ξ ≫ 1 we expect ε = εT. Similar calculations may be possible using routine ARGO float and ship data, allowing more detailed global measurements of εT thereby providing large-scale tests of turbulence scaling in boundary layers.

A Turbulence Scaling Factor that converts laminar solutions to turbulent solutions

The quest to understand turbulent flows continues to be as important as it was during the previous century. Present work shows that if a 'laminar' solution to Navier -Stokes equations can be found then skin friction and heat transfer coefficients for the turbulent case can readily be obtained. There is no need for Reynolds averaging and turbulence modelling. This can be done by defining a turbulence scaling factor which converts 'laminar' diffusivities to turbulent diffusivities. Using turbulent diffusivities in the laminar skin friction coefficient formula and laminar heat transfer coefficient formula gives the corresponding turbulent formula. Five different test cases with credible experimental measurements have been used to show the success of the present approach. This work also gives the lengths of internally generated turbulent eddies and roughness created turbulent eddies. If main flow mixes the turbulent eddies , smaller eddies are merged by the larger ones and this is the suggested model for roughness effects which dominates at large Reynolds numbers. A single effective roughness which determines the friction factor has also been obtained and the fractal dimension of turbulence is given as power to Reynolds number. This fractal dimension is in accord with literature for turbulent/non-turbulent interfaces.

Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence

Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Temperature statistics above a deep-ocean sloping boundary

We present a detailed analysis of temperature statistics in an oceanographic observational dataset. The data are collected using a moored array of thermistors,$100~\text{m}$tall and starting$5~\text{m}$above the bottom, deployed during four months above the slopes of a Seamount in the north-eastern Atlantic Ocean. Turbulence at this location is strongly affected by the semidiurnal tidal wave. Mean stratification is stable in the entire dataset. We compute structure functions, of order up to 10, of the distributions of temperature increments. Strong intermittency is observed, in particular, during the downslope phase of the tide, and farther from the solid bottom. In the lower half of the mooring during the upslope phase, the temperature statistics are consistent with those of a passive scalar. In the upper half of the mooring, the temperature statistics deviate from those of a passive scalar, and evidence of turbulent convective activity is found. The downslope phase is generally thought to be more shear-dominated, but our results suggest on the other hand that convective activity is present. High-order moments also show that the turbulence scaling behaviour breaks at a well-defined scale (of the order of the buoyancy length scale), which is however dependent on the flow state (tidal phase, height above the bottom). At larger scales, wave motions are dominant. We suggest that our results could provide an important reference for laboratory and numerical studies of mixing in geophysical flows.