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Abstract:

Recent analyses of wind measurements obtained from tracking cloud motions in spacecraft images of Jupiter and Saturn[1,2] indicate that nonlinear scale-to-scale transfers of kinetic energy act from small to large scales over a wide range of length scales, much as anticipated for 2D or geostrophic turbulence paradigms. At the smallest resolvable scales, however, there is evidence in observations of a forward (downscale) transfer, at least at low and middle latitudes on Jupiter, much like in the Earth’s atmosphere. Moreover, the upscale transfers at the largest spatial scales are evidently dominated by spectrally non-local, highly anisotropic eddy-zonal interactions associated with the generation of intense zonal jets and equatorial super-rotation by direct eddy-zonal flow exchanges. Most analyses to date have emphasised the global mean interactions for both planets, thereby focusing on the spatially homogeneous and isotropic components of the turbulence. Here we present some new analyses of spectral energy transfers on both Jupiter and Saturn that resolve variations in latitude[cf 3], thereby shedding new light on non-homogeneous aspects of jovian turbulent interactions. The results indicate significant variability and inhomogeneity between different locations, with a clear distinction between the tropics, the extratropical middle latitudes and the polar regions. We discuss these in light of other observations and models of gas giant circulation and related laboratory experimental analogues.[1] Antu˜nano, A., del Río-Gaztelurrutia, T., Sánchez-Lavega, A., & Hueso, R. (2015) Dynamics of Saturn’s polar regions. J. Geophys. Res.: Planets, 120 , 155–176. doi:10.1002/2014JE004709[2] Read, P. L., Antu˜nano, A., Cabanes, S., Colyer, G., del Río-Gaztelurrutia, T., Sánchez-Lavega, A. (2022). Energy exchanges in Saturn’s polar regions fromCassini observations: Eddy-zonal flow interactions. J. Geophys. Res., 127 , e2021JE006973. https://doi.org/10.1029/2021JE006973[3] Chemke, R., & Kaspi, Y. (2015). The latitudinal dependence of atmospheric jet scales and macroturbulent energy cascades. J. Atmos. Sci., 72 , 3891–3907. doi: 10.1175/JAS-D-15-0007.

Abstract:

This study proposes a data-driven methodology to complement existing time-series measurement tools for turbulent flows. Specifically, a cluster-based transition network model is employed for the estimation of velocity time traces and their corresponding statistics. The method is tested on a laboratory-modelled turbulent boundary layer over a step change in surface roughness, where velocity time series are recorded for training and validation purposes via Laser Doppler Anemometry. Results show that our approach can estimate velocity and momentum flux statistics within experimental uncertainty over a rough surface through an unsupervised approach, and across the step change in roughness through a semi-supervised variant. The friction velocity across the domain is also estimated with 10% relative error compared to the measured value. The proposed methodology is interpretable and robust against the main methodological parameters. A reliable data-driven framework is hence provided that can be integrated within existing laboratory setups to supplement or partially replace measurement systems, as well as to reduce wind tunnel running times.

Abstract:

We conducted experimental investigations on the effect of stable thermal conditions on rough-wall boundary layers, with a specific focus on their response to abrupt increases in surface roughness. For stably stratified boundary layers, a new analytical relation between the skin-friction coefficient, $C_f$ , and the displacement thickness was proposed. Following the sharp roughness change, the overshoot in $C_f$ is slightly enhanced in stably stratified layers when compared with that of neutral boundary layers. Regarding the velocity defect law, we found that the displacement thickness multiplied by $\sqrt{2/C_f}$ , performs better than the boundary layer thickness alone when describing the similarity within internal boundary layers for both neutral and stable cases. A non-adjusted region located just beneath the upper edge of the internal boundary layer was observed, with large magnitudes of skewness and kurtosis of streamwise and wall-normal velocity fluctuations for both neutral and stable cases. At a fixed wall-normal location, the greater the thermal stratification, the greater the magnitudes of skewness and kurtosis. Quadrant analysis revealed that the non-adjusted region is characterised by an enhancement/reduction of ejection/sweep events, particularly for stably stratified boundary layers. Spatially, these ejections correspond well with peaks of kurtosis, exhibit stronger intensity and occur more frequently following the abrupt change in surface conditions.

Abstract:

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$ . Under slow rotations ( $Ra\approx 80\,Ra_{c}$ ), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$ . The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ( $4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$ ), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ( $1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$ ), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

Abstract:

Abstract In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development in the log-law region shows good agreement with the diffusion model proposed by Panofsky and Dutton (Atmospheric turbulence, Wiley, New York, 1984) provided that a modified origin condition is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes $$n\approx 0.8$$ n ≈ 0.8 ). For the stably-stratified boundary layers, n is found to further reduce as the bulk Richardson number, $$\textrm{Ri}_\textrm{b}$$ Ri b , increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers. Graphical abstract