Prof. Peter Read

Abstract:

The circulation of the Earth’s atmosphere and those of many other planets is dominated by turbulent interactions in a baroclinically unstable, rotating, stratified flow. Even for the Earth, which has been well observed for many years, the energy spectrum and complex properties of the anisotropic and inhomogeneous turbulent cascades of energy and enstrophy remain poorly understood and difficult to model accurately. Here we measure geostrophic turbulence energised by baroclinic instability in a rotating, differentially heated fluid annulus in the laboratory, which is bounded by convectively-driven warm and cold flows at the outer and inner boundaries, respectively (see Fig. 1a). Horizontal velocity fields (Fig. 1b-c) are obtained via particle image velocimetry of neutrally buoyant particles suspended in the flow, while the temperature structure is sampled using a vertical array of thermocouples located in the middle of the channel. The horizontal kinetic energy spectra exhibit a wavenumber range at relatively large length scales which scales as k−3, where k denotes the horizontal wavenumber (see Fig. 1d-e). Moreover, the spectral amplitude is found to correlate with the square of the Brunt–Vaisala frequency N at the same heights as the velocity measurements. The observed turbulent state exhibits a net forward enstrophy cascade across all scales, along with bidirectional kinetic energy transfer, which is indicated by a reversal in the sign of the spectral energy flux. The change of sign of the kinetic energy cascade occurs at a scale proportional to the internal Rossby radius of deformation Ld. These findings highlight the role of baroclinic instability in shaping the distribution of energy across scales with implications for synoptic- and meso-scale turbulent flows in the atmospheres of the Earth and other terrestrial planet atmospheres and oceans.FIG. 1. (a) Schematic plot of the convective tank. Snapshots of vorticity ζ for thermal Rossby number RoT = 5.41 (b) and RoT = 0.03 (c). On the scale bar, Lid = 2.4 cm and Liid = 22.6 cm are the Rossby radius of deformation for (c) and (b), respectively. (d) Kinetic energy spectra, E(k), for various values of RoT. The arrow indicates the wave number kp corresponding to the peak of E(k) when RoT = 0.03. Inset: radial profiles of temporal- and zonal-averaged azimuthal velocity, Uθ. (e) Kinetic energy spectra compensated by k−3 and normalised by N2 versus LRk. The dashed line indicates the plateau segment for LRk ∈ [2, 10] and has a magnitude of ∼ 0.5. Data are for height h = 0.18 m.

Abstract:

The midlatitude atmospheres of gas giant planets are characteristic of strong and persistent zonal jets; however, the processes governing their formation and the associated energy pathways remain less understood. To investigate these mechanisms, we conducted a laboratory study of zonal jets driven by thermal forcing in an annular cylindrical tank partially filled with distilled water as the working fluid. Heating is applied at the outer boundary, cooling at the inner boundary, the bottom is thermally insulated, and the top is a free surface. An array of laser diodes embedded in the inner cylinder generates an annular laser sheet, enabling the measurement of velocity fields at a fixed height using particle image velocimetry. By systematically varying the rotation rate and the imposed temperature contrast, we adjusted the steepness of the free surface, thus the topographic β effect, and the thermal forcing strength, respectively. The non-dimensional controlling parameter, thermal Rossby number, RoT, ranges from 0.0012 to 0.01 and Taylor number, Ta, from 2.3 × 1010 to1.7 × 1011. We discerned the emergence of robust zonal jets, of which the zonal-mean kinetic energy accounts for up to 70% of the total kinetic energy, corresponding to a zonostrophic index of 2.7. In this regime, two coherent and persistent prograde jets form near the inner and outer boundaries. The radial profile of the potential vorticity develops toward a pronounced staircase-like structure, consistent with previous numerical studies (Scott and Dritschel, J. Fluid Mech., 2012). Analysis of the inter-scale energy transfer reveals a dominant interaction between the zonal-mean flow and eddies, while the kinetic energy spectrum of the zonal-mean component exhibits k−5 (where k denotes the wavenumber), in agreement with the theory of zonostrophic turbulence (Sukoriansky and Galperin, PRL, 2002).                                     Figure 1: A snapshot of azimuthal velocity contour for RoT = 7.1 × 10−3, Ta = 1.44 × 1011 and β =49.7 m−1 s−1.

Abstract:

This dataset provides horizontal flow fields (velocity, relative vorticity, divergence, and shear strain rate) from nine rotating turbulence experiments carried out at TurLab at the University of Turin between November 2016 and February 2017 by a team led by Oxford scientists in collaboration with others at the time from Università degli Studi di Torino, University of South Florida, Università del Piemonte Orientale and Sapienza Università di Roma. The experimental device was a rotating cylinder, 5 m in diameter filled with fresh water to a depth of 56 cm. The tank had a conical bottom, sloping upwards towards the centre from the outer edge over a radius of 2.25 m at an angle of 11.1◦. The flow was mechanically forced by a moving comb of vertical paddles partially immersed in the water, which moved backwards and forwards along a near-radial line over 100–150 s. The resulting flow was visualised using a laser sheet and microscopic particles, imaged using two cameras, and then processed into horizontal velocity fields and derived quantities using UVMAT/CIV (http://servforge.legi. grenoble-inp.fr/projects/soft-uvmat). The main quantity varied between the experiments included in this dataset is the rotation period of the tank. There were minor differences in the comb configuration at each rotation period. †

Abstract:

Barotropic instability represents a class of instabilities, usually of parallel shear flows, for which gravity and buoyancy play a negligible role, at least in their energetics. It is not restricted to purely barotropic fluids (for which ρ = ρ(p), where ρ is density and p is pressure) but can also apply to flows which are stratified and exhibit vertical shear, often leading to instabilities with mixed barotropic and baroclinic characteristics. The primary attribute of barotropic instability is usually taken to be the dominance of energy exchanges in which the kinetic energy of a perturbation grows principally at the expense of the kinetic energy of the basic state. Here we present an introduction to the basic mechanisms involved and the factors that determine the necessary and/or sufficient conditions for instability. Several examples are presented and the occurrence and subsequent nonlinear evolution of the instability is illustrated with reference to both laboratory experiments and observations in the atmospheres and oceans of the Earth and other planets in the Solar System.