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We consider axisymmetric Boussinesq convection in a shallow cylinder of radius $L$ and depth $H (\ll L)$ , which rotates with angular velocity $\varOmega$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $\varOmega$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at sufficiently large Prandtl number $\sigma$ . As $\sigma$ is reduced, the finite amplitude range of applicability of the asymptotics reduces in concert. Though the large meridional convective cell, predicted by the DNS, is approximated adequately by the asymptotics, the azimuthal flow fails almost catastrophically, because of significant angular momentum transport at small $\sigma$ , exacerbated by the cylindrical geometry. To appraise the situation, we propose hybrid methods that build on the meridional streamfunction $\psi$ derived from the asymptotics. With $\psi$ given, we solve the now linear azimuthal equation of motion for the azimuthal velocity $v$ by DNS. Our ‘hybrid’ methods enable us to explain features of the flow at large Rayleigh number, found previously by Oruba et al. (J. Fluid Mech., vol. 812, 2017, pp. 890–904).

International audience; This paper describes first results obtained from the SWIM (Surface Waves Investigation and Monitoring) instrument carried by CFOSAT (China France Oceanography Satellite), which was launched on October 29th, 2018. SWIM is a Ku-Band radar with a near-nadir scanning beam geometry. It was designed to measure the spectral properties of surface ocean waves. First, the good behavior of the instrument is illustrated. It is then shown that the nadir products (significant wave height, normalized radar cross-section and wind speed) exhibit an accuracy similar to standard altimeter missions, thanks to a new retracking algorithm, which compensates a lower sampling rate compared to standard altimetry missions. The off-nadir beam observations are analyzed in details. The normalized radar cross-section varies with incidence and wind speed as expected from previous studies presented in the literature. We illustrate that, in order to retrieve the wave spectra from the radar backscattering fluctuations, it is crucial to apply a speckle correction derived from the observations. Directional spectra of ocean waves and their mean parameters are then compared to wave model data at the global scale and to in situ data from a selection of case studies. The good efficiency of SWIM to provide the spectral properties of ocean waves in the wavelength range [70m-500m] is illustrated. The main limitations are discussed, and the perspectives to improve data quality are presented.

We consider rotating convection in a shallow, cylindrical domain. We examine the conditions under which the resulting vortex develops an eye at its core; that is, a region where the poloidal flow reverses and the angular momentum is low. For simplicity, we restrict ourselves to steady, axisymmetric flows in a Boussinesq fluid. Our numerical experiments show that, in such systems, an eye forms as a passive response to the development of a so-called eyewall, a conical annulus of intense, negative azimuthal vorticity that can form near the axis and separates the eye from the primary vortex. We also observe that the vorticity in the eyewall comes from the lower boundary layer, and relies on the fact the poloidal flow strips negative vorticity out of the boundary layer and carries it up into the fluid above as it turns upward near the axis. This process is effective only if the Reynolds number is sufficiently high for the advection of vorticity to dominate over diffusion. Finally we observe that, in the vicinity of the eye and the eyewall, the buoyancy and Coriolis forces are negligible, and so although these forces are crucial to driving and shaping the primary vortex, they play no direct role in eye formation in a Boussinesq fluid., Comment: 16 pages, 12 figures