For rotationally constrained convection, the Taylor–Proudman theorem enforces an organization of nonlinear flows into tall columnar or compact plume structures. While coherent structures in convection under moderate rotation are exclusively cyclonic, recent experiments for rapid rotation have revealed a transition to equal populations of cyclonic and anticyclonic structures. Direct numerical simulation (DNS) of this regime is expensive, however, and existing simulations have yet to reveal anticyclonic vortical structures. In this paper, we use a reduced system of equations for rotationally constrained convection valid in the asymptotic limit of thin columnar structures and rapid rotation to perform numerical simulation of Rayleigh–Bénard convection in an infinite layer rotating uniformly about the vertical axis. Visualization indicates the existence of cyclonic and anticyclonic vortical populations for all parameters examined. Moreover, it is found that the flow evolves through three distinct regimes with increasing Rayleigh number (Ra). For small, but supercritical Ra, the flow is dominated by a cellular system of hot and cold columns spanning the fluid layer. As Ra increases, the number density of these columns decreases, the up-and down-drafts within them strengthen and the columns develop opposite-signed ‘sleeves’ in all fields. The resulting columns are highly efficient at transporting heat across the fluid layer. In the final regime, lateral mixing plays a dominant role in the interior and the columnar structure is destroyed. However, thermal plumes are still injected and rejected from the thermal boundary layers. We identify the latter two regimes with the vortex-grid and geostrophic turbulence regimes, respectively. Within these regimes, we investigate convective heat transport (measured by the Nusselt number), mean temperature profiles, and root-mean-square profiles of the temperature, vertical velocity and vertical vorticity anomalies. For all Prandtl numbers investigated, the mean temperature saturates in a non-isothermal profile as Ra increases owing to intense lateral mixing.

Turbulent Boussinesq convection under the influence of rapid rotation (i.e. with comparable characteristic rotation and convection timescales) is studied. The transition to turbulence proceeds through a relatively simple bifurcation sequence, starting with unstable convection rolls at moderate Rayleigh (Ra) and Taylor numbers (Ta) and culminating in a state dominated by coherent plume structures at high Ra and Ta. Like non-rotating turbulent convection, the rapidly rotating state exhibits a simple power-law dependence on Ra for all statistical properties of the flow. When the fluid layer is bounded by no-slip surfaces, the convective heat transport (Nu − 1, where Nu is the Nusselt number) exhibits scaling with Ra2/7 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys ‘classical’ scaling (Ra1/3) for a limited range in Ra, then appears to undergo a transition to a different law at Ra ≈ 4 × 107. Important dynamical differences between rotating and non-rotating convection are observed: aside from the (expected) differences in the boundary layers due to Ekman pumping effects, angular momentum conservation forces all plume structures created at flow-convergent sites of the heated and cooled boundaries to spin-up cyclonically; the resulting plume/cyclones undergo strong vortex-vortex interactions which dramatically alter the mean state of the flow and result in a finite background temperature gradient as Ra → ∞, holding Ra/Ta fixed.

Abstract.The highest-resolution 3D direct numerical simulations to date of Kelvin-Helmholtz instability are reported. The ensuing turbulence spans a broad range of spatial scales and exhibits Kolmogorov spectra in horizontal planes. Non-Gaussian statistics are observed, with highly intermittent entrainment zones at the edges of the resulting shear layer. Profiles of the local gradient-Richardson number are presented and shown to remain less than 1/4 throughout the entire evolution of the turbulence.

Direct numerical simulations are employed to examine gravity wave instability dynamics at a high intrinsic frequency, wave amplitudes both above and below nominal convective instability, and a Reynolds number sufficiently high to allow a fully developed turbulence spectrum. Assumptions include no mean shear, uniform stratification, and a monochromatic gravity wave to isolate fluxes due to gravity wave and turbulence structures from those arising from environmental shears or varying wave amplitudes. The results reveal strong wave breaking for both wave amplitudes, severe primary wave amplitude reductions within ;1 or 2 wave periods, an extended turbulence inertial range, significant excitation of additional wave motions exhibiting upward and downward propagation, and a net positive vertical potential temperature flux due to the primary wave motion, with secondary waves and turbulence contributing variable and negative potential temperature fluxes, respectively. Turbulence maximizes within ;1 buoyancy period of the onset of breaking, arises almost entirely owing to shear production, and decays rapidly following primary wave amplitude decay. Secondary waves are excited by wave-wave interactions and the turbulence dynamics accompanying wave breaking; they typically have lower frequencies and smaller momentum fluxes than the primary wave following breaking.

This paper presents results from the first fully three-dimensional direct numerical simulations of initially turbulent wakes with net momentum in unstratified and density stratified fluids. The initial conditions contain a super-position of an initially axisymmetric mean streamwise velocity profile plus a spectrally specified fluctuation velocity field with initially incoherent phases to model initial turbulence. To provide evidence in favor of their validity, we compare results from these simulations with previous measurements behind towed bodies in wind tunnels and towing tanks, and also compare with theories of turbulent wakes. Comparisons with laboratory flow experiments provide agreement, both with statistical quantities and vortex structures and evolution. We subsequently investigate open questions by analysis of the fully three-dimensional flow. Coherent vortices in stratified wakes have their origins in the vortex geometry of the mean wake flow, and do not require stratification or coherent seeding in the initial velocity fluctuations. We conclude that the simulations provide a trustworthy and valuable complement to wake research, and that the vortex structures result from a combination of the necessity that vortices form loops and diffusion of vorticity to smooth the loops into rings.