This work addresses the effect of travelling thermal waves applied at the fluid layer surface, on the formation of global flow structures in 2D and 3D convective systems. For a broad range of Rayleigh numbers ($10^3\leq Ra \leq 10^7$) and thermal wave frequencies ($10^{-4}\leq Ω\leq 10^{0}$), we investigate flows with and without imposed mean temperature gradients. Our results confirm that the travelling thermal waves can cause zonal flows, i.e. strong mean horizontal flows. We show that the zonal flows in diffusion dominated regimes are driven purely by the Reynolds stresses, always travelling retrograde, while in convection dominated regimes, mean flow advection, caused by tilted convection cells, becomes dominant, which generally leads to prograde mean zonal flows. By means of direct numerical simulations we validate theoretical predictions made for the diffusion dominated regime. Furthermore, we make use of the linear stability analysis and explain the existence of the tilted convection cell mode. Our extensive 3D simulations support the results for 2D flows and thus confirm the relevance of the findings for geopyhsical and astrophysical systems.
We study rapidly-rotating Boussinesq convection driven by internal heating in a full sphere. We use a numerical model based on the quasi-geostrophic approximation for the velocity field, whereas the temperature field is three-dimensional. This approximation allows us to perform simulations for Ekman numbers down to 1e-8, Prandtl numbers relevant for liquid metals (~0.1) and Reynolds numbers up to 3e4. Persistent zonal flows composed of multiple jets form as a result of the mixing of potential vorticity. For the largest Rayleigh numbers computed, the zonal velocity is larger than the convective…
Motivated by understanding the dynamics of stellar and planetary interiors, we have performed a set of direct numerical simulations of Boussinesq convection in a rotating full sphere. The domain is internally heated with fixed temperature and stress-free boundary conditions, but fixed heat flux and no-slip boundary conditions are also briefly considered. We particularly focus on the large-scale coherent structures and the mean zonal flows that can develop in the system. At Prandtl number of unity, as the thermal forcing (measured by the Rayleigh number) is increased above the value for the ons…
Using direct numerical simulations, we study rotating Rayleigh-Bénard convection in a cylindrical cell for a broad range of Rayleigh, Ekman, and Prandtl numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode states that occur prior to the onset of bulk convection with the boundary zonal flow that coexists with turbulent bulk convection in the geostrophic regime through the continuity of length and time scales and of convective heat transport. We quantitatively collapse drift frequency, bo…
Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and on the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics, like differential rotation which exists in the outer convective enveloppe of solar-like stars and giant gaseous planets. In particular, tidal waves may strongly interact with zonal flows at the so-called corotation resonances, where the wave's Doppler-shifted frequency cancels out. We aim to …
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Bénard convection in a two-dimensional, rectangular geometry of aspect ratio $Γ$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $Γ= 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the …
In close two-body astrophysical systems, such as binary stars or Hot Jupiter systems, tidal interactions often drive dynamical evolution on secular timescales. Many host stars and presumably giant gaseous planets feature a convective envelope. Tidal flows generated therein by the tidal potential of the companion can be dissipated through viscous friction, leading to the redistribution and exchange of angular momentum within the convective shell and with the companion, respectively. In the tightest systems, nonlinear effects are likely to have a significant impact on the tidal dissipation and t…
Zonal flows in rapidly-rotating celestial objects such as the Sun, gas or ice giants form in a variety of surface patterns and amplitudes. Whereas the differential rotation on the Sun, Jupiter and Saturn features a super-rotating equatorial region, the ice giants, Neptune and Uranus harbour an equatorial jet slower than the planetary rotation. Global numerical models covering the optically thick, deep-reaching and rapidly rotating convective envelopes of gas giants reproduce successfully the prograde jet at the equator. In such models, convective columns shaped by the dominant Coriolis force t…
In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. Tidally-forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tida…
High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Ra…
We present the first detailed thermal and velocity field characterization of convection in a rotating cylindrical tank of liquid gallium, which has thermophysical properties similar to those of planetary core fluids. Our laboratory experiments, and a closely associated direct numerical simulation, are all carried out in the regime prior to the onset of steady convective modes. This allows us to study the oscillatory convective modes, sidewall modes and broadband turbulent flow that develop in liquid metals before the advent of steady columnar modes. Our thermo-velocimetric measurements show th…
Well-resolved numerical simulations are used to study Rayleigh-Bénard-Poiseuille flow over an evolving phase boundary for moderate values of Péclet ($Pe \in \left[0, 50\right]$) and Rayleigh ($Ra \in \left[2.15 \times 10^3, 10^6\right]$) numbers. The relative effects of mean shear and buoyancy are quantified using a bulk Richardson number: $Ri_b = Ra \cdot Pr/Pe^2 \in [8.6 \times 10^{-1}, 10^4]$, where $Pr$ is the Prandtl number. For $Ri_b = \mathcal{O}(1)$, we find that the Poiseuille flow inhibits convective motions, resulting in the heat transport being only due to conduction; and, for $Ri_…
We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse Annulus model zonal jets are generated through the interaction of convectively driven turbulence and rotation; non-trivial dynamics including the emergence of multiple jets and bursting `predator-prey' type dynamics can be found. We formulate the DSS by expanding around the mean flow in terms of equal-time cumulants and arrive at a closed set of equations of motion for the cumulants. Here, we present results using an expansion terminated at the second cumulant (CE2); it …
Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva et al., 2019, Geophys. Astrophys. Fluid Dyn., doi:10.1080/03091929.2019.1640875) are found to persist significantly beyond the onset of ins…
