15 research outputs found
A Heuristic Framework for Next-Generation Models of Geostrophic Convective Turbulence
Many geophysical and astrophysical phenomena are driven by turbulent fluid
dynamics, containing behaviors separated by tens of orders of magnitude in
scale. While direct simulations have made large strides toward understanding
geophysical systems, such models still inhabit modest ranges of the governing
parameters that are difficult to extrapolate to planetary settings. The
canonical problem of rotating Rayleigh-B\'enard convection provides an
alternate approach - isolating the fundamental physics in a reduced setting.
Theoretical studies and asymptotically-reduced simulations in rotating
convection have unveiled a variety of flow behaviors likely relevant to natural
systems, but still inaccessible to direct simulation. In lieu of this, several
new large-scale rotating convection devices have been designed to characterize
such behaviors. It is essential to predict how this potential influx of new
data will mesh with existing results. Surprisingly, a coherent framework of
predictions for extreme rotating convection has not yet been elucidated. In
this study, we combine asymptotic predictions, laboratory and numerical
results, and experimental constraints to build a heuristic framework for
cross-comparison between a broad range of rotating convection studies. We
categorize the diverse field of existing predictions in the context of
asymptotic flow regimes. We then consider the physical constraints that
determine the points of intersection between flow behavior predictions and
experimental accessibility. Applying this framework to several upcoming devices
demonstrates that laboratory studies may soon be able to characterize
geophysically-relevant flow regimes. These new data may transform our
understanding of geophysical and astrophysical turbulence, and the conceptual
framework developed herein should provide the theoretical infrastructure needed
for meaningful discussion of these results.Comment: 36 pages, 8 figures. CHANGES: in revision at Geophysical and
Astrophysical Fluid Dynamic
Geostrophic convective turbulence: The effect of boundary layers
Rayleigh--B\'enard (RB) convection, the flow in a fluid layer heated from
below and cooled from above, is used to analyze the transition to the
geostrophic regime of thermal convection. In the geostrophic regime, which is
of direct relevance to most geo- and astrophysical flows, the system is
strongly rotated while maintaining a sufficiently large thermal driving to
generate turbulence. We directly simulate the Navier--Stokes equations for two
values of the thermal forcing, i.e. and , a
constant Prandtl number~, and vary the Ekman number in the range
to which satisfies both requirements of
super-criticality and strong rotation. We focus on the differences between the
application of no-slip vs. stress-free boundary conditions on the horizontal
plates. The transition is found at roughly the same parameter values for both
boundary conditions, i.e. at~ for~ and at~ for~. However,
the transition is gradual and it does not exactly coincide in~ for
different flow indicators. In particular, we report the characteristics of the
transitions in the heat transfer scaling laws, the boundary-layer thicknesses,
the bulk/boundary-layer distribution of dissipations and the mean temperature
gradient in the bulk. The flow phenomenology in the geostrophic regime evolves
differently for no-slip and stress-free plates. For stress-free conditions the
formation of a large-scale barotropic vortex with associated inverse energy
cascade is apparent. For no-slip plates, a turbulent state without large-scale
coherent structures is found; the absence of large-scale structure formation is
reflected in the energy transfer in the sense that the inverse cascade, present
for stress-free boundary conditions, vanishes.Comment: Submitted to JF
Laboratory Exploration of Heat Transfer Regimes in Rapidly Rotating Turbulent Convection
We report heat transfer and temperature profile measurements in laboratory
experiments of rapidly rotating convection in water under intense thermal
forcing (Rayleigh number as high as ) and unprecedentedly
strong rotational influence (Ekman numbers as low as ).
Measurements of the mid-height vertical temperature gradient connect
quantitatively to predictions from numerical models of asymptotically rapidly
rotating convection, separating various flow phenomenologies. Past the limit of
validity of the asymptotically-reduced models, we find novel behaviors in a
regime we refer to as rotationally-influenced turbulence, where rotation is
important but not as dominant as in the known geostrophic turbulence regime.
The temperature gradients collapse to a Rayleigh-number scaling as
in this new regime. It is bounded from above by a critical convective Rossby
number independent of domain aspect ratio , clearly
distinguishing it from well-studied rotation-affected convection.Comment: 14 pages, 7 figure
The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-B\'enard convection
When the classical Rayleigh-B\'enard (RB) system is rotated about its
vertical axis roughly three regimes can be identified. In regime I (weak
rotation) the large scale circulation (LSC) is the dominant feature of the
flow. In regime II (moderate rotation) the LSC is replaced by vertically
aligned vortices. Regime III (strong rotation) is characterized by suppression
of the vertical velocity fluctuations. Using results from experiments and
direct numerical simulations of RB convection for a cell with a
diameter-to-height aspect ratio equal to one at ()
and we identified the characteristics of the
azimuthal temperature profiles at the sidewall in the different regimes. In
regime I the azimuthal wall temperature profile shows a cosine shape and a
vertical temperature gradient due to plumes that travel with the LSC close to
the sidewall. In regime II and III this cosine profile disappears, but the
vertical wall temperature gradient is still observed. It turns out that the
vertical wall temperature gradient in regimes II and III has a different origin
than that observed in regime I. It is caused by boundary layer dynamics
characteristic for rotating flows, which drives a secondary flow that
transports hot fluid up the sidewall in the lower part of the container and
cold fluid downwards along the sidewall in the top part.Comment: 21 pages, 12 figure
Discontinuous Transitions Towards Vortex Condensates in Buoyancy-Driven Rotating Turbulence: Analogies with First-Order Phase Transitions
Using direct numerical simulations of rotating Rayleigh-B\'enard convection,
we explore the transitions between turbulent states from a 3D flow state
towards a quasi-2D condensate known as the large-scale vortex (LSV). We vary
the Rayleigh number as control parameter and study the system response
(strength of the LSV) in terms of order parameters assessing the energetic
content in the flow and the upscale energy flux. By sensitively probing the
boundaries of the domain of existence of the LSV, we find discontinuous
transitions and we identify the presence of a hysteresis loop as well as
nucleation & growth type of dynamics, manifesting a remarkable correspondence
with first-order phase transitions in equilibrium statistical mechanics. We
show furthermore that the creation of the condensate state coincides with a
discontinuous transition of the energy transport into the largest mode of the
system.Comment: 10 pages, 5 figure
The robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh-B\'enard convection
In confined rotating convection, a strong zonal flow can develop close to the
side wall with a modal structure that precesses anti-cyclonically (counter to
the applied rotation) along the side wall. It is surmised that this is a robust
non-linear evolution of the wall modes observed before the onset of bulk
convection. Here, we perform direct numerical simulations of cylindrically
confined rotating convection at high rotation rates and strong turbulent
forcing. Through comparison with earlier work, we find a fit-parameter-free
relation that links the angular drift frequency of the robust wall mode
observed far into the turbulent regime with the critical wall mode frequency at
onset, firmly substantiating the connection between the observed boundary zonal
flow and the wall modes. Deviations from this relation at stronger turbulent
forcing suggest early signs of the bulk turbulence starting to hamper the
development of the wall mode. Furthermore, by studying the interactive flow
between the robust wall mode and the bulk turbulence, we identify radial jets
penetrating from the wall mode into the bulk. These jets induce a large scale
multipolar vortex structure in the bulk turbulence, dependent on the wavenumber
of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a
quadrupolar vortex driven by the radial jets, while in a wider cylinder the
jets are found to have a finite penetration length and the vortices do not
cover the entire bulk. We also identify the role of Reynolds stresses in the
generation of zonal flows in the region near the sidewall.Comment: 14 pages, 8 figure
Frictional boundary layer effect on vortex condensation in rotating turbulent convection
We perform direct numerical simulations of rotating Rayleigh--B\'enard
convection of fluids with low () and high () Prandtl numbers in a
horizontally periodic layer with no-slip top and bottom boundaries. At both
Prandtl numbers, we demonstrate the presence of an upscale transfer of kinetic
energy that leads to the development of domain-filling vortical structures.
Sufficiently strong buoyant forcing and rotation foster the
quasi-two-dimensional turbulent state of the flow, despite the formation of
plume-like vertical disturbances promoted by so-called Ekman pumping from the
viscous boundary layer.Comment: 12 pages, 4 figure
Vortex plume distribution in confined turbulent rotating convection
Vortical columns are key features of rapidly rotating turbulent Rayleigh-Bénard convection. In this work we probe the structure of the sidewall boundary layers experimentally and show how they affect the spatial vortex distribution in a cylindrical cell. The cell has a diameter-to-height aspect ratio and is operated at Rayleigh number and Prandtl number 6.4. The vortices are detected using particle image velocimetry. We find that for inverse Rossby numbers (expressing the rotation rate in a dimensionless form) the sidewall boundary layer exhibits a rotation-dependent thickness and a characteristic radial profile in the root-mean-square azimuthal velocity with two peaks rather than a single peak typical for the non-rotating case. These properties point to Stewartson-type boundary layers, which can actually cover most of the domain for rotation rates just above the transition point. A zonal ordering of vortices into two azimuthal bands at moderate rotation rates can be attributed to the sidewall boundary layer. Additionally, we present experimental confirmation of the tendency of like-signed vortices to cluster on opposite sides of the cylinder for . At higher rotation rates and away from the sidewall the vortices are nearly uniformly distributed