431 research outputs found
A model for vortical plumes in rotating convection
In turbulent rotating convection a typical flow structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier¿Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices and a prediction for the heat flux (Nusselt number) that is very appropriate compared to the results from direct numerical simulations of the full governing equation
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
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
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
Optimal Prandtl number for heat transfer in rotating Rayleigh-Benard convection
Numerical data for the heat transfer as a function of the Prandtl (Pr) and
Rossby (Ro) numbers in turbulent rotating Rayleigh-Benard convection are
presented for Rayleigh number Ra = 10^8. When Ro is fixed the heat transfer
enhancement with respect to the non-rotating value shows a maximum as function
of Pr. This maximum is due to the reduced efficiency of Ekman pumping when Pr
becomes too small or too large. When Pr becomes small, i.e. for large thermal
diffusivity, the heat that is carried by the vertical vortices spreads out in
the middle of the cell, and Ekman pumping thus becomes less efficient. For
higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs
and therefore the Ekman vortices do not reach the thermal BL. This means that
the fluid that is sucked into the vertical vortices is colder than for lower Pr
which limits the efficiency of the upwards heat transfer.Comment: 5 pages, 6 figure
A model for vortical plumes in rotating convection
In turbulent rotating convection a typical flow-structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier-Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices, and a prediction for the heat flux (Nusselt number) that is very appropriate compared with results from direct numerical simulations of the full governing equations
Saturation of front propagation in a reaction-diffusion process describing plasma damage in porous low-k materials
We propose a three-component reaction-diffusion system yielding an asymptotic
logarithmic time-dependence for a moving interface. This is naturally related
to a Stefan-problem for which both one-sided Dirichlet-type and von
Neumann-type boundary conditions are considered. We integrate the dependence of
the interface motion on diffusion and reaction parameters and we observe a
change from transport behavior and interface motion \sim t^1/2 to logarithmic
behavior \sim ln t as a function of time. We apply our theoretical findings to
the propagation of carbon depletion in porous dielectrics exposed to a low
temperature plasma. This diffusion saturation is reached after about 1 minute
in typical experimental situations of plasma damage in microelectronic
fabrication. We predict the general dependencies on porosity and reaction
rates.Comment: Accepted for publication in Phys. Rev.
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
- …