Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection

2012 ◽  
Vol 712 ◽  
pp. 219-243 ◽  
Author(s):  
Takeshi Watanabe ◽  
Makoto Iima ◽  
Yasumasa Nishiura
Keyword(s):  
Asymptotic Behaviour ◽  
Strong Interactions ◽  
Asymptotic State ◽  
Infinite Domain ◽  
Binary Fluid ◽  
Localized Structures ◽  
Fluid Convection ◽  
Time Periodic ◽  
Conductive State

AbstractWe study spontaneous pattern formation and its asymptotic behaviour in binary fluid flow driven by a temperature gradient. When the conductive state is unstable and the size of the domain is large enough, finitely many spatially localized time-periodic travelling pulses (PTPs), each containing a certain number of convection cells, are generated spontaneously in the conductive state and are finally arranged at non-uniform intervals while moving in the same direction. We found that the role of PTP solutions and their strong interactions (collision) are important in characterizing the asymptotic state. Detailed investigations of pulse–pulse interactions showed the differences in asymptotic behaviour between that in a finite but large domain and in an infinite domain.

Chaotic Mixing: A Sure Way for Optimal Thermal Conditions?

2010 ◽  
Author(s):  
M. F. M. Speetjens
Keyword(s):  
Heat Transfer ◽  
Thermal State ◽  
Electronics Cooling ◽  
Thermal Conditions ◽  
Laminar Flows ◽  
Chaotic Mixing ◽  
Asymptotic State ◽  
Driven Cavity ◽  
Time Periodic

Chaotic fluid mixing is generally considered to enhance fluid-wall heat transfer and thermal homogenisation in laminar flows. However, this essentially concerns the transient stage towards a fully-developed (thermally-homogeneous) asymptotic state and then specifically for high Pe´clet numbers Pe (convective heat transfer dominates). The role of chaos in the asymptotic state at lower Pe, relevant to continuously-operating compact devices as, for instance, micro-electronics cooling systems, remains largely unexplored to date. The present study seeks to gain first insight into this matter by the analysis of a representative model problem: heat transfer in the 2D time-periodic lid-driven cavity flow induced via non-adiabatic walls. The asymptotic time-periodic thermal state is investigated in terms of both the temperature field and the thermal transport routes. This combined Eulerian-Lagrangian approach enables fundamental investigation of the connection between heat transfer and chaotic mixing and its ramifications for temperature distributions and heat-transfer rates. The analysis exposes a very different role of chaos in that its effectiveness for thermal homogenisation and heat-transfer enhancement is in low-Pe asymptotic states marginal at best. Here chaos may in fact locally amplify temperature fluctuations and thus hamper instead of promote thermal homogeneity. These findings reveal that optimal thermal conditions are not always automatic with chaotic mixing and may depend on a more delicate interplay between flow and heat-transfer mechanisms.

Initial and final behaviour of failure rate functions for mixtures and systems

2003 ◽  
Vol 40 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Rate Function ◽  
Coherent Systems ◽  
Failure Rate Function ◽  
Rate Functions ◽  
Limiting Behaviour

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

Characterization of dispersive chaos and related states of binary-fluid convection

1995 ◽  
Vol 85 (1-2) ◽  
pp. 165-224 ◽  
Author(s):  
Paul Kolodner ◽  
Said Slimani ◽  
Nadine Aubry ◽  
Ricardo Lima
Keyword(s):  
Binary Fluid ◽  
Fluid Convection

Onset of oscillatory binary fluid convection in finite containers

1999 ◽  
Vol 59 (6) ◽  
pp. 6730-6741 ◽  
Author(s):  
Oriol Batiste ◽  
Isabel Mercader ◽  
Marta Net ◽  
Edgar Knobloch
Keyword(s):  
Binary Fluid ◽  
Fluid Convection

scholarly journals Numerical Solution of Non-Newtonian Fluid Flow Due to Rotatory Rigid Disk

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 699 ◽  
Author(s):  
Khalil Ur Rehman ◽  
M. Y. Malik ◽  
Waqar A Khan ◽  
Ilyas Khan ◽  
S. O. Alharbi
Keyword(s):  
Brownian Motion ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Rotating Disk ◽  
Casson Fluid ◽  
Infinite Domain ◽  
Nanoparticles Concentration ◽  
Navier’S Slip ◽  
Local Sherwood Number

In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced above the rotating disk. The magnetized flow field is framed with Navier’s slip assumption. The Von Karman scheme is adopted to transform flow narrating equations in terms of reduced system. For better depiction a self-coded computational algorithm is executed rather than to move-on with build-in array. Numerical observations via magnetic, Lewis numbers, Casson, slip, Brownian motion, and thermophoresis parameters subject to radial, tangential velocities, temperature, and nanoparticles concentration are reported. The validation of numerical method being used is given through comparison with existing work. Comparative values of local Nusselt number and local Sherwood number are provided for involved flow controlling parameters.

Influence of through flow on binary fluid convection

2000 ◽  
Vol 61 (4) ◽  
pp. 3793-3810 ◽  
Author(s):  
P. Büchel ◽  
M. Lücke
Keyword(s):  
Binary Fluid ◽  
Through Flow ◽  
Fluid Convection

Asymptotic behaviour of solutions of Fisher–KPP equation with free boundaries in time-periodic environment

2019 ◽  
Vol 31 (3) ◽  
pp. 423-449
Author(s):  
JINGJING CAI ◽  
LI XU
Keyword(s):  
Free Boundary ◽  
Asymptotic Behaviour ◽  
Chemical Species ◽  
Free Boundaries ◽  
Periodic Functions ◽  
Kpp Equation ◽  
Periodic Environment ◽  
A Free Boundary Problem ◽  
Time Periodic ◽  
Asymptotic Spreading

We study a free boundary problem of the form: ut = uxx + f(t, u) (g(t) < x < h(t)) with free boundary conditions h′(t) = −ux(t, h(t)) – α(t) and g′(t) = −ux(t, g(t)) + β(t), where β(t) and α(t) are positive T-periodic functions, f(t, u) is a Fisher–KPP type of nonlinearity and T-periodic in t. This problem can be used to describe the spreading of a biological or chemical species in time-periodic environment, where free boundaries represent the spreading fronts of the species. We study the asymptotic behaviour of bounded solutions. There are two T-periodic functions α0(t) and α*(t; β) with 0 < α0 < α* which play key roles in the dynamics. More precisely, (i) in case 0 < β< α0 and 0 < α < α*, we obtain a trichotomy result: (i-1) spreading, that is, h(t) – g(t) → +∞ and u(t, ⋅ + ct) → 1 with $c\in (-\overline{l},\overline{r})$, where $ \overline{l}:=\frac{1}{T}\int_{0}^{T}l(s)ds$, $\overline{r}:=\frac{1}{T}\int_{0}^{T}r(s)ds$, the T-periodic functions −l(t) and r(t) are the asymptotic spreading speeds of g(t) and h(t) respectively (furthermore, r(t) > 0 > −l(t) when 0 < β < α < α0; r(t) = 0 > −l(t) when 0 < β < α = α0; $0 \gt \overline{r} \gt -\overline{l}$ when 0 < β < α0 < α < α*); (i-2) vanishing, that is, $\lim\limits_{t \to \mathcal {T}}h(t) = \lim\limits_{t \to \mathcal {T}}g(t)$ and $\lim\limits_{t \to \mathcal {T}}\max\limits_{g(t)\leq x\leq h(t)} u(t,x)=0$, where $\mathcal {T}$ is some positive constant; (i-3) transition, that is, g(t) → −∞, h(t) → −∞, $0<\lim\limits_{t \to \infty}[h(t)-g(t)] \lt +\infty$ and u(t, ⋅) → V(t, ⋅), where V is a T-periodic solution with compact support. (ii) in case β ≥ α0 or α ≥ α*, vanishing happens for any solution.

scholarly journals Implications of Nonlocal Transport and Conditionally Averaged Statistics on Monin–Obukhov Similarity Theory and Townsend’s Attached Eddy Hypothesis

2018 ◽  
Vol 75 (10) ◽  
pp. 3403-3431 ◽  
Author(s):  
Qi Li ◽  
Pierre Gentine ◽  
Juan Pedro Mellado ◽  
Kaighin A. McColl
Keyword(s):  
Similarity Theory ◽  
Turbulent Transport ◽  
Strong Interactions ◽  
Similarity Function ◽  
Convective Boundary ◽  
Structure Detection ◽  
Large Eddy ◽  
Attached Eddies ◽  
The Impact

According to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assumptions of Monin–Obukhov similarity theory (MOST). However, previous evidence seems to indicate that outer-scale eddies can impact the ASL, resulting in deviations from the classic MOST scaling. We conduct large-eddy simulations and direct numerical simulations of a dry convective boundary layer to investigate the impact of coherent structures on the ASL. A height-dependent passive tracer enables coherent structure detection and conditional analysis based on updrafts and subsidence. The MOST similarity functions computed from the simulation results indicate a larger deviation of the momentum similarity function ϕ m from classical scaling relationships compared to the temperature similarity function ϕ h. The conditional-averaged ϕ m for updrafts and subsidence are similar, indicating strong interactions between the inner and outer layers. However, ϕ h conditioned on subsidence follows the mixed-layer scaling, while its updraft counterpart is well predicted by MOST. Updrafts are the dominant contributors to the transport of momentum and temperature. Subsidence, which comprises eddies that originate from the outer layer, contributes increasingly to the transport of temperature with increasing instability. However, u′ of different signs are distributed symmetrically in subsidence unlike the predominantly negative θ′ as instability increases. Thus, the spatial patterns of u′ w′ differ compared to θ′ w′ in regions of subsidence. These results depict the mechanisms for departure from the MOST scaling, which is related to the stronger role of subsidence.

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