Extraction of Plumes in Turbulent Thermal Convection

Abstract

We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence of the plume velocity and understand the results using the equations of motion. We further obtain the average local heat flux in the vertical direction at the cell center. Our result shows that heat is not mainly transported through the central region but instead through the regions near the sidewalls of the convection cell. where v is the velocity field, p the pressure divided by density, T the temperature field, andẑ is the unit vector in the vertical direction. Furthermore, δT = T − T 0 where T 0 is the mean temperature of the bulk fluid, g is the acceleration due to gravity and α, ν, and κ are respectively the volume expansion coefficient, kinematic viscosity and thermal diffusivity of the fluid. The state of fluid motion is characterized by the geometry of the cell and two dimensionless parameters: the Rayleigh number, Ra = αg∆L 3 /(νκ), which measures how much the fluid is driven and the Prandtl number, Pr = ν/κ, which is the ratio of the diffusivities of momentum and heat of the fluid. Here ∆ is the maintained temperature difference between the bottom and the top, and L is the height of the cell. When Ra is sufficiently large, the convective motion becomes turbulent. In turbulent convection, local velocity and temperature measurements taken at a point within the convection cell display complex fluctuations in time. On the other hand, visualization of the flow reveals recurring coherent structures. One prominent coherent structure is a plume, which is a mushroom-like flow generated by buoyancy. Thus at least two strategies can be employed to study turbulent thermal convection or turbulent flows in general. One is to analyze and understand the fluctuations of the local measurements. The other is to characterize the coherent structures and study and understand their dynamics. These two approaches are not independent but provide complementary knowledge of turbulent flows. In particular, there is the natural question of whether and how information about the coherent structures can be extracted from the local measurements.For turbulent flows not driven by buoyancy, various methods including proper orthogonal decomposition, conditional sampling and wavelet analysis have been proposed to identify coherent vortical structures from local velocity measurements [2]. On the other hand, much less work has been done in identifying plumes or extracting information about plumes in turbulent thermal convection [3,4,5]. Belmonte and Libchaber[3] used the skewness of the temperature derivative as a signature of the plumes. Zhou and Xia[4] associated the difference in the skewness of the positive and negative parts of the temperature difference with the presence of plumes and identified the plumes whenever the temperature difference becomes larger than a chosen threshold [6]. In Ref.[5], plu...

Plume emission statistics in turbulent Rayleigh–Bénard convection

“…the boundary layers are not yet turbulent, consistent with the theoretical expectation at Ra 10 12 (Grossmann & Lohse 2000, 2001Stevens et al 2013). Various methods for detecting plumes have been used previously, as reviewed by Ching et al (2004). We define a thermal plume as the set of coordinates P where θ (r, φ) − θ r,φ > cθ RMS and √ Ra Pr u z (r, φ)θ (r, φ) > c Nu, as Huang et al (2013) did in their study on confined RB convection.…”

“…In addition, the dynamics of the LSC is highly non-trivial (Brown, Nikolaenko & Ahlers 2005;Ahlers et al 2009;Sugiyama et al 2010), affecting the collective motion of the thermal plumes through an opposing pressure gradient. This complicates the simple (two-dimensional) picture of a stationary LSC with thermal plumes moving alongside it that was sketched by Kadanoff (2001) (see figure 1), as Ching et al (2004) and Emran & Schumacher (2012) have shown that plumes are found in the centre of the cell and even throughout the entire volume. Recently, Ostilla-Mónico et al (2014) found in a Taylor-Couette (TC) flow that the boundary layer transition from laminar to turbulent occurs in plume-ejecting locations at lower driving than in the wind-sheared region.…”

Physical and scale-by-scale analysis of Rayleigh–Bénard convection

“…It is generally assumed that the most prominent structure in turbulent convection is the so-called thermal plume, which can be defined as a localized portion of fluid having a temperature contrast with the background (Chillà & Schumacher 2012). Plumes are responsible for the transport of a large amount of heat across the convection cell (Shang et al 2003, and there are a lot of studies devoted to this subject (Ching et al 2004;Zhou, Sun & Xia 2007;Shishkina & Wagner 2008). The flow topology observed for the DNS at Ra = 1.7 × 10 5 is characterized by large and smooth plumes which emerge distinctly from the turbulent background.…”

New perspectives in turbulent Rayleigh-Bénard convection

“…Several criteria have been suggested which are based on thresholds of certain quantities. These could be the temperature [97], the vertical velocity [98] or the skewness of the temperature derivative [99]. Plume extraction is also possible by local measurement of the thermal dissipation rate [100].…”