arXiv subjects

Herman J. H. Clercx

Publications and source records attributed to Herman J. H. Clercx.

At least 37 records · Page 2Linked to original sources

arXiv2019

Sharp transitions in rotating turbulent convection: Lagrangian acceleration statistics reveal a second critical Rossby number

In RB convection for fluids with Prandtl number $Pr\gtrsim 1$, rotation beyond a critical (small) rotation rate is known to cause a sudden enhancement of heat transfer which can be explained by a change in the character of the BL dynamics near the top and bottom plates of the convection cell. Namely, with increasing rotation rate, the BL signature suddenly changes from Prandtl--Blasius type to Ekman type. The transition from a constant heat transfer to an almost linearly increasing heat transfer with increasing rotation rate is known to be sharp and the critical Rossby number $Ro_{c}$ occurs typically in the range $2.3\lesssim Ro_{c}\lesssim 2.9$ (for Rayleigh number $Ra=1.3\times 10^9$, $Pr=6.7$, and a convection cell with aspect ratio $Γ=\frac{D}{H}=1$, with $D$ the diameter and $H$ the height of the cell). The explanation of the sharp transition in the heat transfer points to the change in the dominant flow structure. At $1/Ro\lesssim 1/Ro_c$ (slow rotation), the well-known LSC is found: a single domain-filling convection roll made up of many individual thermal plumes. At $1/Ro\gtrsim 1/Ro_c$ (rapid rotation), the LSC vanishes and is replaced with a collection of swirling plumes that align with the rotation axis. In this paper, by numerically studying Lagrangian acceleration statistics, related to the small-scale properties of the flow structures, we reveal that this transition between these different dominant flow structures happens at a second critical Rossby number, $Ro_{c_2}\approx 2.25$ (different from $Ro_{c_1}\approx 2.7$ for the sharp transition in the Nusselt number $Nu$; both values for the parameter settings of our present numerical study). When statistical data of Lagrangian tracers near the top plate are collected, it is found that the root-mean-square (rms) values and the kurtosis of the horizontal acceleration of these tracers show a sudden increase at $Ro_{c_2}$.

physics.flu-dyn↗

arXiv2019

Statistical properties of thermally expandable particles in soft Rayleigh-Benard convection

The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS). We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes' force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, $τ_T$, and the thermal expansion coefficient of particles relative to that of the fluid, $K = α_p / α_f$. In particular, the residence time is constant for small thermal response times, $τ_T \lesssim 1$, and increasing with $τ_T$ for larger thermal response times, $τ_T \gtrsim 1$. Also, the thermal BL residence time is increasing with decreasing $K$. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with $τ_T$ for larger response times, thus explaining the trends in the DNS data well.

cond-mat.soft↗

arXiv2017

Frontiers of chaotic advection

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.

nlin.CD↗

arXiv2016

The effect of finger spreading on drag of the hand in human swimming

The effect of finger spreading on hydrodynamic drag in swimming is studied both with a numerical simulation and with laboratory experiments. Both approaches are based on the exact same 3D model of the hand with attached forearm. The virtual version of the hand with forearm was implemented in a numerical code by means of an immersed boundary method and the physical version was studied in a wind tunnel experiment. An enhancement of the drag coefficient of 2 and 5% compared to the case with closed fingers was found for the numerical simulation and experiment, respectively. A 5 and 8% favourable effect on the (dimensionless) force moment at an optimal finger spreading of 10 degrees was found, which indicates that the difference is more outspoken in the force moment. Also an analytical model is proposed, using scaling arguments similar to the Betz actuator disk model, to explain the drag coefficient as a function of finger spacing.

physics.flu-dyn↗

arXiv2016

Finite-size effects on bacterial population expansion under controlled fow conditions

The expansion of biological species in natural environments is usually described as the combined effect of individual spatial dispersal and growth. In the case of aquatic ecosystems flow transport can also be extremely relevant as an extra, advection induced, dispersal factor. There is a lack of reproducible experimental studies on biological fronts of living organisms in controlled streaming habitats. It is thus not clear if, and to which extent, the current theoretical and experimental knowledge on advective-reactive-diffusive fronts for chemical reactions can also apply to the expansion of biological populations. We designed and assembled a dedicated microfluidic device to control and quantify the expansion of populations of $E.coli$ bacteria under both co-flowing and counter-flowing conditions, measuring the front speed at varying intensity of the imposed flow. At variance with respect to the case of autocatalytic reactions, we measure that almost irrespective of the counter-flow velocity, the front speed remains finite at a constant positive value. A simple model incorporating growth, dispersion and drift on finite-size hard beads allows to explain this finding as due to a finite volume effect of the bacteria. This indicates that models based on the Fisher-Kolmogorov-Petrovsky-Piscounov equation (FKPP) that ignore the finite size of organisms may be inaccurate to describe the physics of spatial growth dynamics of bacteria.

physics.bio-ph↗

arXiv2015

Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale, that maximizes the clustering of the particles.

physics.flu-dyn↗

arXiv2013

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $Ω$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $Ω=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_λ\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($Ω\lesssim 0.2$ rad/s) to quasi-2D turbulence ($Ω\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.

physics.flu-dyn↗

arXiv2013

Lagrangian acceleration of passive tracers in statistically-steady rotating turbulence

The statistical properties of the Lagrangian acceleration vector of passive tracers in statistically-steady rotating turbulence is studied by Particle Tracking Velocimetry. Direct effects of the background rotation are the suppression of high-acceleration events parallel to the (vertical) rotation axis, the enhancement of high-acceleration events for the horizontal acceleration, and the strong amplification of the auto-correlation of the acceleration component perpendicular to both the rotation vector Ω and local velocity vector u. The auto-correlation of the acceleration component in the plane set up by Ω and u is only mildly enhanced.

physics.flu-dyn↗

arXiv2013

Lagrangian velocity auto-correlations in statistically-steady rotating turbulence

Lagrangian statistics of passive tracers in rotating turbulence is investigated by Particle Tracking Velocimetry. A confined and steadily-forced turbulent flow is subjected to five different rotation rates. The PDFs of the velocity components clearly reveal the anisotropy induced by background rotation. Although the statistical properties of the horizontal turbulent flow field are approximately isotropic, in agreement with previously reported results by van Bokhoven and coworkers [Phys. Fluids 21, 096601 (2009)], the velocity component parallel to the (vertical) rotation axis gets strongly reduced (compared to the horizontal ones) while the rotation is increased. The auto-correlation coefficients of all three components are progressively enhanced for increasing rotation rates, although the vertical one shows a tendency to decrease for slow rotation rates. The decorrelation is approximately exponential. Lagrangian data compare favourably with previously reported Eulerian data for horizontal velocity components, but show different behaviour for the vertical velocity components at higher rotation rates.

physics.flu-dyn↗

arXiv2013

Spinodal decomposition in homogeneous and isotropic turbulence

We study the competition between domain coarsening in a symmetric binary mixtures below the critical temperature and turbulent fluctuations. We find that the coarsening process is arrested in presence of turbulence. The physics of the process shares remarkable similarities with the behaviour of diluted turbulent emulsions and the arrest length scale can be estimated with an argument similar to the one proposed by Kolmogorov and Hinze for the maximal stability diameter of droplets in turbulence. Although in the absence of flow the microscopic diffusion constant is negative, turbulence does effectively arrest the inverse cascade of concentration fluctuations by making the low wavelength diffusion constant positive for scales above the Hinze length.

physics.flu-dyn↗

arXiv2012

Breakdown of the large-scale wind in Γ=1/2 rotating Rayleigh-Bénard flow

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically-aligned vortices at strong rotation. For a sample with an aspect ratio Γ= D/L = 1 (D is the sample diameter and L its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for Γ= 1/2 Weiss and Ahlers [J. Fluid Mech. {\bf{688}}, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid, while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for Γ= 1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically-aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and non-trivial difference with the Γ=1 sample, where the vertically-aligned vortices are distributed randomly.

physics.flu-dyn↗

arXiv2011

The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-Bénard convection

When the classical Rayleigh-Bénard (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 $Ra \sim 10^8-10^9$ ($Pr=4-6$) and $0 \lesssim 1/Ro \lesssim 25$ 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.

physics.flu-dyn↗

arXiv2011

Effect of Plumes on Measuring the Large Scale Circulation in Turbulent Rayleigh-Bénard Convection

We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Γ=D/L=1/2 and Γ=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Γ=1 sample at $Ra=1\times10^8$ and $5\times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Γ=1/2 sample with $Pr=0.7$ at $Ra=1\times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1\times10^8$ we find that this relative LSC strength is significantly lower in a Γ=1/2 sample than in a Γ=1 sample, reflecting that the LSC is much more pronounced in a Γ=1 sample than in a Γ=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.

physics.flu-dyn↗

arXiv2011

Effect of aspect-ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

Numerical and experimental data for the heat transfer as function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for Prandtl number Pr=4.38 and Rayleigh number $Ra=2.91\times10^8$ up to $Ra=4.52\times10^9$. The aspect ratio Γ= D/L, where L is the height and D the diameter of the cylindrical sample, is varied between Γ=0.5 and Γ=2.0. Without rotation, where the aspect ratio influences the global large scale circulation, we see a small aspect-ratio dependence in the Nusselt number for $Ra=2.91\times10^8$. However, for stronger rotation, i.e. $1/Ro \gg 1/Ro_c$, the heat transport becomes independent of the aspect-ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically-aligned vortices. Since the vertically-aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when $1/Ro \gg 1/Ro_c$. In agreement with the results of Weiss et al. Phys. Rev. Lett., vol 105, 224501 (2010) we find a vortex-depleted area close to the sidewall. Here, we in addition show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.

physics.flu-dyn↗

arXiv2011

Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection

In turbulent thermal convection in cylindrical samples of aspect ratio Γ= D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman vortices that extract additional fluid out of thermal boundary layers at the top and bottom. We show from experiments and direct numerical simulations that the enhancement occurs only above a bifurcation point at a critical inverse Rossby number $1/\Ro_c$, with $1/\Ro_c \propto 1/Γ$. We present a Ginzburg-Landau like model that explains the existence of a bifurcation at finite $1/\Ro_c$ as a finite-size effect. The model yields the proportionality between $1/\Ro_c$ and $1/Γ$ and is consistent with several other measured or computed system properties.

physics.flu-dyn↗

arXiv2010

Boundary layers in rotating weakly turbulent Rayleigh-Benard convection

The effect of rotation on the boundary layers (BLs) in a Rayleigh-Benard (RB) system at a relatively low Rayleigh number, i.e. $Ra = 4\times10^7$, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann-Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation $Ro\gtrsim 1$. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger $Ra \gtrsim 10^8$ by Stevens {\it{et al.}} [Phys. Rev. Lett. {\bf{103}}, 024503, 2009], although only a small shift in the Ra-Ro-Pr phase space is involved.

physics.flu-dyn↗

arXiv2009

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.

physics.flu-dyn↗

arXiv2009

Transitions between turbulent states in rotating Rayleigh-Benard convection

Weakly-rotating turbulent Rayleigh-Benard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number an abrupt transition from a turbulent state with nearly rotation-independent heat transport to another turbulent state with enhanced heat transfer is observed at a critical inverse Rossby number $1/Ro_c \simeq 0.4$. Whereas for $1/Ro < 1/Ro_c$ the strength of the large-scale convection-roll is either enhanced or essentially unmodified depending on parameters, its strength is increasingly diminished beyond $1/Ro_c$ where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.

physics.flu-dyn↗