# Olga Shishkina's research while affiliated with Max Planck Institute for Dynamics and Self-Organization and other places

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## Publications (171)

Rotation with thermally induced buoyancy governs many astrophysical and geophysical processes in the atmosphere, ocean, sun, and Earth's liquid-metal outer core. Rotating Rayleigh–Bénard convection (RRBC) is an experimental system that has features of rotation and buoyancy, where a container of height H and temperature difference Δ between its bott...

A scaling theory for the passive scalar transport in Couette flow, i.e. the flow between two parallel plates moving with different velocities, is proposed. This flow is determined by the bulk Reynolds number $Re_b$ and the Prandtl number $Pr$ . In the turbulent regime, for moderate shear Reynolds number $Re_{\tau }$ and moderate $Pr$ , we derive th...

This work addresses the effects of different thermal sidewall boundary conditions on the formation of flow states and heat transport in two- and three-dimensional Rayleigh–Bénard convection (RBC) by means of direct numerical simulations and steady-state analysis for Rayleigh numbers ${\textit {Ra}}$ up to $4\times 10^{10}$ and Prandtl numbers ${\te...

While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of...

Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number...

Streaming Dynamic Mode Decomposition (sDMD) is a low-storage version of dynamic mode decomposition (DMD), a data-driven method to extract spatiotemporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to...

Using direct numerical simulations, we study rotating Rayleigh-Bénard convection in a cylindrical cell with aspect ratio Γ=1/2, for Prandtl number 0.8, Ekman number 10−6, and Rayleigh numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode stat...

To study turbulent thermal convection, one often chooses a Rayleigh-Bénard flow configuration, where a fluid is confined between a heated bottom plate, a cooled top plate of the same shape, and insulated vertical sidewalls. When designing a Rayleigh-Bénard setup, for specified fluid properties under Oberbeck-Boussinesq conditions, the maximal size...

Using direct numerical simulations, we study rotating Rayleigh-B\'enard convection in a cylindrical cell for a broad range of Rayleigh, Ekman, and Prandtl numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode states that occur prior to the on...

Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. As example we pick the canonical Rayleigh-Bénard geometry, but now with the bottom plate temperature T b > 4 • C, the top plate temperature T t 4 • C, and the den...

Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting vs. plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-...

This work addresses the effect of travelling thermal waves applied at the fluid layer surface, on the formation of global flow structures in two-dimensional (2-D) and 3-D convective systems. For a broad range of Rayleigh numbers (10^3≤Ra≤10^7) and thermal wave frequencies (10^−4≤Ω≤10^0), we investigate flows with and without imposed mean temperatur...

Thermally driven vertical convection (VC)-the flow in a box heated on one side and cooled on the other side, is investigated using direct numerical simulations with Rayleigh numbers over the wide range of 10 7 ≤ Ra ≤ 10 14 and a fixed Prandtl number Pr = 10 in a two-dimensional convection cell with unit aspect ratio. It is found that the dependence...

Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting versus plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional...

Using a closed set of boundary layer equations [E. S. C. Ching et al., Phys. Rev. Research 1, 033037 (2019)] for turbulent Rayleigh-Bénard convection, we derive analytical results for the dependence of the heat flux, measured by the Nusselt number (Nu), on the Reynolds (Re) and Prandtl (Pr) numbers and two parameters that measure fluctuations in th...

Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. We chose the most relevant example, namely thermally driven flow of water with a temperature around $T_m\approx 4^\circ\rm{C}$, where it has its density maximum....

Vertical convection is investigated using direct numerical simulations over a wide range of Rayleigh numbers $10^7\le Ra\le10^{14}$ with fixed Prandtl number $Pr=10$, in a two-dimensional convection cell with unit aspect ratio. It is found that the dependence of the mean vertical centre temperature gradient $S$ on $Ra$ shows three different regimes...

We offer a unifying theory for turbulent purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for Rayleigh--B\'enard turbulence and of Shishkina, Grossmann and Lohse (2016) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in...

Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency f) on global transport properties has hardly been studied. Here, we perform numerical simulations of Rayleigh-Benard convection with time periodic modulation in the temperat...

Tenacious wall states in thermal convection in rapidly rotating containers - Volume 898 - Olga Shishkina

Recently, in Zhang et al. (2020), it was found that in rapidly rotating turbulent Rayleigh--B\'enard convection (RBC) in slender cylindrical containers (with diameter-to-height aspect ratio $\Gamma=1/2$) filled with a small-Prandtl-number fluid ($Pr \approx0.8$), the Large Scale Circulation (LSC) is suppressed and a Boundary Zonal Flow (BZF) develo...

This work addresses the effect of travelling thermal waves applied at the fluid layer surface, on the formation of global flow structures in 2D and 3D convective systems. For a broad range of Rayleigh numbers ($10^3\leq Ra \leq 10^7$) and thermal wave frequencies ($10^{-4}\leq \Omega \leq 10^{0}$), we investigate flows with and without imposed mean...

Wall-bounded turbulent flows can take different statistically stationary turbulent states, with different
transport properties, even for the very same values of the control parameters. What state the system takes
depends on the initial conditions. Here we analyze the multiple states in large-aspect ratio (Γ) twodimensional
turbulent Rayleigh-B´enar...

The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh-Bénard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each...

Classical and symmetrical horizontal convection: detaching plumes and oscillations - Volume 892 - Philipp Reiter, Olga Shishkina

Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through...

Recent findings suggest that wall-bounded turbulent flow can take different statistically stationary turbulent states, with different transport properties, even for the very same values of the control parameters. What state the system takes depends on the initial conditions. Here we analyze the multiple states in large-aspect ratio ($\Gamma$) two-d...

Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency $f$) on global transport properties has hardly been studied. Here, we perform numerical simulations of Rayleigh-B\'enard (RB) convection with time periodic modulation in the...

For rapidly rotating turbulent Rayleigh--B\'enard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of...

Turbulent Rayleigh-B\'enard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and mome...

The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection - Volume 884 - Lukas Zwirner, Ruslan Khalilov, Ilya Kolesnichenko, Andrey Mamykin, Sergei Mandrykin, Alexander Pavlinov, Alexander Shestakov, Andrei Teimurazov, Peter Frick, Olga Shishkina

Natural convection in cylindrical containers with isothermal ring-shaped obstacles - Volume 882 - Mohammad S. Emran, Olga Shishkina

For rapidly rotating turbulent Rayleigh--B\'enard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of...

In turbulent Rayleigh-Bénard convection, the boundary layers are nonsteady with fluctuations, the time-averaged large-scale circulating velocity vanishes far away from the top and bottom plates, and the motion arises from buoyancy. In this paper, we derive the full set of boundary layer equations for both the temperature and velocity fields from th...

In turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surface roughness, the scaling exponent $\unicode[STIX]{x1D6FD}$ in the relationship between the Nusselt number $Nu$ and the Rayleigh number $Ra$ , $Nu\sim Ra^{\unicode[STIX]{x1D6FD}}$ can be ${\approx}1/2$ locally, provided that $Ra$ is large enough to ensure that the thermal b...

Inclined turbulent thermal convection by large Rayleigh numbers in extremely small-Prandtl-number fluids is studied based on results of both, measurements and high-resolution numerical simulations. The Prandtl number $Pr\approx0.0093$ considered in the experiments and the Large-Eddy Simulations (LES) and $Pr=0.0094$ considered in the Direct Numeric...

Any tilt of a Rayleigh–Bénard convection cell against gravity changes the global flow structure inside the cell, which leads to a change of the heat and momentum transport. Especially sensitive to the inclination angle is the heat transport in low-Prandtl-number fluids and confined geometries. The purpose of the present work is to investigate the g...

We critically analyse the different ways to evaluate the dependence of the Nusselt number ( $\mathit{Nu}$ ) on the Rayleigh number ( $\mathit{Ra}$ ) in measurements of the heat transport in turbulent Rayleigh–Bénard convection under general non-Oberbeck–Boussinesq conditions and show the sensitivity of this dependence to the choice of the reference...

Computational codes for direct numerical simulations of Rayleigh–Bénard (RB) convection are compared in terms of computational cost and quality of the solution. As a benchmark case, RB convection at Ra=10⁸ and Pr=1 in a periodic domain, in cubic and cylindrical containers is considered. A dedicated second-order finite-difference code (AFID/RBFLOW)...

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-B\'enard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh number $Ra$ fixed at $10^8$. The width-to-height asp...

To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation has to be solved. Starting from a thermal BL equation that takes into account fluctuations in terms of an eddy thermal diffusivity [Shishkina et al., Phys. Rev. Lett. 114 (2015)], we make use of the idea of Prandtl's mixing length mode...

In this study we follow Grossmann and Lohse, Phys. Rev. Lett. 86 (2001), who derived various scalings regimes for the dependence of the Nusselt number $Nu$ and the Reynolds number $Re$ on the Rayleigh number $Ra$ and the Prandtl number $Pr$. We focus on theoretical arguments as well as on numerical simulations for the case of large-$Pr$ natural the...

We discuss three classical paradigmatic systems of thermally driven flows: Rayleigh–Bénard convection, where a fluid is confined between a heated bottom plate and a cooled top plate, horizontal convection, where the fluid is heated at one part of the bottom and cooled at some other part, and vertical convection, where the fluid is confined between...

We investigate the effect of fluctuations in thermal boundary layer on heat transfer in turbulent Rayleigh–Bénard convection for Prandtl number greater than one in the regime where the thermal dissipation rate is dominated by boundary layer contribution and in the presence of a large-scale circulating flow.

We analyse the global flow structures in horizontal convection systems, where the heat supply and removal takes place through separated parts of a lower horizontal surface of a fluid layer. The results are based on direct numerical simulations for the length-to-height aspect ratio of the convection cell $\unicode[STIX]{x1D6E4}=10$ , Rayleigh number...

We propose a recipe to calculate accurately the Nusselt number Nu in turbulent Rayleigh-Bénard convection, using the measured total heat flux q and known parameters of the fluid and convection cell. More precisely, we present a method to compute the conductive heat flux q̂, which is a normalization of q in the definition of Nu, for conditions where...

We derive the dependence of the Reynolds number Re and the Nusselt number Nu on the Rayleigh number Ra and the Prandtl number Pr in laminar vertical convection (VC), where a fluid is confined between two differently heated isothermal vertical walls. The boundary layer equations in laminar VC yield two limiting scaling regimes: Nu∼Pr1/4Ra1/4, Re∼Pr−...

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle
${\it\beta}$
,
$0\leqslant {\it\beta}\leqslant {\rm\pi}/2$
, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number
$\mathit{Nu}$
and Reynolds number
$\mathit{Re}$
. The considered Rayleigh numbers
$\mathit{Ra}$
range from...

In a horizontal convection (HC) system heat is supplied and removed exclusively through a single, top, or bottom, surface of a fluid layer. It is commonly agreed that in the studied Rayleigh number (Ra) range, the convective heat transport, measured by the Nusselt number, follows the Rossby (1965) scaling, which is based on the assumptions that the...

We report the Prandtl-number (Pr) and Rayleigh-number (Ra) dependencies of the Reynolds number (Re) and mean convective heat transport, measured by the Nusselt number (Nu), in horizontal convection (HC) systems, where the heat supply and removal are provided exclusively through a lower horizontal surface of a fluid layer. For laminar HC, we find th...

We report a new thermal boundary layer equation for turbulent Rayleigh–Bénard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean tempe...

Direct numerical simulations (DNS) of turbulent thermal convection in a boxed-shaped domain with rough heated bottom and cooled top surfaces are conducted for Prandtl number Pr=0.786 and Rayleigh numbers Ra between 10e6 and 10e8. The surface roughness is introduced by 4 parallelepiped equidistantly distributed obstacles attached to the bottom plate...

We consider rotating Rayleigh–Bénard convection of a fluid with a Prandtl number of \$\mathit{Pr}=0.8\$ in a cylindrical cell with an aspect ratio \${\it\Gamma}=1/2\$. Direct numerical simulations (DNS) were performed for the Rayleigh number range \$10^{5}\leqslant \mathit{Ra}\leqslant 10^{9}\$ and the inverse Rossby number range \$0\leqslant 1/\ma...

As a simplified model of a large class of convective processes, Rayleigh-Bénard convection (RBC) enables fundamental and numerical studies of convection including Direct Numerical Simulations (DNS). Although it has been investigated for more than 100 years there are still many open questions including the influence of the geometrical characteristic...

We report a new thermal boundary layer equation for turbulent Rayleigh-Benard
convection for Prandtl number Pr>1 that takes into account the effect of
turbulent fluctuations. These fluctuations are neglected in existing equations,
which are based on steady-state and laminar assumptions. Using this new
equation, we derive analytically the mean tempe...

Rotating Rayleigh-Benard convection in water is studied in direct numerical simulations, where the temperature dependence of the viscosity, the thermal conductivity, and the density within the buoyancy term is taken into account. In all simulations, the arithmetic mean of the lowest and highest temperature in the system equals 40 degrees C, corresp...

We consider rotating Rayleigh-B\'enard convection of a fluid with a Prandtl
number of $Pr = 0.8$ in a cylindrical cell with an aspect ratio $\Gamma = 1/2$.
Direct numerical simulations were performed for the Rayleigh number range $10^5
\leq Ra \leq 10^9$ and the inverse Rossby number range $0 \leq 1/Ro \leq 20$.
We propose a method to capture regim...

We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers Pr as functions of the angle β between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we...

The key requirement for setting up a direct numerical simulation (DNS) is a sufficiently fine grid allowing to resolve locally all relevant micro-scales. In case of turbulent Rayleigh-Bénard convection (RBC) this is usually done by fulfilling different analytically derived criteria for the boundary layers and the bulk flow. In order to analyse if t...

Direct numerical simulations (DNS) of Rayleigh-Bénard convection in a cube and a cylinder with equal diameter and height are performed to investigate the main responses of the system, namely heat flux and motion. Differences in the latter two quantities for the two geometries suggest a transition between different flow states in the cube, which is...

We report on a numerical study of the aspect-ratio dependency of Rayleigh-Bénard convection, using direct numerical simulations. The investigated domains have equal height and width while the aspect ratio Γ of depth per height is varied between 1/10 and 1. The Rayleigh numbers Ra for this study variate between 105 and 109, while the Prandtl number...

To approximate the velocity and temperature within the boundary layers in turbulent thermal convection at moderate Rayleigh numbers, we consider the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a non-zero-pressure-gradient case. This ansatz takes into account the influence of the angle of attack β of the large-scale...

To study the classical problem of Rayleigh-Bénard convection, i.e. a fluid layer confined between a heating-plate at the bottom and a cooling-plate at the top, a common assumption is that all material properties are temperature independent, except for the density ρ within the buoyancy part, that changes like

Recently, there has been a surge of interest from the industry in unsteady turbulent flows computations. Most of the Computational Fluid Dynamics (CFD) methods employed so far proceed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations that are based on semi-empirical turbulence models. It is well known, however, that the RANS-based com...

Recently, there has been a surge of interest from the industry in unsteady turbulent flows computations. Most of the Computational Fluid Dynamics (CFD) methods employed so far proceed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations that are based on semi-empirical turbulence models. It is well known, however, that the RANS-based com...

In the present work experimental and numerical investigations of the large-scale structures of isothermal air flow in a highly simplified model room are reported and discussed. We compare the measured velocity distribution with direct numerical simulations (DNSs) for the reference Reynolds number Reref 2.4 104, which is based on the maximum inlet v...

We perform Direct Numerical Simulations of rotating turbulent Rayleigh–Bénard convection in water, assuming that the material properties are either constant (Oberbeck–Boussinesq conditions) or vary with temperature (non-Oberbeck–Boussinesq conditions). One of the most remarkable features of rotating Rayleigh–Bénard convection in is the generation o...

Turbulent Rayleigh-Bénard convection of water is studied by means of three-dimensional Direct Numerical Simulations. The generated flow fields are analysed with respect to deviations from the Oberbeck-Boussinesq case. For this purpose simulations in a cylindrical domain with various temperature differences between the plates are performed. We obtai...

We present investigations on the motion of the large-scale circulations (LSCs) in turbulent mixed convection in a cuboidal
cavity. The experimental studies are performed by combined temperature and velocity measurements. Analysis of temperature measurements in previous studies revealed three different dynamical scenarios: stable LSCs, LSCs with
spo...

To approximate main flow characteristics like the velocity or temperature within the boundary layers which appear in turbulent thermal convection at moderate Rayleigh numbers (up to 10^14), one can use the Falkner–Skan boundary layer equations, which are obtained through a generalization of the Prandtl–Blasius ansatz to a non-zero-pressure-gradient...

To approximate main flow characteristics like the velocity or temperature within the boundary layers which appear in turbulent thermal convection at moderate Rayleigh numbers (up to 10^14), one can use the Falkner–Skan boundary layer equations, which are obtained through a generalization of the Prandtl–Blasius ansatz to a non-zero-pressure-gradient...

We construct a low-dimensional model (LDM) of turbulent mixed convection in a Cartesian cell with in-and outlets and local sources of heat which is narrow in one of the two horizontal space directions. The basis is a high-resolution three-dimensional direct numerical simulation (DNS) record. The model is derived with basis functions, which have bee...

The influence of non-Oberbeck-Boussinesq (NOB) effects on Rayleigh-Bénard convection in liquids is investigated by means of three-dimensional direct numerical simulations (DNS). For this purpose the impact of temperature dependent material properties is studied in water with a Prandtl number of Pr = 4.38 within a range of Rayleigh numbers of 10^7 ≤...

The influence of non-Oberbeck-Boussinesq (NOB) effects on Rayleigh-Bénard convection in liquids is investigated by
means of three-dimensional direct numerical simulations (DNS). For this purpose the impact of temperature dependent material properties is studied in water with a Prandtl number of Pr = 4.38 within a range of Rayleigh numbers of 10^7 ≤...

By means of direct numerical simulations (DNS), we investigate instantaneous and statistical characteristics of turbulent mixed convection in parallelepiped convective cells with heated parallelepiped obstacles inside. Cold air enters the cell through thin ducts located at the side walls close to the top, and warmer air leaves the cell through the...

We analyse the wind and boundary layer properties of turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio one for Prandtl number Pr = 0.786 and Rayleigh numbers (Ra) up to 10^9 by means of highly resolved direct numerical simulations. We identify time periods in which the orientation of the large scale circulation (LSC)...

Recently, there has been a surge of interest from the industry in unsteady turbulent flows computations. Most of the Computational Fluid Dynamics (CFD) methods employed so far proceed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations that are based on semi-empirical turbulence models. It is well known, however, that the RANS-based com...

Highly resolved direct numerical simulations (DNS) of turbulent Rayleigh-Benard convection in a cylindrical container with aspect ratio unity and Prandtl number Pr=0.786 have been performed for Rayleigh numbers Ra up to 10e9. The key ingredient for setting up a DNS is a sufficiently fine grid allowing to resolve the
the local Kolmogorov scales. Usu...

Direct numerical
simulations (DNS) of Rayleigh-Bénard convection in a cube and a cylinder with equal diameter and height are performed to investigate the main responses of the system, namely heat flux and motion. Differences in the latter two quantities for the two geometries suggest a transition between different flow states in the cube, which is...

The influence of temperature-dependent material properties on Rayleigh–Bénard convection is investigated in three different liquids, ranging from a very small Prandtl number for mercury with Pr = 0.0232, over a moderate one for water with Pr = 4.38, to a very large one for glycerol with Pr = 2548. For this purpose, three-dimensional direct numerica...