The presence of salt in seawater strongly affects the melt rate and the shape evolution of ice, both of utmost relevance in ice–ocean interactions and thus for the climate. To get a better quantitative understanding of the physical mechanics at play in ice melting in salty water, we numerically investigate the lateral melting of an ice block in stably stratified saline water. The developing ice shape from our numerical results shows good agreement with the experiments and theory from Huppert & Turner (J. Fluid Mech., vol. 100, 1980, pp. 367–384). Furthermore, we find that the melt rate of ice depends non-monotonically on the mean ambient salinity: it first decreases for increasing salt concentration until a local minimum is attained, and then increases again. This non-monotonic behaviour of the ice melt rate is due to the competition among salinity-driven buoyancy, temperature-driven buoyancy and salinity-induced stratification. We develop a theoretical model based on the force balance which gives a prediction of the salt concentration for which the melt rate is minimal, and is consistent with our data. Our findings give insight into the interplay between phase transitions and double-diffusive convective flows.

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to $Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to $Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wang et al. (Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

Immiscible and incompressible liquid–liquid flows are considered in a Taylor–Couette geometry and analysed by direct numerical simulations coupled with the volume-of-fluid method and a continuum surface force model. The system Reynolds number $Re \equiv r_i \omega _i d / \nu$ is fixed to $960$, where the single-phase flow is in the steady Taylor vortex regime, whereas the secondary-phase volume fraction $\varphi$ and the system Weber number $We \equiv \rho r_i^2 \omega _i^2 d / \sigma$ are varied to study the interactions between the interface and the Taylor vortices. We show that different Weber numbers lead to two distinctive flow regimes, namely an advection-dominated regime and an interface-dominated regime. When $We$ is high, the interface is easily deformed because of its low surface tension. The flow patterns are then similar to the single-phase flow, and the system is dominated mainly by advection (advection-dominated regime). However, when $We$ is low, the surface tension is so large that stable interfacial structures with sizes comparable to the cylinder gap can exist. The background velocity field is modulated largely by these persistent structures, thus the overall flow dynamics is governed by the interface (interface-dominated regime). The effect of the interface on the global system response is assessed by evaluating the Nusselt number $Nu_{\omega }$ based on the non-dimensional angular velocity transport. It shows non-monotonic trends as functions of the volume fraction $\varphi$ for both low and high $We$. We explain how these dependencies are closely linked to the velocity and interfacial structures.

We numerically investigate turbulent Rayleigh–Bénard convection with gas bubbles attached to the hot plate, mimicking a core feature in electrolysis, catalysis or boiling. The existence of bubbles on the plate reduces the global heat transfer due to the much lower thermal conductivity of gases as compared with liquids and changes the structure of the boundary layers. The numerical simulations are performed in three dimensions at Prandtl number $\mbox{Pr}=4.38$ (water) and Rayleigh number $10^7\leqslant \mbox{Ra}\leqslant 10^8$. For simplicity, we assume the bubbles to be equally sized and having pinned contact lines. We vary the total gas-covered area fraction $0.18 \leqslant S_0 \leqslant 0.62$, the relative bubble height $0.02\leqslant h/H \leqslant 0.05$ (where $H$ is the height of the Rayleigh–Bénard cell), the bubble number $40 \leqslant n \leqslant 144$ and their spatial distribution. In all cases, asymmetric temperature profiles are observed, which we quantitatively explain based on the heat flux conservation at each horizontal section. We further propose the idea of using an equivalent single-phase set-up to mimic the system with attached bubbles. Based on this equivalence, we can calculate the heat transfer. Without introducing any free parameter, the predictions for the Nusselt number, the upper and lower thermal boundary layer thicknesses and the mean centre temperature agree well with the numerical results. Finally, our predictions also work for the cases with much larger $\mbox{Pr}$ (e.g. $400$), which indicates that our results can also be applied to predict the mass transfer in water electrolysis with bubbles attached to the electrode surface or in catalysis.

We investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$, Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$. These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$, which occurs at $1/Ri=1.0$, is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$, we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity within the thermal BL. Additionally, we find that the domain size has a limited effect on the heat and momentum transfer in the sheared RB system as long as the domain can accommodate the small-scale convective structures at the thermal BL height, signifying that capturing the large-scale superstructures is not essential to obtain converged values of $Nu$ and shear Reynolds number $Re_{\tau }$. When the domain is smaller than these small-scale convective structures, the overall heat and momentum transfer reduces drastically.

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 that the passive scalar transport characterised by the Nusselt number $Nu$ scales as $Nu \sim Pr^{1/2}Re_{\tau }^{2}Re_b^{-1}$. We then use the well-established scaling for the friction coefficient $C_f \sim Re_b^{-1/4}$ (corresponding to a shear Reynolds number $Re_{\tau } \sim Re_b^{7/8}$) which holds reasonably well within the range $3\times 10^{3} \leqslant Re_b \leqslant 10^{5}$, to obtain $Nu \sim Pr^{1/2}Re_b^{3/4}$ for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges $81 \leqslant Re_b \leqslant 22361$ and $0.1 \leqslant Pr \leqslant 10$, finding good agreement. Analyses of the numerically obtained turbulent flow fields confirm logarithmic mean wall-parallel profiles of the velocity and the passive scalar in the inertial sublayer.

We perform direct numerical simulations to study the effect of the gravity centre offset in spherical Rayleigh–Bénard convection. When the gravity centre is shifted towards the south, we find that the shift of the gravity centre has a pronounced influence on the flow structures. At low Rayleigh number $Ra$, a steady-state large-scale meridional circulation induced by the baroclinic imbalance, created by the misalignment of the gravity potentials and isotherms, is formed. At high $Ra$, an energetic jet is created on the northern side of the inner sphere that is directed towards the outer sphere. The large-scale circulation induces a strong co-latitudinal dependence in the local heat flux. Nevertheless, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity centre offset.

We study the statistics of passive scalars at $Pr=1$, for turbulent flow within a smooth straight pipe of circular cross section up to $Re_{\tau } \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. While featuring a general organisation similar to the axial velocity field, passive scalar fields show additional energy at small wavenumbers, resulting in a higher degree of mixing and in a $k^{-4/3}$ spectral inertial range. The DNS results highlight logarithmic growth of the inner-scaled bulk and mean centreline scalar values with the friction Reynolds number, implying an estimated scalar von Kármán constant $k_{\theta } \approx 0.459$, which also nicely fits the mean scalar profiles. The DNS data are used to synthesise a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15 (12), 1972, pp. 2329–2351), which points to some shortcomings of the original formulation. Universality of the mean core scalar profile in defect form is recovered, with very nearly parabolic shape. Logarithmic growth of the buffer-layer peak of the scalar variance is found in the Reynolds number range under scrutiny, which well conforms with Townsend's attached-eddy hypothesis, whose validity is also supported by the spectral maps. The behaviour of the turbulent Prandtl number shows good universality in the outer wall layer, with values $Pr_t \approx 0.84$, as also found in previous studies, but closer to unity near the wall, where existing correlations do not reproduce the observed trends.

Moderate rotation and moderate horizontal confinement similarly enhance the heat transport in Rayleigh–Bénard convection (RBC). Here, we systematically investigate how these two types of flow stabilization together affect the heat transport. We conduct direct numerical simulations of confined-rotating RBC in a cylindrical set-up at Prandtl number $\textit {Pr}=4.38$, and various Rayleigh numbers $2\times 10^{8}\leqslant {\textit {Ra}}\leqslant 7\times 10^{9}$. Within the parameter space of rotation (given as inverse Rossby number $0\leqslant {\textit {Ro}}^{-1}\leqslant 40$) and confinement (given as height-to-diameter aspect ratio $2\leqslant \varGamma ^{-1}\leqslant 32$), we observe three heat transport maxima. At lower $ {\textit {Ra}}$, the combination of rotation and confinement can achieve larger heat transport than either rotation or confinement individually, whereas at higher $ {\textit {Ra}}$, confinement alone is most effective in enhancing the heat transport. Further, we identify two effects enhancing the heat transport: (i) the ratio of kinetic and thermal boundary layer thicknesses controlling the efficiency of Ekman pumping, and (ii) the formation of a stable domain-spanning flow for an efficient vertical transport of the heat through the bulk. Their interfering efficiencies generate the multiple heat transport maxima.

We numerically investigate turbulent Rayleigh–Bénard convection through two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $\mbox {Nu}$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $\mbox {Ra}=10^8$, Prandtl number $\mbox {Pr}=4.38$ and Weber number $\mbox {We}=5$. We vary the relative thickness of the upper layer between $0.01 \le \alpha \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 \le \lambda _k \le 10$. Two flow regimes are observed. In the first regime at $0.04\le \alpha \le 0.96$, convective flows appear in both layers and $\mbox {Nu}$ is not sensitive to $\alpha$. In the second regime at $\alpha \le 0.02$ or $\alpha \ge 0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $\mbox {Nu}$ is sensitive to $\alpha$. To predict $\mbox {Nu}$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann–Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $\mbox {Nu}$ and for the temperature at the interface agree well with our numerical results and previous experimental data.

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$. Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit {Ta}=6\times 10^5$) and we explain why.

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, using only $10\,\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\,\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is only of about $20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.

Indoor ventilation is essential for a healthy and comfortable living environment. A key issue is to discharge anthropogenic air contamination such as CO$_2$ gas or, of potentially more direct consequence, airborne respiratory droplets. Here, by employing direct numerical simulations, we study mechanical displacement ventilation with a wide range of ventilation rates $Q$ from 0.01 to 0.1 m$^3$ s$^{-1}$ person$^{-1}$. For this ventilation scheme, a cool lower zone is established beneath a warm upper zone with interface height $h$, which depends on $Q$. For weak ventilation, we find the scaling relation $h\sim Q^{3/5}$, as suggested by Hunt & Linden (Build. Environ., vol. 34, 1999, pp. 707–720). Also, the CO$_{2}$ concentration decreases with $Q$ within this regime. However, for too strong ventilation, the interface height $h$ becomes insensitive to $Q$, and the ambient averaged CO$_2$ concentration decreases towards the ambient value. At these values of $Q$, the concentrations of pollutants are very low and so further dilution has little effect. We suggest that such scenarios arise when the vertical kinetic energy associated with the ventilation flow is significant compared with the potential energy of the thermal stratification.

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$. This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$. For the considered parameter range $1\leq {Pr} \leq 100$, $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$, we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$, the heat flux is found to scale linearly with the friction velocity $V_\ast$. Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$, which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$, which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$, as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameters are the Péclet number $Pe$, which quantifies the ratio of the solutal advection rate to the diffusion rate, and the Schmidt number $Sc$, which is the ratio of viscosity and diffusivity. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for $Pe$ larger than $8{\rm \pi}$ mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger $Pe$, nonlinear terms become important. For $Pe > 16{\rm \pi}$, multiple concentration plumes are emitted from the catalytic plane, which eventually merge into a single larger one. When $Pe$ is even larger ($Pe \gtrsim 603$ for Schmidt number $Sc=1$), there are continuous emissions and merging events of the concentration plumes. The newly found flow states have different flow structures for different $Sc$: for $Sc\geqslant 1$, we observe the chaotic emission of plumes, but the fluctuations of concentration are only present in the region near the catalytic plane. In contrast, for $Sc<1$, chaotic flow motion occurs also in the bulk. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Péclet number again find continuous plume emission and plume merging, now leading to a chaotic motion of the phoretic particle. Our results thus help us to understand the experimentally observed chaotic motion of catalytic particles in the high $Pe$ regime.

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 $10^7\le Ra\le 10^{14}$ and a fixed Prandtl number $Pr=10$ in a two-dimensional convection cell with unit aspect ratio. It is found that the dependence of the mean vertical centre temperature gradient $S$ on $Ra$ shows three different regimes: in regime I ($Ra \lesssim 5\times 10^{10}$), $S$ is almost independent of $Ra$; in the newly identified regime II ($5\times 10^{10} \lesssim Ra \lesssim 10^{13}$), $S$ first increases with increasing $Ra$ (regime $\textrm {{II}}_a$), reaches its maximum and then decreases again (regime $\textrm {{II}}_b$); and in regime III ($Ra\gtrsim 10^{13}$), $S$ again becomes only weakly dependent on $Ra$, being slightly smaller than in regime I. The transition from regime I to regime II is related to the onset of unsteady flows arising from the ejection of plumes from the sidewall boundary layers. The maximum of $S$ occurs when these plumes are ejected over approximately half of the area (downstream) of the sidewalls. The onset of regime III is characterized by the appearance of layered structures near the top and bottom horizontal walls. The flow in regime III is characterized by a well-mixed bulk region owing to continuous ejection of plumes over large fractions of the sidewalls, and, as a result of the efficient mixing, the mean temperature gradient in the centre $S$ is smaller than that of regime I. In the three different regimes, significantly different flow organizations are identified: in regime I and regime $\textrm {{II}}_a$, the location of the maximal horizontal velocity is close to the top and bottom walls; however, in regime $\textrm {{II}}_b$ and regime III, banded zonal flow structures develop and the maximal horizontal velocity now is in the bulk region. The different flow organizations in the three regimes are also reflected in the scaling exponents in the effective power law scalings $Nu\sim Ra^\beta$ and $Re\sim Ra^\gamma$. Here, $Nu$ is the Nusselt number and $Re$ is the Reynolds number based on maximal vertical velocity (averaged over vertical direction). In regime I, the fitted scaling exponents ($\beta \approx 0.26$ and $\gamma \approx 0.51$) are in excellent agreement with the theoretical predictions of $\beta =1/4$ and $\gamma =1/2$ for laminar VC (Shishkina, Phys. Rev. E., vol. 93, 2016, 051102). However, in regimes II and III, $\beta$ increases to a value close to 1/3 and $\gamma$ decreases to a value close to 4/9. The stronger $Ra$ dependence of $Nu$ is related to the ejection of plumes and the larger local heat flux at the walls. The mean kinetic dissipation rate also shows different scaling relations with $Ra$ in the different regimes.

It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also buoyancy can play an important role at breakup. In order to better understand this role, here we numerically study two-dimensional Rayleigh–Bénard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5\leqslant We \leqslant 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 \leqslant \varLambda \leqslant 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $\varLambda$, two breakup types are observed. The first type occurs at small $\varLambda \ll 1$ (e.g. air–water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $\varLambda$ with roughly $0.5 < \varLambda \leqslant 1$ (e.g. oil–water systems): the layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types, the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results.

In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper, we report the results of direct numerical simulations of such sheared Rayleigh–Bénard convection, at fixed Rayleigh number $Ra=10^{6}$, varying the wall Reynolds number in the range $0 \leqslant Re_w \leqslant 4000$ and Prandtl number $0.22 \leqslant Pr \leqslant 4.6$, extending our prior work by Blass et al. (J. Fluid Mech., vol. 897, 2020, A22), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 \leqslant Ri \leqslant 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $Re_w$, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of $Re_w$ on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and $Pr$ numbers, we observe the emergence of a Prandtl–von Kármán log layer, signalling the onset of turbulent dynamics in the boundary layer.