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Abstract: The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free-slip), about one half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is send to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on "slippery" or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet-droplet collisions) and for impacts on no-slip surfaces.

Abstract: Here we study the heat/mass transfer effects on revolving flow of Maxwell fluid due to unidirectional stretching surface. Mass transfer process is modeled in terms of binary chemical reaction and activation energy. Modified Arrhenius function for activation energy is invoked. Traditional boundary layer approximations are utilized to simplify the governing equations. Using similarity method, self-similar form of boundary layer equations are derived which are solved numerically. The solutions depend on dimensionless numbers such as the rotation parameter λ , the Deborah number β , the Prandtl number Pr , the Schmidt number Sc , activation energy E , fitted rate constant n and temperature difference parameter δ . We found that the solute concentration in binary mixture is proportional to both rotation parameter λ and activation energy E . The reaction rate σ and fitted rate n both provide reduction in the solute concentration. Thermal boundary layer becomes thicker and heat transfer rate diminishes when fluid is subjected to a larger rotation rate.

Abstract: In the present article, the problem of boundary layer flow of MHD electrically conducting fluid past a cone and a wedge with non-uniform heat source/sink along with Cattaneo-Christov heat flux is investigated numerically. At first, the flow equations are converted into ODE via appropriate self similarity transforms and the resulting equations are solved with the assistance of R.-K. and Newton’s methods. The influence of several dimensionless parameters on velocity and temperature fields in addition to the friction factor and reduced heat transfer coefficient has been examined with the support of graphs and numerical values. The heat transfer phenomenon in the flow caused by the cone is excessive when compared to the wedge flow. Also, the thermal and momentum boundary layers are not the same for the flow over a cone and wedge.

Abstract: Most of the ocean kinetic energy is contained in the large scale currents and the vigorous geostrophic eddy field, at horizontal scales of order 100 km. To achieve equilibrium the geostrophic currents must viscously dissipate their kinetic energy at much smaller scale. However, geostrophic turbulence is characterized by an inverse cascade of energy towards larger scale, and the pathways of energy toward dissipation are still in question. Here, we present a mechanism, in the context of the Gulf Stream, where energy is transferred from the geostrophic flow to submesoscale wakes through anticyclonic vertical vorticity generation in the bottom boundary layer. The submesoscale turbulence leads to elevated local dissipation and mixing outside the oceanic boundary layers. This process is generic for boundary slope currents that flow in the direction of Kelvin wave propagation. Topographic generation of submesoscale flows potentially provides a new and significant route to energy dissipation for geostrophic flows.

Abstract: We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as , where is the spatially/temporally averaged fluid velocity, is the wall normal distance, represents the height of the roughness elements and is the velocity at . The attenuation factor depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman–Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter , wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between ‘ ’ and ‘ ’ type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

Abstract: Rapid vertical transport of small aerosol particles from the free troposphere to the atmospheric boundary layer occurs during precipitation and maintains the population of aerosol particles over Amazonia. The Amazon rainforest is one of the few continental regions where atmospheric aerosol processes can be studied under near-natural conditions, but the origin of small aerosol particles that grow into cloud condensation nuclei in the Amazon boundary layer remains poorly understood. This paper reports rapid vertical transport of small aerosol particles from the free troposphere into the boundary layer during precipitation events by strong convective downdrafts and weaker downward motions in the trailing stratiform region. This effect can help to maintain the population of aerosol particles in the pristine Amazon boundary layer, so may influence cloud properties and climate under natural conditions. The nucleation of atmospheric vapours is an important source of new aerosol particles that can subsequently grow to form cloud condensation nuclei in the atmosphere1. Most field studies of atmospheric aerosols over continents are influenced by atmospheric vapours of anthropogenic origin (for example, ref. 2) and, in consequence, aerosol processes in pristine, terrestrial environments remain poorly understood. The Amazon rainforest is one of the few continental regions where aerosol particles and their precursors can be studied under near-natural conditions3,4,5, but the origin of small aerosol particles that grow into cloud condensation nuclei in the Amazon boundary layer remains unclear6,7,8. Here we present aircraft- and ground-based measurements under clean conditions during the wet season in the central Amazon basin. We find that high concentrations of small aerosol particles (with diameters of less than 50 nanometres) in the lower free troposphere are transported from the free troposphere into the boundary layer during precipitation events by strong convective downdrafts and weaker downward motions in the trailing stratiform region. This rapid vertical transport can help to maintain the population of particles in the pristine Amazon boundary layer, and may therefore influence cloud properties and climate under natural conditions.

Abstract: The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Gortler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.

Abstract: Structural properties of regions of uniform streamwise momentum in turbulent boundary layers are examined using experimental databases obtained from particle image velocimetry. This investigation employs a large range of Reynolds numbers, spanning more than an order of magnitude ( ), enabling us to provide a detailed description of uniform momentum zones as a function of Reynolds number. Our analysis starts by examining the identification criterion used by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) to report the presence of uniform momentum zones in turbulent boundary layers. This criterion is then applied to show that a zonal-like structural arrangement is prevalent in all datasets examined, emphasising its importance in the structural organisation. Streamwise velocity fluctuations within the zones are observed to be small but they are bounded by distinct step changes in streamwise momentum which indicate that shear layers of intense vorticity separate each zone. A log-linear increase in the number of these zones with increasing Reynolds number is revealed, together with an increase in the thicknesses of zones with increasing distance from the wall. These results support a hierarchical length-scale distribution of coherent structures, which generate zonal-like organisation within turbulent boundary layers. Interpretation of these findings is aided by employing synthetic velocity fields generated using a model based on the attached eddy hypothesis, which is described in the work of Perry and co-workers. Comparisons between the model and experimental results show that a hierarchy of self-similar structures leads to population densities and length-scale distributions of uniform momentum zones that closely adhere to those observed experimentally in this study.

Abstract: A theoretical decomposition of mean skin friction generation into physical phenomena across the whole profile of the incompressible zero-pressure-gradient smooth-flat-plate boundary layer is derived from a mean streamwise kinetic-energy budget in an absolute reference frame (in which the undisturbed fluid is not moving). The Reynolds-number dependences in the laminar and turbulent cases are investigated from direct numerical simulation datasets and Reynolds-averaged Navier–Stokes simulations, and the asymptotic trends are consistently predicted by theory. The generation of the difference between the mean friction in the turbulent and laminar cases is identified with the total production of turbulent kinetic energy (TKE) in the boundary layer, represented by the second term of the proposed decomposition of the mean skin friction coefficient. In contrast, the analysis introduced by Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), based on a streamwise momentum budget in the wall reference frame, relates the turbulence-induced excess friction to the Reynolds shear stress weighted by a linear function of the wall distance. The wall-normal distribution of the linearly-weighted Reynolds shear stress differs from the distribution of TKE production involved in the present discussion, which consequently draws different conclusions on the contribution of each layer to the mean skin friction coefficient. At low Reynolds numbers, the importance of the buffer-layer dynamics is confirmed. At high Reynolds numbers, the present decomposition quantitatively shows for the first time that the generation of the turbulence-induced excess friction is dominated by the logarithmic layer. This is caused by the well-known decay of the relative contributions of the buffer layer and wake region to TKE production with increasing Reynolds numbers. This result on mean skin friction, with a physical interpretation relying on an energy budget, is consistent with the well-established general importance of the logarithmic layer at high Reynolds numbers, contrary to the friction breakdown obtained from the approach of Fukagata et al. (Phys. Fluids, vol. 14 (11), 2002, pp. 73–76), essentially based on a momentum budget. The new decomposition suggests that it may be worth investigating new drag reduction strategies focusing on TKE production and on the nature of the logarithmic layer dynamics. The decomposition is finally extended to the pressure-gradient case and to channel and pipe flows.

Abstract: A theory is presented for the Great Plains low-level jet in which the jet emerges in the sloping atmospheric boundary layer as the nocturnal phase of an oscillation arising from diurnal variations in turbulent diffusivity (Blackadar mechanism) and surface buoyancy (Holton mechanism). The governing equations are the equations of motion, mass conservation, and thermal energy for a stably stratified fluid in the Boussinesq approximation. Attention is restricted to remote (far above slope) geostrophic winds that blow along the terrain isoheights (southerly for the Great Plains). Diurnally periodic solutions are obtained analytically with diffusivities that vary as piecewise constant functions of time and slope buoyancies that vary as piecewise linear functions of time. The solution is controlled by 11 parameters: slope angle, Coriolis parameter, free-atmosphere Brunt–Vaisala frequency, free-atmosphere geostrophic wind, radiative damping parameter, day and night diffusivities, maximum and minimum surfa...

Abstract: The present work investigates the micropolar fluid flow due to a permeable stretching sheet and the resulting heat transfer. Unlike the existing numerical works on the flow phenomenon in the literature, the prime interest here is to analytically work out shape of the solutions and identify whether they are unique. Indeed, unique solutions are detected and presented in the exact formulas for the associated boundary layer equations. Temperature field influenced by the microrotation is also mathematically resolved in the cases of constant wall temperature, constant heat flux and Newtonian heating. To discover the salient physical features of many mechanisms acting on the considered problem, it is adequate to have the analytical velocity and temperature fields and also closed-form skin friction/couple stress/heat transfer coefficients, all as given in the current paper. For instance, the practically significant rate of heat transfer is represented by a single formula valid for all three temperature cases.

Abstract: Analytic expression for unsteady free convective hydromagnetic boundary layer Casson fluid flow past an oscillating vertical plate embedded through porous medium in the presence of uniform transverse magnetic field, thermal radiation and chemical reaction is obtained. Both isothermal and ramped wall temperatures are taken into account. The governing equations are solved using Laplace transform technique and the solutions are presented in closed form. The numerical values of Casson fluid velocity, temperature and concentration at the plate are presented graphically for several values of the pertinent parameters. Effect of governing parameters on Skin friction, Nusselt number and Sherwood number is also discussed. Casson parameter γ is inversely proportional to the yield stress and it is observed that for the large value of Casson parameter, the fluid is close to the Newtonian fluid where the velocity is less than the Non-Newtonian fluid. It is seen that velocity increases and Temperature decreases with increase in thermal radiation R . Radiation parameter R signifies the relative contribution of conduction heat transfer to thermal radiation transfer. Concentration decreases tendency with chemical reaction parameter R ′ .

Abstract: A field observation array for the atmospheric surface layer (ASL) was built on a dry flat bed of Qingtu Lake in Minqin (China) as the Qingtu Lake Observation Array (QLOA) site, which is similar to the Surface Layer Turbulence and Environmental Science Test (SLTEST) site in the Utah (USA) Western desert. The present observation array can synchronously perform multi-point measurements of wind velocity and temperature at different vertical and streamwise positions. In other words, three-dimensional turbulent ASL flows can be measured at the QLOA station and Reynolds numbers as high as can be achieved with steady wind conditions. By careful selection and pretreatment for measured data of more than 1200 h, the QLOA data have been validated to be reliable for high Reynolds number turbulent boundary layer research. Results from correlation and spectral analysis confirm that very large scale motions (VLSMs) exist in the ASL at a Reynolds number up to . Through premultiplied spectral analysis, it is revealed that the spectral energy in the high-wavenumber region decreases with height, similar to turbulent boundary layers at low or moderate Reynolds numbers, while it increases with height in the low-wavenumber region resulting in a log–linear increase of VLSMs energy with height, which is different from turbulent boundary layers at low or moderate Reynolds numbers. The present analyses support the view that the evolution of the VLSMs cannot be fully attributed to a ‘bottom-up’ mechanism alone, and probably other mechanisms, including a ‘top-down’ mechanism, also play a role.

Abstract: Purpose The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues. Design/methodology/approach The resulting non-linear system is solved through the homotopy analysis method. Findings An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

Abstract: A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (‘vortex-in-cell plus’, VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.

Abstract: In wall-bounded turbulent flow simulations, periodic boundary conditions combined with insufficiently long domains lead to persistent spanwise locking of large-scale turbulent structures. This leads to statistical inhomogeneities of 10%–15% that persist in time averages of 60 eddy turnover times and more. We propose a shifted periodic boundary condition that eliminates this effect without the need for excessive streamwise domain lengths. The method is tested based on a set of direct numerical simulations of a turbulent channel flow, and large-eddy simulations of a high Reynolds number rough-wall half-channel flow. The method is very useful for precursor simulations that generate inlet conditions for simulations that are spatially inhomogeneous, but require statistically homogeneous inlet boundary conditions in the spanwise direction. The method’s advantages are illustrated for the simulation of a developing wind-farm boundary layer.

Abstract: The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a ‘tank-treading’ motion. These observations are apprehended with the help of a variant of Wagner theory for liquid impact. This framework offers a simple analogy where the fluid motion within the impacting drop may be viewed as the flow induced by a flat rising expanding disk. The theoretical predictions are found to be in very close agreement both qualitatively and quantitatively with the numerical observations for approximately three decades in time. Interestingly, the inviscid self-similar impact pressure and velocities are shown to depend solely on the self-similar variables . The structure of the boundary layer developing along the wet substrate is investigated as well. It is found to be in first approximation analogous to the boundary layer growing in the trail of a shockwave. Interestingly, the corresponding boundary layer structure only depends on the impact self-similar variables. This allows us to construct a seamless uniform analytical approximation encompassing both impact and viscous effects. The depiction of the different dynamical fields enables to quantitatively predict observables of interest, such as the evolution of the integral viscous shearing force and of the net normal force.

Abstract: We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within \({\varepsilon}\) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time \({T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}\).

Abstract: Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially-developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from the Taylor's hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The freestream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the freestream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.