Boundary Layer Region Research Articles

The role of leading-edge serrations in controlling the flow over owls’ wing

We studied the effects of leading-edge serrations on the flow dynamics developed over an owl wing model. Owls are predatory birds. Most owl species are nocturnal, with some active during the day. The nocturnal ones feature stealth capabilities that are partially attributed to their wing microfeatures. One of these microfeatures is small rigid combs (i.e. serrations) aligned at an angle with respect to the incoming flow located at the wings’ leading-edge region of the primaries. These serrations are essentially passive flow control devices that enhance some of the owls’ flight characteristics, such as aeroacoustics and, potentially, aerodynamics. We performed a comparative study between serrated and non-serrated owl wing models and investigated how the boundary layer over these wings changes in the presence of serrations over a range of angles of attack. Using particle image velocimetry, we measured the mean and turbulent flow characteristics and analyzed the flow patterns within the boundary layer region. Our experimental study suggests that leading-edge serrations modify the boundary layer over the wing at all angles of attack, but not in a similar manner. At low angles of attack (<20°), the serrations amplified the turbulence activity over the wing planform without causing any significant change in the mean flow. At 20° angle of attack, the serrations act to suppress existing turbulence conditions, presumably by causing an earlier separation closer to the leading-edge region, thus enabling the flow to reattach prior to shedding downstream into the wake. Following the pressure Hessian equation, turbulence suppression reduces the pressure fluctuations gradients. This reduction over the wing would weaken, to some extent, the scattering of aerodynamic noise in the near wake region.

Assessment of Total Pressure and Swirl Distortions in a Busemann Inlet at Mach 6

Flow distortions in high-speed inlet systems are complex, and high-performance air-breathing propulsion systems. In this paper, large eddy simulations are performed to study the total pressure and swirl distortions in a Busemann inlet at freestream Mach number 6. The on-design flow condition with both the Attack Angle and Sideslip Angle equal to zero and two off-design conditions (Attack Angle = 6 deg, Sideslip Angle = 0 deg and Attack Angle = 6 deg, Sideslip Angle = 6 deg) are considered to explore the flow characteristics inside the inlet duct as well as the distortions at the inlet exit plane. It is found that under the on-design flow condition, the shock structures and boundary layer development are nearly axisymmetric about the inlet axis. The captured freestream is compressed smoothly through inlet duct. The total pressure loss is limited primarily to within the boundary layer region, and nearly no swirling flow is introduced during the flow compression process. Under the off-design flow conditions, the shock structures inside the inlet duct become non-axisymmetric, and localized strong shock–boundary layer interactions occur. In the case of the off-design flow condition with Attack Angle = 6 deg, Sideslip Angle = 0 deg, a large flow separation zone appears owing to the incidence of a strong curved shock on the wall surface at the leeward side in the inlet duct, and the low-kinetic-energy flow contained in this flow separation zone leads to an obvious total-pressure reduction at the exit plane of inlet. Meanwhile, a large-scale swirling flow is formed at the exit plane of inlet owing to the appearance of a nonuniform transverse pressure gradient. Under the off-design conditions, a pair of vortex is observed at the exit plane of inlet. The shock wave–boundary layer interactions under the off-design conditions are stronger than those under the on-design condition, which results in more intense total pressure and swirl distortions. The averages of the fluctuating distortions are more evident than the temporal-averaged total-pressure and swirl distortions. These results show that turbulent flow fluctuations are important in determining the overall distortion level in a Busemann inlet.

Comparison study of fluid thermal boundary-bulk behaviors in the close-to-critical region under different property trends

The high-efficiency energy system based on the utilization of supercritical CO2 has been widely developed in recent years to meet the growing demands of clean energy and the elimination of CO2 emissions. Within this field, the design of the corresponding equipment requires an understanding of the thermodynamic behavior of supercritical fluid affected by the singular thermophysical properties. The analysis of this study is based on the asymptotic expansion of hydrodynamic equations and the thermophysical properties characterized by the exponential trends. The asymptotic model finds the wave and diffusion modes valid within the bulk region in second-order and within the boundary layer region (BLR) in first-order, respectively. Main findings include: (1) The wave mode is found in the bulk region with the wave celerity Γ. When the critical point is approached, Γ decreases from (γ0Mac0/κT0)0.5 = 1 to [(γ0–1)Mac0/κT0]0.5, which; (2) The diffusion mode found in BLR is characterized by non-dimensional diffusion coefficient ζ. This coefficient has the same behavior as thermal diffusivity, which is enlarged by thermal conductivity but weakened by isobaric specific heat. (3) Mass transport from BLR to bulk leads to the generation of the thermal wave, which can be measured by mass transport coefficient Mb=ζβp. Mb also characterizes the magnitude of the thermal wave as u2=Mb(Tb1)z|z=0 (that is, 0.17 mm/s when ϕ=10−4). The behavior of Mb is similar to one of ζ. However, the effect of cp is limited; (4) Two different modes of viscosity are identified. The increase in viscosity leads to the change of viscous stress mode from the second order to the first order, which also leads to a decrease in mass transport.

About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

Scallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. Anad hoccorrection applied to the turbulent closure and due to Hanrattyet al.(Thorsnesset al.,Chem. Engng Sci., vol. 33, issue 5, 1978, pp. 579–592; Abrams &amp; Hanratty,J. Fluid Mech., vol. 151, issue 1, 1985, p. 443; Frederick &amp; Hanratty,Exp. Fluids, vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.

Experimental study on flow and turbulence characteristics of jet impinging on cylinder using three-dimensional Lagrangian particle tracking velocimetry

When a round jet impinges on a convex cylindrical surface, complex three-dimensional (3D) flow structures occur, accompanied by the Coanda effect. To characterize the flow and turbulence properties of the general system, ensemble averages of 3D Lagrangian particle tracking velocimetry measurements were taken. The radial bin-averaging method was used in post-processing the tracked particles and corresponding instantaneous velocity vectors to generate appropriate ensemble-averaged statistics. Two impinging angles were selected, and at a fixed Reynolds number, the ensemble-averaged volumetric velocity field and turbulent stress tensor components were measured. The flow and turbulence characteristics of the impinging jet on the cylinder were notably different based on the impinging angle, especially in the downstream region. Surprisingly, the attached wall jet with a half-elliptic shape was abruptly thickened in the wall-normal direction, similar to the axis switching phenomenon observed in elliptic jets in the case of oblique impingement. In the jet-impinging region, the flow spread in all directions with high mean vorticity values. With the development of a 3D curved wall jet, both the Coanda effect and centrifugal force played a significant role in the flow behavior. A notable feature of the self-preserving region was the similarity of mean velocity profiles with scaling by the maximum velocity and the jet half-width for both impinging angle cases. Local isotropy of turbulent normal stresses was observed in this region, supporting the existence of self-preservation in the 3D curved wall jet. The volumetric ensemble-averaged Reynolds stress tensor revealed strong inhomogeneous turbulence in the boundary layer region and the curvature effect on the Reynolds shear stress in the free shear layer.

Effects of the gravitational force on the convection turbulence driven by heat-releasing point particles

In this work, we study the convection turbulence driven by heat-releasing point particles, which absorb energy for external sources. Two-way coupling is considered for both momentum and temperature fields, and the particle dynamics includes both the Stokes drag, which is measured by the Stokes number, and the gravity force, which is measured by the Froude number. The gravity effect of particles on the convection turbulence is mainly researched. Two regimes are identified at large and small Froude numbers, respectively. For a large Froude number, the flow can reach a statistically steady state with particles being constantly advected over the whole domain. Within this regime, the transport properties exhibit weak dependence on the Froude number but strong dependence on the Stokes number. When the Froude number is small enough, all particles eventually accumulate toward the boundary layer region near the bottom plate. Scaling laws are derived for the critical Froude number between the two regimes, which agree well with the numerical results.

Statistical evaluation of stability margin of a multi-stage compressor with geometric variability using adaptive polynomial chaos-Kriging model

Compressed air energy storage systems must promptly adapt to power network demand fluctuations, necessitating a high surge margin in the compression system to ensure safety. It is challenging to completely eliminate blade geometric variations caused by limited machining precision, the important effects of which should be considered during aerodynamic shape design and production inspection. The present paper explores the uncertainty impact of geometric deviations on the stability margin of a multi-stage axial compressor at a low rotational speed. Initially, an adaptive polynomial chaos expansion-based universal Kriging model is introduced, and its superior response performance in addressing high-dimensional uncertainty quantification problems is validated through rigorous analytical and engineering tests. Then, this model is used to statistically evaluate the stability margin improvement (SMI) of the compressor due to the Gaussian and realistic geometric variabilities separately. The results show that the mean and standard deviation of SMI are −0.11% and 0.5% under the Gaussian geometric variability, while those are 0.33% and 0.39% under the realistic variability. For both the geometric variabilities, the stagger angle and maximum thickness deviations of the first-stage rotor are the most influential parameters controlling the uncertainty variations in the stability margin. Finally, the underlying impact mechanism of the influential geometric deviations is investigated. The variation in the stability margin caused by the geometric deviations primarily results from the alteration of inlet incidences, affecting the size of the tip leakage vortex blockage and boundary-layer separation regions near the blade tip of the first-stage rotor.

Profiling of Aerosols and Clouds over High Altitude Urban Atmosphere in Eastern Himalaya: A Ground-Based Observation Using Raman LIDAR

Profiles of aerosols and cloud layers have been investigated over a high-altitude urban atmosphere in the eastern Himalayas in India, for the first time, using a Raman LIDAR. The study was conducted post-monsoon season over Darjeeling (latitude 27°01′ N longitude 88°36′ E, 2200 masl), a tourist destination in north-eastern India. In addition to the aerosols and cloud characterization and atmospheric boundary layer detection, the profile of the water vapor mixing ratio has also been analyzed. Effects of atmospheric dynamics have been studied using the vertical profiles of the normalized standard deviation of RCS along with the water vapor mixing ratio. The aerosol optical characteristics below and above the Atmospheric Boundary Layer (ABL) region were studied separately, along with the interrelation of their optical and microphysical properties with synoptic meteorological parameters. The backscatter coefficient and the extinction coefficient were found in the range from 7.15×10−10 m−1 sr−1 to 3.01×10−5 m−1 sr−1 and from 1.02×10−5 m−1 to 2.28×10−3 m−1, respectively. The LIDAR ratio varies between 3.9 to 78.39 sr over all altitudes. The variation of the linear depolarization ratio from 0.19 to 0.32 indicates the dominance, of non-spherical particles. The periodicity observed in different parameters may be indicative of atmospheric wave phenomena. Cloud parameters, such as scattering coefficients, top and bottom height, and optical depth for different cloud phases, have been evaluated. A co-located Micro Rain Radar has been used with LIDAR for cloud life cycle study.

Research on time series prediction of the flow field in supersonic combustor based on deep learning

The detection of supersonic combustion flow field provides valuable reference information for the efficient combustion of hypersonic vehicles. From the perspectives of scramjet operation during flight as well as experiment where the measured information is limited, flow field prediction using deep learning technology is a promising method that can provide future flow field evolution in scramjet combustors. This study proposes a convolutional neural network model of multi-temporal pressure information fusion to predict combustion flow field based on wall pressure. In addition, it analyzes the effect of various wall pressures on the flow field prediction. An experimental dataset of supersonic ground-pulse wind tunnel tests with different injection pressures is built through the combustion chamber wall under self-ignition conditions of a hydrogen-fueled scramjet. The results showed that the predicted flow field of the combustor agrees with the ground test, average correlation coefficient reached more than 90% and when the wall pressure number is 32, the average peak signal to noise ratio reaches about 23. and the main wave structure and turbulent boundary layer region are restored even if there is a shock boundary layer interaction.

Statistical and numerical analysis of unsteady hybrid nanoliquid flows over an elongating surface with oblique Lorentz force: A comparison of Cu–Al2O3/H2O, Cu–Al2O3/CH3OH and Cu–Al2O3/H2O–EG

The current work investigates the effects of oblique Lorentz force and Navier’s slip boundary condition on unsteady hybrid nanoliquid flow with three different base liquids (H2O, CH3OH and H2O–EG) across a nonlinearly elongating surface set in a porous medium. This research considers the effects of viscous–Ohmic dissipation, nonlinearly variable thermal radiation, internal heat source, the Soret effect, first-order chemical reaction and thermal and solutal jump conditions at the boundary. Proper thermo-physical relationships for the hybrid nanoliquid have been established. Rosseland’s estimate for an optically thick regime is used when calculating the heat flow owing to radiation. The dimensional governing equations are translated into nondimensional forms using appropriate similarity transformations. The velocity, energy and concentration fields are numerically solved using a shooting strategy based on the secant iteration and the Runge–Kutta–Fehlberg method. The physical implications of several essential parameters on the hybrid nanoliquid velocity, temperature and concentration are investigated using graphical and tabular representations of numerical data. Furthermore, the multiple (quadratic) regression analysis reveals that physical parameters strongly influence the local skin friction coefficient, Sherwood and Nusselt numbers. For continuously growing values of the unsteadiness parameter, the velocity, thermal and concentration scattering declined everywhere within the boundary layer region.

Surface properties of ferromagnetic films and spin wave modes

Ferromagnetic films are a fundamental platform in Magnonics, the area that studies spin wave propagation and its possible applications. These films have been studied for a long time experimentally and theoretically, either individually or as parts of multifilms structures. The present study delves into an issue of interest that remains to be studied in detail, which is the relation between the surface properties of these films and the spin wave propagation in them. The main idea of this work is that the frequencies of spin waves may be determined experimentally with precision and through their relation with surface properties one may theoretically validate and derive the main parameters of models that describe the behavior of the surfaces. Several parameters may be changed in the process of testing the relation between surface properties and spin waves, like an applied magnetic field orientation and strength, the angle of in-plane spin wave propagation, etc. This study uses a continuum micromagnetic model for the description of the magnetization dynamics, in this case, the surface properties enter through effective boundary conditions. Three models of surface properties are studied: uniaxial surface anisotropy, the latter combined with bulk uniaxial anisotropy, and surfaces with Dzyaloshinskii-Moriya interactions (DMI). In general, the boundary conditions affect the equilibrium magnetization in boundary layer regions close to the surfaces: an asymptotic analysis predicts their penetration lengths for reasonable surface anisotropies. For very thin films, this is quite relevant since the boundary layers are of the order of the film thickness, we propose this as a practical way to define what may be considered a very thin film. Effective physical parameters of thin films and very thin films clearly depend on the surface properties. The main effects of the surfaces on spin waves occur for angles of inclination of the applied magnetic field close to perpendicular to the plane, and they may be of significant magnitude. Several different numerical methods were used to solve for the spin waves, in the context of an orthogonality equation method.

Transient rotating three-dimensional flow of micropolar fluid induced by Riga plate: Finite element approach

This study assessed the boundary layer flow of micropolar fluid induced by the Riga plate. The significance of the flow is conducted from a rotating frame of perspective to produce consistency for enhanced thermodynamics across the Riga plate for fluid flow. The Riga plate is a familiar operator consisting of stably deployed magnetic and electrostatic elements that produce Lorentz force in an alternative way that substantially reduces with distance from the Riga plate. The unsteady, partially differentiated, three-dimensional expressions are reduced to two impartial dimensions ( τ , η ) . For steady-state responses, ( τ = 1 ) , Glerikin quantization is performed with MATLAB software for finite element simulation. For the resulting set of transformed equations, approximative series remedies are attained as convergent. The fluid temperature increased as a result of the rotational parameter, the Hartmann number, and the unstable parameter. The modifications to the Hartmann number ( M h ) and the material parameter ( Λ ) decelerate the primary flow velocity in the boundary layer region, while the secondary flow velocity accelerates. The greater modified Hartmann number ( M h ) and material parameters have a decreasing impact on the skin friction in the primary direction and an increasing impact on the magnitude of the coefficient in the secondary direction. An excellent agreement between the ongoing and previously existing results establishes the validity of the current findings.

Policy transfer of reinforcement learning-based flow control: From two- to three-dimensional environment

In the current paper, the zero-mass synthetic jet flow control combined with a proximal policy optimization (PPO) algorithm in deep reinforcement learning is constructed, and a policy transfer strategy which is trained in two-dimensional (2D) environment and migrated to three-dimensional (3D) environment is proposed and analyzed. By policy, we mean the flow control strategy of the agent learned by interacting with environment through deep reinforcement learning (DRL) algorithm. Through comprehensive evaluations of vortex separation in the cylindrical boundary layer and wake region at different Reynolds (Re) numbers, the PPO model trained in the 2D environment can reduce the drag coefficient by approximately 6.3%, 18.6%, and 23.7% at Re = 100, 200, and 300, respectively, when the spanwise length of the 3D environment is equal to the cylinder's diameter. Moreover, when the spanwise length is three times the diameter, the drag reduction capability is about 5.8%, 15.4%, and 13.1% at the three Re numbers, respectively. Additionally, the PPO model trained in the 2D environment also demonstrated outstanding migration learning capability in a new 3D flow field environment with varying Re numbers, successfully suppressing vortex shedding and reducing drag coefficient. Furthermore, the results illustrate that the model trained at high Re numbers could still reduce the drag coefficient in the 3D environment with low Re numbers, while the model trained at low Re numbers was not as effective at achieving drag reduction in the environments under high Re numbers. Overall, the proposed policy transfer strategy has been proven to be an effective method applying DRL agent trained in 2D flow to a new 3D environment.

An experimental investigation on the isoenergetic supersonic cooling films subjected to different ratios of static pressure

Ratio of static pressure (RSP) is a critical factor affecting the development of supersonic cooling film flow field. To give a good account of flow characteristics and physical mechanisms on the influences of RSPs, experiments are conducted employing the nanoparticle planar laser scattering (NPLS) and particle-image velocimetry (PIV) techniques. A supersonic cooling film is tangentially injected at a Mach number of Maj=2 into a laminar boundary layer at a mainstream Mach number of Ma∞=3 with different RSP cases. The flow field is divided into four sections: the wake region, the potential core region, the wall-jet region, and the fully developed turbulent boundary layer region. The velocity profile extracted at the fully developed turbulent boundary layer region is proved to be consistent with the theoretical composite profile. Moreover, a new criterion that distinguishes the specific position of the impingement point where the mixing layer approaches the bottom boundary layer is proposed based on the distribution of principal strain rate of the mean velocity field. The analysis of turbulent structures finds that the K–H vortex structures are sensitive to RSPs, and more broken vortices generated when the two fluids mix. The intensity of wave structures is depicted in the synthetic schlieren images when subjected to different RSPs. In addition, the turbulent characteristics show a weaker mixing process with increased RSP, indicating a prolonging in the effective cooling length. Furthermore, the disturbance at the slot and variations of velocity gradient downstream are addressed and analyzed to reveal the physical mechanisms for the mixing process on RSP differences.

Streamline Diffusion Finite Element Method for Singularly Perturbed 1D-Parabolic Convection Diffusion Differential Equations with Line Discontinuous Source

This article presents a study on singularly perturbed 1D parabolic Dirichlet’s type differential equations with discontinuous source terms on an interior line. The time derivative is discretized using the Euler backward method, followed by the application of the streamline–diffusion finite element method (SDFEM) to solve locally one-dimensional stationary problems on a Shishkin mesh. Our proposed method is shown to achieve first-order convergence in time and second-order convergence in space. Our proposed method offers several advantages over existing techniques, including more accurate approximations of the solution on the boundary layer region, better efficiency, and robustness in dealing with discontinuous line source terms. The numerical examples presented in this paper demonstrate the effectiveness and efficiency of our method, which has practical applications in various fields, such as engineering and applied mathematics. Overall, our proposed method provides an effective and efficient solution to the challenging problem of solving singularly perturbed parabolic differential equations with discontinuous line source terms, making it a valuable tool for researchers and practitioners in various domains.

Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag

In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.

Homogeneous–heterogeneous reactions for Maxwell nanofluid flow over an elongating cylindrical pipe via finite element method

AbstractHomogeneous–heterogeneous chemical reactions in simultaneous heat and mass transport for Maxwell fluid subjected to thermophoresis and Brownian motion are modeled and governing mathematical models are simplified using approximations proposed models are simplified using approximations proposed by Ludwing Prandtl. The simplified governing mathematical models under Buongiorno's theory are numerically solved via finite element method (FEM). The convergence and mesh free solution are solved for parametric study. The momentum relaxation phenomenon is the characteristic of liquid to restore its equilibrium state. Therefore, a remarkable reduction in the motion of fluid particles against an increase in Deborah number is noticed. A rise in temperature distribution is noticed when Brownian motion parameter is enhanced. The flow is decelerated as the curvature of the cylinder increases. As a consequence, the viscous region shrinks and its thickness becomes smaller. Hence, it is concluded that flow over flat surface has wider boundary layer region than the boundary layer region associated with flow over the cylindrical surface. The wall shear stress for the flow over a cylindrical object is higher than that for the flow over a flat surface. The wall heat and mass fluxes have an increasing tendency when the curvature parameter is increased. Wall heat flux and wall mass flux have opposite behavior due to rise in thermophorsis and Brownian motion effects.

Thermosolutal Marangoni convection on a permeable flat surface with aligned magnetic field and thermophoretic effect: an OHAM solution

In this venture, the challenge to study the mathematical model and its approximate solution for boundary layer thermosolutal Marangoni convection on a permeable flat surface with thermophoretic velocity and aligned magnetic field has been undertaken. Using a special type of transformation, governing PDEs are converted into ODEs. A semi-analytical method known as optimal homotopy analysis method(OHAM) has been used to develop solutions for proposed mathematical model. The novelty of the study is in the exploration of simultaneous impacts of thermophoretic velocity and inclined magnetic field on flow and heat-mass transport while mass suction/injection is using OHAM. Solutions obtained by OHAM are compared with other published literature and it is revealed that our numerical values are improved by approximately up to 7%. The obtained solutions for various important parameters are displayed in the form of graphs and tables. The study explores the variable behaviors of velocity, temperature, and concentration for growths of Marangoni number, magnetic parameter, and thermophoretic parameter, while there exists mass suction or injection. It reveals that in both cases, i.e. suction and injection cases, velocity grows and temperature and concentration reduce with increasing magnetic parameters and inclination angle of aligned magnetic field and these variations are more prominent in case injection. If the magnetic field is orthogonal to the flat surface, then corresponding Lorentz force produces maximum resistance for the transport phenomenon. The spreading effect of induced surface velocity due to Marangoni convection is observed in the entire boundary layer region in case of mass suction, while for injection case it is witnessed only near the surface. Whereas, for higher value of thermophoretic velocity, the concentration exhibits a reducing trend. For rising values of Marangoni number, wall velocity, Nusselt number, and Sherwood number significantly grow, while magnetic field has contrary impacts.

Observational evidence of salt finger in the diurnal thermocline

Due to strong turbulent mixing, the ocean surface boundary layer region is generally not conducive to double diffusion. However, vertical microstructure profiles observations in the northeastern Arabian Sea during May 2019 imply the formation of salt fingers in the diurnal thermocline (DT) region during the daytime. In the DT layer, conditions are favorable for salt fingering: Turner angle values are between 50 and 55° with both temperature and salinity decreasing with depth; shear-driven mixing is weak with a turbulent Reynolds number of about 30. The presence of salt fingering in the DT is confirmed by the presence of staircase-like structures with step sizes larger than the Ozmidov length and by the dissipation ratio that is larger than the mixing coefficient. The unusual daytime salinity maximum in the mixed layer that supports salt fingering is primarily due to a daytime reduction in vertical entrainment of fresh water along with minor contributions from evaporation and horizontal advection and a significant contribution from detrainment processes.

Outer scaling of the mean momentum equation for turbulent boundary layers under adverse pressure gradient

A new scaling of the mean momentum equation is developed for the outer region of turbulent boundary layers (TBLs) under adverse pressure gradient (APG). The maximum Reynolds shear stress location, denoted as $y_{m}$ , is employed to determine the proper scales for the outer region of an APG TBL. An outer length scale is proposed as $\delta _e - y_{m}$ , where $\delta _e$ is the boundary layer thickness. An outer velocity scale for the mean streamwise velocity deficit is proposed as $U_e - U_{m}$ , where $U_e$ and $U_m$ are the mean streamwise velocities at the boundary layer edge and $y_{m}$ , respectively. An outer velocity scale for the mean wall-normal velocity deficit is proposed as $V_e - V_{m}$ , where $V_e$ and $V_{m}$ are the wall-normal velocities at $\delta _e$ and $y_{m}$ , respectively. The maximum Reynolds shear stress is found to scale as $(\delta _e - y_{m}) U_e \,{\rm d}U_e/{{\rm d}x}$ . The new outer scaling collapses well the experimental and numerical data on APG TBLs over a wide range of Reynolds numbers and strengths of pressure gradient. Approximations of the new scaling are developed for TBLs under strong APG and at high Reynolds numbers. The relationships between the new scales and previously proposed scales are discussed.