Boundary Layer Scaling Research Articles

The coupling of winds, ocean turbulence, and High Salinity Shelf Water in the Terra Nova Bay Polynya

The Terra Nova Bay (TNB) Polynya in the Western Ross Sea of Antarctica is a major producer of High Salinity Shelf Water (HSSW), a precursor to Antarctica Bottom Water (AABW). Processes occurring in and around the polynya can therefore effect change in the lower limb of overturning circulation in this region. Here, we use data from a densely-instrumented upper-ocean mooring, deployed for 1 year in a region of active HSSW formation within TNB, to examine the coupling of surface brine rejection and vertical mixing to katabatic wind forcing. We find a high correlation between salinity and winds during the wintertime HSSW production season at the mooring site, with a lag-response of 20 h in near-surface (∼47 m) salinity to winds measured at the nearby Automatic Weather Station (AWS) Manuela. Salinity and temperature measurements show a fully destratified water column by June, with a lag-response of near-seabed (∼360 m) salinity to near-surface salinity of just 5 h. Measurements of turbulent kinetic energy (TKE) dissipation rate (ɛ) from moored pulse-coherent acoustic Doppler current profilers (ADCPs) show general agreement with classic boundary layer scaling (BLS), and calculations of a vertical mixing timescale using the Obukhov length scale average to ∼2.5 h during austral winter, consistent with the 5-h lag time observed in the salinity data. Comparisons to data from concurrent mooring deployments along the southern boundary of TNB, as well as to previously published assessments of model simulations and data from Climatic Long-term Interaction for the Mass-balance in Antarctica (CLIMA) moorings, allow us to explore spatial variability in the coupling of winds and salinity across TNB and to speculate on possible HSSW circulation pathways.

Diurnal warming rectification in the tropical Pacific linked to sea surface temperature front

Sharp and rapid changes in the sea surface temperature (SST) associated with fronts and the diurnal cycle can drive changes in the atmospheric boundary-layer stability and circulation. Here we show how a one-dimensional surface ocean model forced with either high-resolution or daily averaged surface fluxes can be used to distinguish diurnal versus frontal SST anomalies observed from an uncrewed surface vehicle. The model, forced with daily satellite fluxes, shows that the diurnal warming is largest within the equatorial Pacific cold tongue of SST. The strong persistent SST front north of the cold tongue is evident in both the oceanic and atmospheric boundary-layer stability scales and, as a consequence, in the magnitude of the diurnal ocean warming. Using SST, barometric pressure and surface wind measurements from moorings at 0°, 95° W and 2° N, 95° W, we show that the front in the SST diurnal warming results in a weakened SST front in the afternoon and a corresponding reduced meridional gradient in the barometric pressure that appears to contribute to a diurnal pulsing of the surface meridional winds. To the extent that these modulate the surface branch of the Hadley cell, these diurnal variations may have remote impacts.

Rayleigh–Bénard Convection in a Gas-Saturated Porous Medium at Low Darcy Numbers

Abstract Natural convection heat transfer is measured in a horizontal enclosure filled with a gas-saturated porous medium composed of glass spheres. The height-to-pore scale ratio (H/d) is in the range of 25–150, yielding a low Darcy number (5.87×10−8≤Da≤1.94×10−6), which satisfies the porous medium assumption more rigorously. The maximum values attained for the modified Rayleigh numbers (Ra* up to 6150) and fluid Rayleigh numbers (Raf up to 2.5×1011) at these low Darcy numbers enable access to both the Darcy and Forchheimer flow regimes. The heat transfer relationship just beyond the onset of convection is in good accordance with theory and previous experiments, varying linearly with the modified Rayleigh number. For higher modified Rayleigh numbers, the data diverge as a function of the Darcy number, depending on both Da and the modified Rayleigh number. Transition points between the Darcy and Forchheimer regimes are estimated. At the highest fluid Rayleigh numbers, the data with the largest pore scales show some evidence of moving toward a regime similar to that of Rayleigh–Bénard convection, where boundary layer and plume length scales are small enough that the details of the porous medium cease to matter. It is argued that even in this regime, the boundary layer length scales are not diminished enough to make the contribution of Brinkman drag significant.

Decomposition of the drag force in steady and oscillatory flow through a hexagonal sphere pack

We investigate steady and oscillatory flow through a hexagonal close-packed arrangement of spheres in the framework of the volume-averaged momentum equation. We quantify the friction and pressure drag based on a direct numerical simulation dataset. Using the pressure decomposition of Graham (J. Fluid Mech., vol. 881, 2019), the pressure drag can be further split up into an accelerative, a viscous and a convective contribution. For the accelerative pressure, a closed-form expression can be given in terms of the potential flow solution. We investigate the contributions of the different drag components to the volume-averaged momentum budget and their Reynolds number scaling. For steady flow, we find that the friction and viscous pressure drag are proportional to $Re$ at low Reynolds numbers and scale with $Re^{1.4}$ for high Reynolds numbers. This is close to the steady laminar boundary layer scaling. For the convective pressure drag, we find a cubic scaling at low and a quadratic scaling at high Reynolds numbers. The Reynolds stresses have a minor contribution to the momentum budget. For oscillatory flow at low and medium Womersley numbers, the amplitudes of the drag components are similar to the steady cases at the same Reynolds number. At high Womersley numbers, the drag components behave quite differently and the friction and viscous pressure drag are relatively insignificant. The drag components are not in phase with the forcing and the superficial velocity; the phase lag increases with the Womersley number. This suggests that new models beyond the current quasisteady approaches need to be developed.

Development of a Dynamic Downscaling Method for Use in Short-Range Atmospheric Dispersion Modeling Near Nuclear Power Plants

Background: High-fidelity meteorological data is a prerequisite for the realistic simulation of atmospheric dispersion of radioactive materials near nuclear power plants (NPPs). However, many meteorological models frequently overestimate near-surface wind speeds, failing to represent local meteorological conditions near NPPs. This study presents a new high-resolution (approximately 1 km) meteorological downscaling method for modeling short-range (< 100 km) atmospheric dispersion of accidental NPP plumes.Materials and Methods: Six considerations from literature reviews have been suggested for a new dynamic downscaling method. The dynamic downscaling method is developed based on the Weather Research and Forecasting (WRF) model version 3.6.1, applying high-resolution land-use and topography data. In addition, a new subgrid-scale topographic drag parameterization has been implemented for a realistic representation of the atmospheric surface-layer momentum transfer. Finally, a year-long simulation for the Kori and Wolsong NPPs, located in southeastern coastal areas, has been made for 2016 and evaluated against operational surface meteorological measurements and the NPPs’ on-site weather stations.Results and Discussion: The new dynamic downscaling method can represent multiscale atmospheric motions from the synoptic to the boundary-layer scales and produce three-dimensional local meteorological fields near the NPPs with a 1.2 km grid resolution. Comparing the year-long simulation against the measurements showed a salient improvement in simulating near-surface wind fields by reducing the root mean square error of approximately 1 m/s. Furthermore, the improved wind field simulation led to a better agreement in the Eulerian estimate of the local atmospheric dispersion. The new subgrid-scale topographic drag parameterization was essential for improved performance, suggesting the importance of the subgrid-scale momentum interactions in the atmospheric surface layer.Conclusion: A new dynamic downscaling method has been developed to produce high-resolution local meteorological fields around the Kori and Wolsong NPPs, which can be used in short-range atmospheric dispersion modeling near the NPPs.

Wind tunnel research, dynamics, and scaling for wind energy

The interaction of wind turbines with turbulent atmospheric boundary layer (ABL) flows represents a complex multi-scale problem that spans several orders of magnitudes of spatial and temporal scales. These scales range from the interactions of large wind farms with the ABL (on the order of tens of kilometers) to the small length scale of the wind turbine blade boundary layer (order of a millimeter). Detailed studies of multi-scale wind energy aerodynamics are timely and vital to maximize the efficiency of current and future wind energy projects, be they onshore, bottom-fixed offshore, or floating offshore. Among different research modalities, wind tunnel experiments have been at the forefront of research efforts in the wind energy community over the last few decades. They provide valuable insight about the aerodynamics of wind turbines and wind farms, which are important in relation to optimized performance of these machines. The major advantage of wind tunnel research is that wind turbines can be experimentally studied under fully controlled and repeatable conditions allowing for systematic research on the wind turbine interactions that extract energy from the incoming atmospheric flow. Detailed experimental data collected in the wind tunnel are also invaluable for validating and calibrating numerical models.

A two‐fluid single‐column model of turbulent shallow convection. Part 1: Turbulence equations in the multifluid framework

AbstractThe multifluid equations are derived from the compressible Euler equations (or any of the usual approximate equation sets used in meteorology) by conditional filtering. They have the potential to provide the basis for an improved representation of cumulus convection and its coupling to the boundary layer and larger scale flow in numerical models. The present article derives the prognostic equations for subfilter‐scale turbulent second moments in the multifluid framework, along with certain systematic simplifications of them, thus providing a multifluid analogue of the well‐known Mellor and Yamada hierarchy of turbulence closures. As well as enabling a more accurate calculation of subfilter‐scale fluxes and the effects of subfilter‐scale variability on cloud fraction, liquid water, and buoyancy, the second moment information can be used to obtain a more accurate parameterization of entrainment and detrainment. A subset of the turbulence equations derived here is employed in the two‐fluid single‐column model described in Part 2 and applied to the simulation of shallow cumulus cases in Part 3.

Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model

Although it is understood that surface roughness can impact boundary layer physics in high-speed flows, there has been little research aimed at understanding the potential impact of surface roughness on high-speed shock-wave/boundary-layer interactions. Here, a hollow cylinder flare model was used to study the potential impact of distributed surface roughness on shock-wave/boundary-layer interaction unsteadiness. Two surface conditions were tested—a smooth steel finish with an average roughness of 0.85 μm and a rough surface (3K carbon fiber) with an average roughness value of 9.22 μm. The separation shock foot from the shock-wave/boundary-layer interaction on the hollow cylinder flare was tracked by analyzing schlieren images with a shock tracking algorithm. The rough surface increased boundary layer thickness by approximately a factor of 10 compared to the smooth case, significantly altering the interaction scaling. Despite normalizing results, based on this boundary layer scaling, the rough surface case still exhibited mean shock foot positions further upstream more than the smooth surface case. Power spectra of the unsteady shock foot location data demonstrated that the rough surface case exhibited unsteady motion with attenuated energy relative to the smooth-wall case.

Strong Rayleigh–Darcy convection regime in three-dimensional porous media

We perform large-scale numerical simulations to study Rayleigh–Darcy convection in three-dimensional fluid-saturated porous media up to Rayleigh–Darcy number $Ra=8\times 10^4$ . At these large values of $Ra$ , the flow is dominated by large columnar structures – called megaplumes – which span the entire height of the domain. Near the boundaries, the flow is hierarchically organized, with fine-scale structures interacting and nesting to form larger-scale structures called supercells. We observe that the correlation between the flow structure in the core of the domain and at the boundaries decreases only slightly for increasing $Ra$ , and remains rather high even at the largest $Ra$ considered here. This confirms that supercells are the boundary footprint of megaplumes dominating the core of the domain. In agreement with available literature predictions, we show that the thickness of the thermal boundary layer scales very well with the Nusselt number as $\delta \sim 1/ Nu$ . Measurements of the mean wavenumber – inverse of the mean length scale – in the core of the flow support the scaling $\bar {k} \sim Ra^{0.49}$ , in very good agreement with theoretical and numerical predictions. Interestingly, the behaviour of the mean wavenumber near the boundaries scales as $\bar {k} \sim Ra^{0.81}$ , which is distinguishably different from the presumed linear behaviour. We hypothesize that a linear behaviour can only be observed in the ultimate regime, which we argue to set in only at $Ra$ in excess of $5\times 10^5$ , whereas a sublinear behaviour is recovered at more modest $Ra$ . The present results are expected to help the development of long desired reliable models to predict the large- and fine-scale structure of Rayleigh–Darcy convection in the high- $Ra$ regime typically encountered in geophysical processes, such as for instance in geological carbon dioxide sequestration.

Viscoplastic corner eddies

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.

Closure modeling in near-wall region of steep resolution variation for partially averaged Navier-Stokes simulations

Accurate representation of the near-wall flow physics at high Reynolds numbers is computationally prohibitive for many uniform resolution turbulence models. Therefore, a closure with spatially varying resolution is sought which seamlessly transitions from low resolution RANS near-wall to high-resolution PANS in the outer region. This new modeling strategy systematically accounts for the energy exchange terms between the resolved and unresolved scales in the region of resolution change. By ensuring energy conservation and equilibrium boundary layer (EBL) scaling, the model accurately captures the flow behavior near-wall for turbulent channel flow at high Reynolds numbers.

Batchelor Prize Lecture: Measurements in wall-bounded turbulence

Our understanding of turbulent boundary layer scaling and structure has advanced greatly in the past 20 to 30 years. On the computational side, direct numerical simulations and large-eddy simulations have made extraordinary contributions as numerical methods and computational resources have advanced, while on the experimental side major advances in instrumentation have made available new imaging and quantitative techniques that provide unprecedented accuracy and detail. Here, I illustrate how the development of such experimental methods have aided our progress by reference to some particular topics related to the structure of turbulent boundary layers: the power law scaling of the mean velocity and its relationship to the mesolayer; the scaling of the outer layer with regard to the log law in turbulence; the development of the outer peak; and the scaling of the turbulent stresses in the near-wall region, with an emphasis on the streamwise component.

Pressure fluctuations due to ‘trapped waves’ in the initial region of compressible jets

An experimental study is conducted on unsteady pressure fluctuations occurring near the nozzle exit and just outside the shear layer of compressible jets. These fluctuations are related to ‘trapped waves’ within the jet's potential core, as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of various aspect ratios are studied. The fluctuations manifest as a series of peaks in the spectra of the fluctuating pressure. Usually the first peak at the lowest frequency (fundamental) has the highest amplitude and the amplitude decreases progressively for successive peaks at higher frequencies. These ‘trapped wave spectral peaks’ are found to occur with all jets at high subsonic conditions and persist into the supersonic regime. Their characteristics and variations with axial and radial distances, jet Mach number and aspect ratio of the nozzle are documented. For round nozzles, the frequency of the fundamental is found to be independent of the jet's exit boundary layer characteristics and scales with the nozzle diameter. On a Strouhal number (based on diameter) versus jet Mach number plot it is represented by a unique curve. Relative to the fundamental the frequencies of the successive peaks are found to bear the ratios of 5/3, 7/3, 9/3 and so on, at a given Mach number. For rectangular nozzles, the number of peaks observed on the major axis is found to be greater than that observed on the minor axis by a factor approximately equal to the nozzle's aspect ratio; the fundamental is the same on either edge. For all nozzles the onset of screech tones appears as a continuation of the evolution of these peaks; it is as if one of these peaks abruptly increases in amplitude and turns into a screech tone as the jet Mach number is increased.

Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin\u2013Obukhov Similarity Theory

The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.

Large Roll Vortices Exhibited by Post-Tropical Cyclone Sandy during Landfall

Roll vortices are frequent features of a hurricane’s boundary layer, with kilometer or sub-kilometer horizontal scale. In this study, we found that large roll vortices with O (10 km) horizontal wavelength occurred over land in Post-Tropical Cyclone Sandy (2012) during landfall on New Jersey. Various characteristics of roll vortices were corroborated by analyses of Doppler radar observations, a 500 m resolution Weather Research and Forecasting (WRF) simulation, and an idealized roll vortex model. The roll vortices were always linear-shaped, and their wavelengths of 5–14 km were generally larger than any previously published for a tropical cyclone over land. Based on surface wind observations and simulated WRF surface wind fields, we found that roll vortices significantly increased the probability of hazardous winds and likely caused the observed patchiness of treefall during Sandy’s landfall.

Aging in a mean field elastoplastic model of amorphous solids

We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are driven by power-law distributed mechanical noise from yield events throughout the material, in contrast to the well-studied Hébraud–Lequeux model where the noise is Gaussian. We first use a mapping to a mean first passage time problem to study the phase diagram in the absence of shear, which shows a transition between an arrested and a fluid state. We then introduce a boundary layer scaling technique for low yield rate regimes, which we first apply to study the scaling of the steady state yield rate on approaching the arrest transition. These scalings are further developed to study the aging behavior in the glassy regime for different values of the exponent μ characterizing the mechanical noise spectrum. We find that the yield rate decays as a power-law for 1 < μ < 2, a stretched exponential for μ = 1, and an exponential for μ < 1, reflecting the relative importance of far-field and near-field events as the range of the stress propagator is varied. A comparison of the mean-field predictions with aging simulations of a lattice elastoplastic model shows excellent quantitative agreement, up to a simple rescaling of time.

Boundary-layer effects on electromagnetic and acoustic extraordinary transmission through narrow slits.

We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the matched-asymptotics analysis of Holley & Schnitzer (2019 Wave Motion 91, 102381 (doi:10.1016/j.wavemoti.2019.102381)), who considered a single-slit system assuming an idealized formulation where dissipation is neglected and the electromagnetic and acoustic problems are analogous. We here extend that theory to include thin dissipative boundary layers associated with finite conductivity of the plate in the electromagnetic problem and viscous and thermal effects in the acoustic problem, considering both single-slit and slit-array configurations. By considering a distinguished boundary-layer scaling where dissipative and diffractive effects are comparable, we develop accurate analytical approximations that are generally valid near resonance; the electromagnetic-acoustic analogy is preserved up to a single parameter that is provided explicitly for both scenarios. The theory is shown to be in excellent agreement with GHz-microwave and kHz-acoustic experiments in the literature.

Entropy production of an active particle in a box

A run-and-tumble particle in a one-dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the walls. The mesoscopic steady state entropy production rate of the system is derived from coupled Fokker-Planck equations with a linear reaction term, resulting in an exact analytic expression. The entropy production density is shown to peak at the walls. Additionally, the derivative of the entropy production rate peaks at a system size proportional to the length scale of the accumulation boundary layer, suggesting that the behavior of the entropy production rate and its derivatives as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.

Sound radiated by turbulent flow over unrounded and rounded forward-facing steps

This study presents measurements of the far-field noise radiated by forward-facing steps with and without rounded corners. A noise prediction formula, obtained by combining theory and measurements, to predict noise radiated by an unrounded forward step is also presented. The prediction methodology has also been extended to include the effects of rounding the step corner. The height of the step in measurements ranged between 78% to 84% of the incoming, turbulent wall-jet boundary layer. The Reynolds number based on step height was between 8300 and 16,800. Six roundings of the step corner were considered with radii equal to 0%, 6.25%, 12.5%, 25%, 50%, and 100% of the step height. It was found that rounding the forward step corner reduces the noise without affecting its directivity and scaling significantly. A slight rounding of the corner only affects the noise at high frequencies, however, a further increase in rounding leads to a broadband noise reduction. The prediction formula for the unrounded forward step yields reasonably good agreement with both past and present measurements. The predictions also suggest that the noise generated by a forward step is independent of the incoming boundary-layer thickness and scales with the step height. The predictions for rounded forward steps show that the noise attenuation due to corner rounding can be reasonably approximated if it is assumed that the unsteady surface loading in the vicinity of rounded steps scales with the reattachment length associated with each rounding.

Numerical investigation of dust sedimentation effects on wall adsorption of indoor SVOC by the immersed boundary-lattice Boltzmann method

In this work the lattice Boltzmann method (LBM) is used to investigate semi-volatile organic compounds (SVOCs) mass transfer under the influence of particle sedimentation in the boundary-layer scale region. For the fluid-particle interaction, the direct-forcing immersed boundary (IB) method is applied to calculate the hydro-dynamic force. A mass-transfer IB method is employed to calculate the fluid-particle SVOC flux. Particles with zero and saturated initial-concentrations are studied to investigate the effects of clean and polluted particles. Effects of fluid/particle equilibrium coefficients, as well as particle diameters, are discussed. Wall adsorptions under the influence of multiple particles are also investigated. Numerical simulations reveal that a particle always intensifies wall adsorption independent of its initial SVOC concentration. The influences of particles on wall adsorption are associated with disturbance effect (disturbing air due to particle moving) and medium effect (SVOC mass transfer between particles and their surrounding air). Disturbance effect of clean particles overwhelms their medium effect while medium effect is dominant for saturated particles. Disturbance effect and medium effect both increase with particle diameter, and medium effect is more sensitive to particle diameter. Competitive adsorption occurs in presence of a number of particles and has an indirect impact on wall adsorption.