Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Selected wheat seed defense proteins exhibit competitive binding to model microbial lipid interfaces

Puroindolines (Pins) and purothionins (Pths) are basic, amphiphilic, cysteine-rich wheat proteins that play a role in plant defense against microbial pathogens. We have examined the co-adsorption and sequential addition of Pins (Pin-a, Pin-b and a mutant form of Pin-b with Trp-44 to Arg-44 substitution) and β-purothionin (β-Pth) model anionic lipid layers, using a combination of surface pressure measurements, external reflection FTIR spectroscopy and neutron reflectometry. Results highlighted differences in the protein binding mechanisms, and in the competitive binding and penetration of lipid layers between respective Pins and β-Pth. Pin-a formed a blanket-like layer of protein below the lipid surface that resulted in the reduction or inhibition of β-Pth penetration of the lipid layer. Wild-type Pin-b participated in co-operative binding with β-Pth, whereas the mutant Pin-b did not bind to the lipid layer in the presence of β-Pth. The results provide further insight into the role of hydrophobic and cationic amino acid residues in antimicrobial activity.

The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

A note on boundary layer friction in baroclinic cyclones

The interaction between extratropical cyclones and the underlying boundary layer has been a topic of recent discussion in papers by Adamson et al (2006) and Beare (2007). Their results emphasise different mechanisms through which the boundary layer dynamics may modify the growth of a baroclinic cyclone. By using different sea-surface temperature distributions and comparing the low-level winds, the differences are exposed and both of the proposed mechanisms appear to be acting within a single simulation.

Numerical simulation of baroclinic waves with a parameterized boundary layer

A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on mid-latitude cyclones. Simulations are performed of life cycles for two basic states, both with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale-flow structures. The analysis focuses on the generation of potential-vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to be also the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the north-east of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

A case study of boundary layer ventilation by convection and coastal processes

It is often assumed that ventilation of the atmospheric boundary layer is weak in the absence of fronts, but is this always true? In this paper we investigate the processes responsible for ventilation of the atmospheric boundary layer during a nonfrontal day that occurred on 9 May 2005 using the UK Met Office Unified Model. Pollution sources are represented by the constant emission of a passive tracer everywhere over land. The ventilation processes observed include shallow convection, turbulent mixing followed by large-scale ascent, a sea breeze circulation and coastal outflow. Vertical distributions of tracer are validated qualitatively with AMPEP (Aircraft Measurement of chemical Processing Export fluxes of Pollutants over the UK) CO aircraft measurements and are shown to agree impressively well. Budget calculations of tracers are performed in order to determine the relative importance of these ventilation processes. Coastal outflow and the sea breeze circulation were found to ventilate 26% of the boundary layer tracer by sunset of which 2% was above 2 km. A combination of coastal outflow, the sea breeze circulation, turbulent mixing and large-scale ascent ventilated 46% of the boundary layer tracer, of which 10% was above 2 km. Finally, coastal outflow, the sea breeze circulation, turbulent mixing, large-scale ascent and shallow convection together ventilated 52% of the tracer into the free troposphere, of which 26% was above 2 km. Hence this study shows that significant ventilation of the boundary layer can occur in the absence of fronts (and thus during high-pressure events). Turbulent mixing and convection processes can double the amount of pollution ventilated from the boundary layer.

Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer

The influence of surface waves and an applied wind stress is studied in an ensemble of large eddy simulations to investigate the nature of deeply penetrating jets into an unstratified mixed layer. The influence of a steady monochromatic surface wave propagating parallel to the wind direction is parameterized using the wave-filtered Craik-Leibovich equations. Tracer trajectories and instantaneous downwelling velocities reveal classic counterrotating Langmuir rolls. The associated downwelling jets penetrate to depths in excess of the wave's Stokes depth scale, δs. Qualitative evidence suggests the depth of the jets is controlled by the Ekman depth scale. Analysis of turbulent kinetic energy (tke) budgets reveals a dynamical distinction between Langmuir turbulence and shear-driven turbulence. In the former, tke production is dominated by Stokes shear and a vertical flux term transports tke to a depth where it is dissipated. In the latter, tke production is from the mean shear and is locally balanced by dissipation. We define the turbulent Langmuir number Lat = (v*/Us)0.5 (v* is the ocean's friction velocity and Us is the surface Stokes drift velocity) and a turbulent anisotropy coefficient Rt = /( + ). The transition between shear-driven and Langmuir turbulence is investigated by varying external wave parameters δs and Lat and by diagnosing Rt and the Eulerian mean and Stokes shears. When either Lat or δs are sufficiently small the Stokes shear dominates the mean shear and the flow is preconditioned to Langmuir turbulence and the associated deeply penetrating jets.