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.

Modelling metal cutting using modern ductile fracture mechanics: Quantitative explanations for some longstanding problems

The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.

Toughness, the shearing of self-mated junctions and friction

Since ductile fracture (rupture) is the process by which junctions are separated and which prevents ever-increasing plasticity and junction growth, it is argued that models of friction ought to include toughness as well as yield strength. An expression for the coefficient of sliding friction is derived using ductile fracture mechanics. The predictions are quite reasonable.

Toughness & cutting: A new way of determining ductile fracture toughness and strength

A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.

Extending the friction cone algorithm for arbitrary polygon based haptic objects

Most haptic environments are based on single point interactions whereas in practice, object manipulation requires multiple contact points between the object, fingers, thumb and palm. The Friction Cone Algorithm was developed specifically to work well in a multi-finger haptic environment where object manipulation would occur. However, the Friction Cone Algorithm has two shortcomings when applied to polygon meshes: there is no means of transitioning polygon boundaries or feeling non-convex edges. In order to overcome these deficiencies, Face Directed Connection Graphs have been developed as well as a robust method for applying friction to non-convex edges. Both these extensions are described herein, as well as the implementation issues associated with them.

Force shading and bump mapping using the friction cone algorithm

Previous work has presented the friction cone algorithm, a generalised method to resolve forces on a simulated haptic object when two or more fingers are in contact. Two extensions to the friction cone algorithm are presented: force shading and bump mapping. Force shading removes the discontinuities that are present when transitioning from one face to the next, whilst bump mapping provides a mechanism for rendering haptic textures on polygonal surfaces. Both these extensions can be combined whilst still maintaining the friction cone algorithm's intrinsic ability to simulate arbitrarily complex friction models.

Friction and inertia: business change, corporate real estate portfolios and the UK office market

It has been asserted that business reorganisation and new working practices are transforming the nature of demand for business space. Downsizing, delayering, business process reengineering and associated initiatives alter the amount, type and location of space required by firms. The literature has neglected the impact of real estate market structures on the ability of organisations to successfully implement these new organisational forms or contemporary working practices. Drawing from UK research, the paper demonstrates that, while new working practices are widespread, their impact on the corporate real estate portfolio is less dramatic than often supposed. In part, this is attributed to inflexibility in market structures which constrains the supply of appropriate space.

Boundary-layer friction in midlatitude cyclone

Results from an idealized three-dimensional baroclinic life-cycle model are interpreted in a potential vorticity (PV) framework to identify the physical mechanisms by which frictional processes acting in the atmospheric boundary layer modify and reduce the baroclinic development of a midlatitude storm. Considering a life cycle where the only non-conservative process acting is boundary-layer friction, the rate of change of depth-averaged PV within the boundary layer is governed by frictional generation of PV and the flux of PV into the free troposphere. Frictional generation of PV has two contributions: Ekman generation, which is directly analogous to the well-known Ekman-pumping mechanism for barotropic vortices, and baroclinic generation, which depends on the turning of the wind in the boundary layer and low-level horizontal temperature gradients. It is usually assumed, at least implicitly, that an Ekman process of negative PV generation is the mechanism whereby friction reduces the strength and growth rates of baroclinic systems. Although there is evidence for this mechanism, it is shown that baroclinic generation of PV dominates, producing positive PV anomalies downstream of the low centre, close to developing warm and cold fronts. These PV anomalies are advected by the large-scale warm conveyor belt flow upwards and polewards, fluxed into the troposphere near the warm front, and then advected westwards relative to the system. The result is a thin band of positive PV in the lower troposphere above the surface low centre. This PV is shown to be associated with a positive static stability anomaly, which Rossby edge wave theory suggests reduces the strength of the coupling between the upper- and lower-level PV anomalies, thereby reducing the rate of baroclinic development. This mechanism, which is a result of the baroclinic dynamics in the frontal regions, is in marked contrast with simple barotropic spin-down ideas. Finally we note the implications of these frictionally generated PV anomalies for cyclone forecasting.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.

Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.