An adaptive finite element water column model using the Mellor-Yamada level 2.5 turbulence closure scheme

A one-dimensional water column model using the Mellor and Yamada level 2.5 parameterization of vertical turbulent fluxes is presented. The model equations are discretized with a mixed finite element scheme. Details of the finite element discrete equations are given and adaptive mesh refinement strategies are presented. The refinement criterion is an "a posteriori" error estimator based on stratification, shear and distance to surface. The model performances are assessed by studying the stress driven penetration of a turbulent layer into a stratified fluid. This example illustrates the ability of the presented model to follow some internal structures of the flow and paves the way for truly generalized vertical coordinates. (c) 2005 Elsevier Ltd. All rights reserved.

In situ atmospheric turbulence measurement using the terrestrial magnetic field - A compass for a radiosonde

A method for in situ detection of atmospheric turbulence has been developed using an inexpensive sensor carried within a conventional meteorological radiosonde. The sensor-a Hall effect magnetometer-was used to monitor the terrestrial magnetic field. Rapid time scale (10 s or less) fluctuations in the magnetic field measurement were related to the motion of the radiosonde, which was strongly influenced by atmospheric turbulence. Comparison with cloud radar measurements showed turbulence in regions where rapid time-scale magnetic fluctuations occurred. Reliable measurements were obtained between the surface and the stratosphere.

Mean flow and turbulence statistics over groups of urban-like cubical obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant 'dispersive stress' whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.

Reaching for the skies: Time and turbulence in digital technologies and practices

This research examines dynamics associated with new representational technologies in complex organizations through a study of the use of a Single Model Environment, prototyping and simulation tools in the mega-project to construct Terminal 5 at Heathrow Airport, London. The ambition of the client, BAA. was to change industrial practices reducing project costs and time to delivery through new contractual arrangements and new digitally-enabled collaborative ways of working. The research highlights changes over time and addresses two areas of 'turbulence' in the use of: 1) technologies, where there is a dynamic tension between desires to constantly improve, change and update digital technologies and the need to standardise practices, maintaining and defending the overall integrity of the system; and 2) representations, where dynamics result from the responsibilities and liabilities associated with sharing of digital representations and a lack of trust in the validity of data from other firms. These dynamics are tracked across three stages of this well-managed and innovative project and indicate the generic need to treat digital infrastructure as an ongoing strategic issue.

On the structure of Langmuir turbulence

The Stokes drift induced by surface waves distorts turbulence in the wind-driven mixed layer of the ocean, leading to the development of streamwise vortices, or Langmuir circulations, on a wide range of scales. We investigate the structure of the resulting Langmuir turbulence, and contrast it with the structure of shear turbulence, using rapid distortion theory (RDT) and kinematic simulation of turbulence. Firstly, these linear models show clearly why elongated streamwise vortices are produced in Langmuir turbulence, when Stokes drift tilts and stretches vertical vorticity into horizontal vorticity, whereas elongated streaky structures in streamwise velocity fluctuations (u) are produced in shear turbulence, because there is a cancellation in the streamwise vorticity equation and instead it is vertical vorticity that is amplified. Secondly, we develop scaling arguments, illustrated by analysing data from LES, that indicate that Langmuir turbulence is generated when the deformation of the turbulence by mean shear is much weaker than the deformation by the Stokes drift. These scalings motivate a quantitative RDT model of Langmuir turbulence that accounts for deformation of turbulence by Stokes drift and blocking by the air–sea interface that is shown to yield profiles of the velocity variances in good agreement with LES. The physical picture that emerges, at least in the LES, is as follows. Early in the life cycle of a Langmuir eddy initial turbulent disturbances of vertical vorticity are amplified algebraically by the Stokes drift into elongated streamwise vortices, the Langmuir eddies. The turbulence is thus in a near two-component state, with suppressed and . Near the surface, over a depth of order the integral length scale of the turbulence, the vertical velocity (w) is brought to zero by blocking of the air–sea interface. Since the turbulence is nearly two-component, this vertical energy is transferred into the spanwise fluctuations, considerably enhancing at the interface. After a time of order half the eddy decorrelation time the nonlinear processes, such as distortion by the strain field of the surrounding eddies, arrest the deformation and the Langmuir eddy decays. Presumably, Langmuir turbulence then consists of a statistically steady state of such Langmuir eddies. The analysis then provides a dynamical connection between the flow structures in LES of Langmuir turbulence and the dominant balance between Stokes production and dissipation in the turbulent kinetic energy budget, found by previous authors.

Magnetic discontinuities in the near-earth solar wind: evidence of in-transit turbulence or remnants of coronal structure?

Fluctuations in the solar wind plasma and magnetic field are well described by the sum of two power law distributions. It has been postulated that these distributions are the result of two independent processes: turbulence, which contributes mainly to the smaller fluctuations, and crossing the boundaries of flux tubes of coronal origin, which dominates the larger variations. In this study we explore the correspondence between changes in the magnetic field with changes in other solar wind properties. Changes in density and temperature may result from either turbulence or coronal structures, whereas changes in composition, such as the alpha-to-proton ratio are unlikely to arise from in-transit effects. Observations spanning the entire ACE dataset are compared with a null hypothesis of no correlation between magnetic field discontinuities and changes in other solar wind parameters. Evidence for coronal structuring is weaker than for in-transit turbulence, with only ∼ 25% of large magnetic field discontinuities associated with a significant change in the alpha-to-proton ratio, compared to ∼ 40% for significant density and temperature changes. However, note that a lack of detectable alpha-to-proton signature is not sufficient to discount a structure as having a solar origin.

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.

An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm

Recent research has shown that Lighthill–Ford spontaneous gravity wave generation theory, when applied to numerical model data, can help predict areas of clear-air turbulence. It is hypothesized that this is the case because spontaneously generated atmospheric gravity waves may initiate turbulence by locally modifying the stability and wind shear. As an improvement on the original research, this paper describes the creation of an ‘operational’ algorithm (ULTURB) with three modifications to the original method: (1) extending the altitude range for which the method is effective downward to the top of the boundary layer, (2) adding turbulent kinetic energy production from the environment to the locally produced turbulent kinetic energy production, and, (3) transforming turbulent kinetic energy dissipation to eddy dissipation rate, the turbulence metric becoming the worldwide ‘standard’. In a comparison of ULTURB with the original method and with the Graphical Turbulence Guidance second version (GTG2) automated procedure for forecasting mid- and upper-level aircraft turbulence ULTURB performed better for all turbulence intensities. Since ULTURB, unlike GTG2, is founded on a self-consistent dynamical theory, it may offer forecasters better insight into the causes of the clear-air turbulence and may ultimately enhance its predictability.

The influence of Langmuir turbulence on the scaling for the dissipation rate in the oceanic boundary layer

A model for estimating the turbulent kinetic energy dissipation rate in the oceanic boundary layer, based on insights from rapid-distortion theory, is presented and tested. This model provides a possible explanation for the very high dissipation levels found by numerous authors near the surface. It is conceived that turbulence, injected into the water by breaking waves, is subsequently amplified due to its distortion by the mean shear of the wind-induced current and straining by the Stokes drift of surface waves. The partition of the turbulent shear stress into a shear-induced part and a wave-induced part is taken into account. In this picture, dissipation enhancement results from the same mechanism responsible for Langmuir circulations. Apart from a dimensionless depth and an eddy turn-over time, the dimensionless dissipation rate depends on the wave slope and wave age, which may be encapsulated in the turbulent Langmuir number La_t. For large La_t, or any Lat but large depth, the dissipation rate tends to the usual surface layer scaling, whereas when Lat is small, it is strongly enhanced near the surface, growing asymptotically as ɛ ∝ La_t^{-2} when La_t → 0. Results from this model are compared with observations from the WAVES and SWADE data sets, assuming that this is the dominant dissipation mechanism acting in the ocean surface layer and statistical measures of the corresponding fit indicate a substantial improvement over previous theoretical models. Comparisons are also carried out against more recent measurements, showing good order-of-magnitude agreement, even when shallow-water effects are important.

Turbulence dynamics near a turbulent/non-turbulent interface

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (epsilon), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), epsilon decays as z^{-6}, where z is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and epsilon display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness delta of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that delta ~ eta (where eta is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Dissipation of shear-free turbulence near boundaries

The rapid-distortion model of Hunt & Graham (1978) for the initial distortion of turbulence by a flat boundary is extended to account fully for viscous processes. Two types of boundary are considered: a solid wall and a free surface. The model is shown to be formally valid provided two conditions are satisfied. The first condition is that time is short compared with the decorrelation time of the energy-containing eddies, so that nonlinear processes can be neglected. The second condition is that the viscous layer near the boundary, where tangential motions adjust to the boundary condition, is thin compared with the scales of the smallest eddies. The viscous layer can then be treated using thin-boundary-layer methods. Given these conditions, the distorted turbulence near the boundary is related to the undistorted turbulence, and thence profiles of turbulence dissipation rate near the two types of boundary are calculated and shown to agree extremely well with profiles obtained by Perot & Moin (1993) by direct numerical simulation. The dissipation rates are higher near a solid wall than in the bulk of the flow because the no-slip boundary condition leads to large velocity gradients across the viscous layer. In contrast, the weaker constraint of no stress at a free surface leads to the dissipation rate close to a free surface actually being smaller than in the bulk of the flow. This explains why tangential velocity fluctuations parallel to a free surface are so large. In addition we show that it is the adjustment of the large energy-containing eddies across the viscous layer that controls the dissipation rate, which explains why rapid-distortion theory can give quantitatively accurate values for the dissipation rate. We also find that the dissipation rate obtained from the model evaluated at the time when the model is expected to fail actually yields useful estimates of the dissipation obtained from the direct numerical simulation at times when the nonlinear processes are significant. We conclude that the main role of nonlinear processes is to arrest growth by linear processes of the viscous layer after about one large-eddy turnover time.