Recent Developments in Rapid-Distortion Theory

Savill, A. M.

doi:10.1146/annurev.fl.19.010187.002531

Cited by 85 publications

(47 citation statements)

References 52 publications

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“…Thus, with decreasing height, the inverse turbulent Prandtl number (Prt ' = KH / KJ,J) increases from around 1.1 in the near-neutral inertial sublayer (Garratt, 1992) to around 2 just above z = h. Finally, in the canopy layer below z = h, observations of KM and I<H become very erratic, often exhibiting singularities and regions of negative values. This behaviour is associated with observations of countergradient fluxes within canopies (Denmead and Bradley, 1985;1987), indicating that the turbulent transfer process is essentially nonlocal and cannot be described by a local gradient-diffusion relationship. Reasons for this behaviour can be advanced in both an Eulerian framework (Finnigan and Raupach, 1987) and a Lagrangian framework (Raupach, 1989), the latter offering a fairly straightforward replacement for a gradient-diffusion theory of turbulent transfer within canopies.…”

Section: Eddy Diffusivitiessupporting

confidence: 53%

“…Rapid Distortion Theory (RDT), reviewed by Townsend (1976), Savill (1987) and Hunt and Carruthers (1990) offers some explanation for the differences in statistical flow properties between mixing layers and boundary layers, and thence 371 for the behaviour of these properties in canopy flow near z = h. RDT uses the linearised equations of motion to calculate what happens to an initially specified turbulent velocity field under various kinds of meamflow distortion, specified in our case by U(z). In this respect RDT differs from 'HIST (another linearised theory), which seeks the fastest-growing eigenmodes or resonant modes of the flow.…”

Section: Tests Based Onstatistical Flowpropertiesmentioning

confidence: 99%

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Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

Raupach

Finnigan

Brunet

1996

Boundary-Layer Meteorol

929

458

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This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observeddistinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio KH/KM of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale L, = U(h)/U'(h) (where h is canopy height, U(z) is mean velocity as a function of height Z, and U' = dU/dz). In particular, the streamwise spacing of the dominant canopy eddies is A, = mL,, with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.

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Section: Eddy Diffusivitiessupporting

confidence: 53%

Section: Tests Based Onstatistical Flowpropertiesmentioning

confidence: 99%

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

Raupach

Finnigan

Brunet

1996

Boundary-Layer Meteorol

929

458

View full text Add to dashboard Cite

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“…On the other hand, the characteristics method has been used in the context of rapid distortion theory for analyzing the fluid turbulence 6 and in the eikonal representation of the ballooning mode stability. 7 If we can treat the non-Hermitian part of the whole operator as a singular perturbation to a Hermitian operator, 8,9 we may be able to construct the theory in the framework of the perturbation theory for the operator.…”

Section: Introductionmentioning

confidence: 99%

Transient phenomena and secularity of linear interchange instabilities with shear flows in homogeneous magnetic field plasmas

2001

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Transient and secular behaviors of interchange fluctuations are analyzed in an ambient shear flow by invoking Kelvin’s method of shearing modes. Because of its non-Hermitian property, complex transient phenomena can occur in a shear flow system. The combined effect of shear flow mixing and Alfvén wave propagation overcomes the instability driving force at sufficiently large time, and damps all fluctuations of the magnetic flux. On the other hand, electrostatic perturbations can be destabilized for sufficiently strong interchange drive. The time asymptotic behavior in each case is algebraic (nonexponential).

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“…The first is a representation of the spatial structure of the turbulence, guided by the rapid distortion solution for initially isotropic turbulence in mean shear (Townsend 1980) and consistent with the one-dimensional wavenumber cospectrum equation [(1)]. The rapid distortion solution provides a dynamically consistent framework and has proven successful, in spite of its simplicity, in other contexts (e.g., Savill 1987;Hunt and Carruthers 1990;Cambon and Scott 1999). The second model element is the Lumley and Terray (1983) mapping of the spatial structure of the turbulence to the temporal fluctuations measured by fixed sensors in the presence of waves, adapted to the difference between measurements obtained by two fixed sensors.…”

Section: Introductionmentioning

confidence: 99%

The Cospectrum of Stress-Carrying Turbulence in the Presence of Surface Gravity Waves

Trowbridge

Scully

Sherwood

2018

Journal of Physical Oceanography

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The cospectrum of the horizontal and vertical turbulent velocity fluctuations, an essential tool for understanding measurements of the turbulent Reynolds shear stress, often departs in the ocean from the shape that has been established in the atmospheric surface layer. Here, we test the hypothesis that this departure is caused by advection of standard boundary layer turbulence by the random oscillatory velocities produced by surface gravity waves. The test is based on a model with two elements. The first is a representation of the spatial structure of the turbulence, guided by rapid distortion theory, and consistent with the one-dimensional cospectra that have been measured in the atmosphere. The second model element is a map of the spatial structure of the turbulence to the temporal fluctuations measured at fixed sensors, assuming advection of frozen turbulence by the velocities associated with surface waves. The model is adapted to removal of the wave velocities from the turbulent fluctuations using spatial filtering. The model is tested against previously published laboratory measurements under wave-free conditions and two new sets of measurements near the seafloor in the coastal ocean in the presence of waves. Although quantitative discrepancies exist, the model captures the dominant features of the laboratory and field measurements, suggesting that the underlying model physics are sound.

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Recent Developments in Rapid-Distortion Theory

Cited by 85 publications

References 52 publications

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

Transient phenomena and secularity of linear interchange instabilities with shear flows in homogeneous magnetic field plasmas

The Cospectrum of Stress-Carrying Turbulence in the Presence of Surface Gravity Waves

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