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  • Eddies
  • Turbulence
  • Springer  (7)
  • American Meteorological Society
  • MDPI Publishing
  • Nature P. G.
  • 2005-2009  (2)
  • 1985-1989  (5)
  • 1
    Publication Date: 2022-05-25
    Description: © 2008 The Author. This is an open-access article distributed under the terms of the Creative Commons Attribution Noncommercial License. The definitive version was published in Environmental Fluid Mechanics 8 (2008): 551-560, doi:10.1007/s10652-008-9076-5.
    Description: Experiments are reviewed in which a two-layer salt-stratified tank of water was mixed by turbulence. The density profile began as a single step and evolved to a smooth mixed profile. The turbulence was generated by many excursions of a horizontally moving vertical rod with Richardson number Ri 〉 0.9 and Reynolds Number Re 〉 600. There was almost perfect collapse of all the profiles to one universal profile as a function of a similarity variable. We develop a theoretical model for a simple mixing law with a buoyancy flux that is a function of internal Richardson number Rii. A similarity equation is found. A flux law that increases with small Rii and decreases with large Rii is considered next. Since no analytical solution is known, the similarity concept is tested by numerically integrating the equations in space and time. With buoyancy flux monotonically increasing with internal Richardson number, the similarity approach is valid for a profile starting from a slightly smoothed step. However, a shock forms for a mixing law with higher initial Rii (so that buoyancy flux decreases with Richardson number) and the similarity approach is invalid for those initial conditions.
    Keywords: Turbulence ; Mixing ; Stratified ; Similarity solution ; Layered fluid
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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  • 2
    Publication Date: 2022-05-25
    Description: © 2008 The Authors. This is an open-access article distributed under the terms of the Creative Commons Attribution Noncommercial License. The definitive version was published in Environmental Fluid Mechanics 8 (2008): 495-509, doi:10.1007/s10652-008-9107-2.
    Description: Estuarine turbulence is notable in that both the dissipation rate and the buoyancy frequency extend to much higher values than in other natural environments. The high dissipation rates lead to a distinct inertial subrange in the velocity and scalar spectra, which can be exploited for quantifying the turbulence quantities. However, high buoyancy frequencies lead to small Ozmidov scales, which require high sampling rates and small spatial aperture to resolve the turbulent fluxes. A set of observations in a highly stratified estuary demonstrate the effectiveness of a vessel-mounted turbulence array for resolving turbulent processes, and for relating the turbulence to the forcing by the Reynolds-averaged flow. The observations focus on the ebb, when most of the buoyancy flux occurs. Three stages of mixing are observed: (1) intermittent and localized but intense shear instability during the early ebb; (2) continuous and relatively homogeneous shear-induced mixing during the mid-ebb, and weakly stratified, boundary-layer mixing during the late ebb. The mixing efficiency as quantified by the flux Richardson number Rf was frequently observed to be higher than the canonical value of 0.15 from Osborn (J Phys Oceanogr 10:83–89, 1980). The high efficiency may be linked to the temporal–spatial evolution of shear instabilities.
    Description: The funding for this research was obtained from ONR Grant N00014-06-1-0292 and NSF Grant OCE-0729547.
    Keywords: Turbulence ; Estuaries ; Shear instability ; Buoyancy flux
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 130 (1989), S. 547-569 
    ISSN: 1420-9136
    Keywords: Turbulence ; atmospheric turbulence ; clear air turbulence ; middle atmosphere ; heat flux
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The physical nature of motions with scales intermediate between approximately isotropic turbulence and quasi-linear internal gravity waves is not understood at the present time. Such motions play an important role in the energetics of small scales processes, both in the ocean and in the atmosphere, and in vertical transport of heat and constituents. This scale range is currently interpreted either as a saturated gravity waves field or as a buoyancy range of turbulence. We first discuss some distinctive predictions of the classical (Lumley, Phillips) buoyancy range theory, recently improved (Weinstock, Dalaudier and Sidi) to describe potential energy associated with temperature fluctuations. This theory predicts the existence of a spectral gap in the temperature spectra and of an upward mass flux (downward buoyancy and heat fluxes), strongly increasing towards large scales. These predictions are contrasted with an alternate theory, assuming “energetically insignificant” buoyancy flux, proposed by Holloway. Then we present experimental evidences of such characteristic features obtained in the lower stratosphere with an instrumented balloon. Spectra of temperature, vertical velocity, and cospectra of both, obtained in homogeneous, weakly turbulent regions, are compared with theoretical predictions. These results are strongly consistent with the improved classical buoyancy range theory and support the existence of a significant downward heat flux in the buoyancy range. The theoretical implications of the understanding of this scale range are discussed. Many experimental evidences consistently show the need for an anisotropic theory of the buoyancy range of turbulence.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 53 (1988), S. 95-108 
    ISSN: 1572-9613
    Keywords: Turbulence ; self-organization ; helicity ; incompressible fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of incompressible turbulent fluids with respect to weak mean flow perturbations is discussed. It is shown that for a statistically homogeneous, isotropic, and stationary model such perturbations will decay. This is in marked contrast to the compressible case.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 53 (1988), S. 1261-1271 
    ISSN: 1572-9613
    Keywords: Turbulence ; probability density function ; generating functional ; Hopf's equation ; microscopic phase density ; Vlasov's equation ; functional integration ; Bogolyubov's functional formalism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A generating functional for the equal-time spatial probability density functions which represent the ensemble of turbulent incompressible Navier-Stokes fluids is introduced. By formally solving the linear evolution equation satisfied by this functional, the probability densities are represented as functional integrals. It is shown that the generating functional can be regarded as the space characteristic functional of a generalized random field defined on the phase space spanned by the material position and velocity fields of a fluid particle. The interpretation of this random field, which satisfies a dynamical equation similar to Vlasov's, is clarified through the formal analogies between the statistics of molecules and fluid particles at the functional level. A class of statistically realizable and solvable models is also considered within the context of the present formalism.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 51 (1988), S. 949-963 
    ISSN: 1572-9613
    Keywords: Turbulence ; Karhunen-Loeve ; Liapunov ; decimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Navier-Stokes turbulence at ordinarily large Reynolds numbers can involve excitation of perhaps 1018 Fourier modes. A variety of proposals for reduced description have been offered, both to gain physical insight and to make computation feasible. The present brief and idiosyncratic survey discusses Galerkin approximations, Liapunov bases, Karhunen-Loeve decompositions, and statistically based decimation techniques.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of scientific computing 3 (1988), S. 139-147 
    ISSN: 1573-7691
    Keywords: Turbulence ; renormalization group ; numerical simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The results of numerical simulations of random-force-driven Navier-Stokes turbulence designed to test predictions of the renormalization group theory of turbulence are presented. By specially choosing the random force, we generate fully developed turbulence with a relatively long inertial range. The results of these simulations provide direct numerical verification of the correspondence principle [V. Yakhot and S.A. Orszag,Phys. Rev. Lett. 57, 1722 (1986)] and agree with the theoretical predictions based on the ɛ-expansion to about 2%–5%.
    Type of Medium: Electronic Resource
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