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| Titel |
Intermittency in Complex Flows |
| VerfasserIn |
Otman Ben Mahjoub, Jose M. Redondo |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250154137
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| Publikation (Nr.) |
 EGU/EGU2017-19201.pdf |
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| Zusammenfassung |
| Experimental results of the complex turbulent wake of a cilinder in 2D [1] and 3D flows [2]
were used to investigate the scaling of structure functions, similar research was also
performed on wave propagation and breaking in the Ocean [3], in the the stratified
Atmosphere (ABL) [4] and in a 100large flume (UPC) for both regular and irregular waves,
where long time series of waves propagating and generating breaking turbulence velocity rms
and higher order measurements were taken in depth. [3,5] by means of a velocimeter
SONTEK3-D. The probability distribution functions of the velocity differences
and their non Gaussian distribution related to the energy spectrum indicate that
irregularity is an important source of turbulence. From Kolmogorov’s K41 and K61
intermittency correction: the p th-order longitudinal velocity structure function δul at scale
l in the inertial range of three-dimensional fully developed turbulence is related
by
⟨δup⟩ = ⟨(u(x+ l)− u(x))p⟩ ∼ εp0∕3lp∕3
l
where ⟨...⟩ represents the spatial average over flow domain, with ε0 the mean energy
dissipation per unit mass and l is the separation distance. The importance of the random
nature of the energy dissipation led to the K62 theory of intermittency, but locality and
non-homogeneity are key issues.
p p∕3 p∕3 ξd
⟨δul⟩ ∼ ⟨εl ⟩l ∼ l
and ξp = p
3 + τp∕3 , where now εl is a fractal energy dissipation at scale l, τp∕3 is the
scaling of < ɛℓp∕3 > and ξp is the scaling exponent of the velocity structure function of order
p. Both in K41 and K62, the structure functions of third order related to skewness is ξ3 = 1.
But this is not true either.
We show that scaling exponents ξp do deviate from early studies that only investigated
homogeneous turbulence, where a large inertial range dominates. The use of multi-fractal
analysis and improvements on Structure function calculations on standard Enhanced mixing
is an essential property of turbulence and efforts to alter and to control turbulent mixing is a
subject of great importance because it has a broad range of practical applications.
In the chemical industry in particular mixing is desirable to facilitate fast mixing
of reactants coupled with PIV, and on other methods used in experimental fluids
mechanics, both in Eulerian and Lagrangian frameworks towards the understanding of
molecular mixing and the role of vorticity and helicity in the analysis of stream function
parameter oundaries of spatial dynamic features. Already we used multi-fractal
analysis techniques and apply these techniques to understand the scale to scale
transport related to mixing and the velocity structure function,used by [1, 2] in the
form
⟨| δul |p⟩ ∝ ⟨| δul |s⟩ζp∕ζs
where ζp∕ζs is a general relative scaling exponent that can be expressed as
dlog⟨| δul |p⟩
ζp∕ζs = ---------s-
dlog⟨| δul | ⟩ In
these relations ζp can be different from ξp for odd values of p because absolute values of
velocity increments are used. Clearly, the scale-invariance for relative exponents when ζp and
ζs are scale-dependent cannot be easily interpreted.
We estimate different intermittency parameters as a function of local instability e.g.
Kelvin/Helmholtz, Rayleigh-Taylor or Holbmoe. Different scalar interfaces show
different structures, that also depend on local Richardsons numbers, this may be
due to different levels of intermittency and thus different spectra, which are not
necessarily inertial nor in equilibrium. the analysis of the statistical properties of the
velocity structure function is performed using a relative scaling. In the areas of
breaking-induced turbulence and foam, which corespond to active, highly intermittent,
turbulent regions, using(ESS), we define local intermittency at different depths and horizontal
positions. The deviation from the -5/3 law for the power spectra at certain positions is
clear, (PDF) of velocity differences highly deviate from a gaussian distribution,
and depend on the depth or with downstream distance for intermediate Reynolds
numbers.
[1] A. Babiano, B. Dubrulle. and P. Frick; Phys. Rev. E. 55(3): 2693-2706 (1997).
[2] E. Gaudin, B. Protas, S. Goujon-Durand, J. Wojciechowski, J. E. Wesfreid; Phys. Rev.
E. 57, 9-12 (1998).
[3] O. B. Mahjoub; Non-local dynamics and intermittency in non-homogeneous flows.
PhD Thesis UPC Barcelona Tech. 139 p.(2000)
[4] Vindel J.M. Yague C and Redondo J.M.; Relationship between intermittency and
stratification. Il. Nuovo Cimento 31, C. 669-678. (2008).
[5] J.M. Redondo; Mixing efficiencies of different kinds of turbulent processes and
instabilities, Applications to the environment, Turbulent mixing in geophysical flows. Eds.
Linden P.F. and Redondo J.M. 131-157. (2001).
[6] J.M. Redondo; Turbulent mixing in the Atmosphere and Ocean ,Fluid Physics. 5:
584-597. World Scientific. New York. (1994).
[7] O. B. Mahjoub, J. M. Redondo and A. Babiano; Applied Scientific R8search, 59,
299-313 (1998).
[8] O. B. Mahjoub, J. M. Redondo and A. Babiano; Self simmilarity and intermittency in
a turbulent non-homogeneous wake. Ed. C. Dopazo et al. Advances in Turbulence VIII.
783-786. (2000) |
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