- Title
- Transport equations for the normalized nth-order moments of velocity derivatives in grid turbulence
- Creator
- Tang, S. L.; Antonia, R. A.; Djenidi, L.
- Relation
- Journal of Fluid Mechanics Vol. 930, no. A31
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2021.927
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2021
- Description
- Transport equations for the normalized moments of the longitudinal velocity derivative Fn+1 (here, n is 1,2,3…) are derived from the Navier–Stokes (N–S) equations for shearless grid turbulence. The effect of the (large-scale) streamwise advection of Fn+1 by the mean velocity on the normalized moments of the velocity derivatives can be expressed as C1Fn+1/Reλ, where C1 is a constant and Reλ is the Taylor microscale Reynolds number. Transport equations for the normalized odd moments of the transverse velocity derivatives Fy,n+1 (here, n is 2, 4, 6), which should be zero if local isotropy is satisfied, are also derived and discussed in sheared and shearless grid turbulence. The effect of the (large-scale) streamwise advection term on the normalized moments of the velocity derivatives can also be expressed in the form C2Fy,n+1/Reλ, where C2 is a constant. Finally, the contribution of the mean shear in the transport equation for Fn+1 can be modelled as 15B/Reλ, where B (=S∗Ss,n+1) is the product of the non-dimensional shear parameter S∗ and the normalized mixed longitudinal-transverse velocity derivatives Ss,n+1; if local isotropy is satisfied, Ss,n+1 should be zero. These results indicate that if Fn+1, Fy,n+1 and B do not increase as rapidly as Reλ, then the effect of the large-scale structures on small-scale turbulence will disappear when Reλ becomes sufficiently large.
- Subject
- isotropic turbulence; turbulence theory; velocity derivatives; transport equation
- Identifier
- http://hdl.handle.net/1959.13/1459710
- Identifier
- uon:45753
- Identifier
- ISSN:0022-1120
- Language
- eng
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