Role of pressure in nonlinear velocity gradient dynamics in turbulence

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
Ravi K. Bikkani ◽  
Sharath S. Girimaji
Keyword(s):  
Velocity Gradient ◽  
Gradient Dynamics ◽  
Nonlinear Velocity

On velocity gradient dynamics and turbulent structure

2015 ◽  
Vol 780 ◽  
pp. 60-98 ◽  
Author(s):  
J. M. Lawson ◽  
J. R. Dawson
Keyword(s):  
Velocity Gradient ◽  
Local Strain ◽  
Turbulent Structure ◽  
Stochastic Estimation ◽  
Spatially Resolved ◽  
Gradient Dynamics ◽  
Layer Structures ◽  
Non Local ◽  
Conditional Averaging

The statistics of the velocity gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by $\unicode[STIX]{x1D63C}$. Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the $Q$ field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.

Role of Shear in the Isotropic to Lamellar Transition

1989 ◽  
Vol 177 ◽  
Author(s):  
S. T. Milner ◽  
M. E. Cates
Keyword(s):  
Transition Temperature ◽  
Shear Rate ◽  
Effective Potential ◽  
Velocity Gradient ◽  
Steady Shear ◽  
High Shear ◽  
First Order ◽  
Experimental Systems ◽  
Nonlinear Fluctuation

ABSTRACTIn the isotropic to lamellar transition, nonlinear fluctuation terms lower the transition temperature τc and drive the transition first order. Here we show that steady shear, by suppressing the fluctuations, raises τc; in a certain temperature range the lamellar phase can be induced by applying shear. A study of the effective potential indicates that the transition remains first order, though becoming very weak at high shear rate. We argue heuristically that the lamellar ordering first occurs with wavevector normal to both the velocity and the velocity gradient. We estimate the characteristic shear rate for two current experimental systems.

The role of ballast specific gravity and velocity gradient in ballasted flocculation

2020 ◽  
Vol 399 ◽  
pp. 122970 ◽  
Author(s):  
Muhammad Qasim ◽  
Seongjun Park ◽  
Jong-Oh Kim
Keyword(s):  
Specific Gravity ◽  
Velocity Gradient
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