scholarly journals Nonlinear effects in buoyancy-driven variable-density turbulence

2016 ◽  
Vol 810 ◽  
pp. 362-377 ◽  
Author(s):  
P. Rao ◽  
C. P. Caulfield ◽  
J. D. Gibbon
Keyword(s):  
Density Gradient ◽  
Blow Up ◽  
Nonlinear Effects ◽  
Variable Density ◽  
Density Field ◽  
Strong Mixing ◽  
Spatial Average ◽  
Large Growth ◽  
Variable Density Turbulence ◽  
Using Data

We consider the time dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\unicode[STIX]{x1D714}}$ and $D_{m,\unicode[STIX]{x1D703}}$ of the vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ and the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D703}=\log (\unicode[STIX]{x1D70C}^{\ast }/\unicode[STIX]{x1D70C}_{0}^{\ast })$, in a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid Mech., vol. 591, 2007, pp. 43–71). Here, $\unicode[STIX]{x1D70C}^{\ast }(\boldsymbol{x},t)$ is the composition density of a mixture of two incompressible miscible fluids with fluid densities $\unicode[STIX]{x1D70C}_{2}^{\ast }>\unicode[STIX]{x1D70C}_{1}^{\ast }$, and $\unicode[STIX]{x1D70C}_{0}^{\ast }$ is a reference normalization density. Using data from the publicly available Johns Hopkins turbulence database, we present evidence that the $L^{2}$-spatial average of the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ can reach extremely large values at intermediate times, even in flows with low Atwood number $At=(\unicode[STIX]{x1D70C}_{2}^{\ast }-\unicode[STIX]{x1D70C}_{1}^{\ast })/(\unicode[STIX]{x1D70C}_{2}^{\ast }+\unicode[STIX]{x1D70C}_{1}^{\ast })=0.05$, implying that very strong mixing of the density field at small scales can arise in buoyancy-driven turbulence. This large growth raises the possibility that the density gradient $\unicode[STIX]{x1D735}\unicode[STIX]{x1D703}$ might blow up in a finite time.

The mixing region in freely decaying variable-density turbulence

2015 ◽  
Vol 772 ◽  
pp. 386-426 ◽  
Author(s):  
Pooya Movahed ◽  
Eric Johnsen
Keyword(s):  
Kinetic Energy ◽  
Density Gradient ◽  
Kinematic Viscosity ◽  
Density Ratio ◽  
Variable Density ◽  
Unit Mass ◽  
Material Interface ◽  
Variable Density Turbulence ◽  
Set Up ◽  
Density Ratios

A novel set-up is proposed to numerically study turbulent multimaterial mixing, starting from an unperturbed material interface between a light and a heavy fluid. We conduct direct numerical simulation (DNS) to better understand the role of density gradient alone on the turbulence, specifically with regard to the mixing region dynamics and anisotropy across scales. Freely decaying isotropic turbulent fields of different densities but identical kinematic viscosities are juxtaposed. The rationale for this strategy is that conventional turbulence scalings are based on kinetic energy per unit mass and kinematic viscosity. Thus, by matching the initial kinematics (root-mean-square velocity) and the dissipation (kinematic viscosity), the turbulence (kinetic energy per unit mass) decays at the same rate in both fluids. With this set-up, the effect of the density gradient alone on the turbulence can be considered, independently from other contributions (e.g. mismatch in kinetic energy per unit mass, acceleration field, etc.). We examine the mixing region dynamics at large and small scales for different density ratios and Reynolds numbers. After an initial transient, we observe a self-similar growth of the mixing region, which we explain via theoretical arguments verified by the DNS results. Inside the mixing region, the momentum of the heavier eddies causes the mean interface location to shift toward the light fluid. A higher density ratio leads to a wider, less molecularly mixed mixing region. Although anisotropy is evident at the large scales, the dissipation scales remain essentially isotropic, even at the highest density ratio under consideration (12:1). The intermittency of the velocity field exhibits isotropy, while the mass fraction field is more intermittent in the direction of the density gradient.

scholarly journals Does School Desegregation Promote Diverse Interactions? An Equilibrium Model of Segregation within Schools

2020 ◽  
Vol 12 (2) ◽  
pp. 228-257 ◽  
Author(s):  
Angelo Mele
Keyword(s):  
Equilibrium Model ◽  
School Desegregation ◽  
Racial Segregation ◽  
Add Health ◽  
Nonlinear Effects ◽  
School Segregation ◽  
Friendship Formation ◽  
Using Data ◽  
Diverse Interactions

This paper studies racial segregation in schools using data on student friendships from Add Health. I estimate an equilibrium model of friendship formation, with preferences allowing both homophily and heterophily in direct and indirect ties. I find that homophily goes beyond direct links: students also prefer racially homogeneous indirect friends, while there is heterophily in income. I simulate policies reallocating students across schools. Race-based policies have nonlinear effects on within-school segregation and other network features such as clustering and centrality. Policies increasing diversity through reallocations based on income have less impact on racial segregation. (JEL H75, I21, I28, J15)

scholarly journals Can You Ever Be Too Smart for Your Own Good? Comparing Linear and Nonlinear Effects of Cognitive Ability on Life Outcomes

2020 ◽  
Author(s):  
Matt Brown ◽  
Jonathan Wai ◽  
Christopher Chabris
Keyword(s):  
Cognitive Ability ◽  
Linear Trend ◽  
Positive Association ◽  
Nonlinear Effects ◽  
Popular Literature ◽  
Evidence Based ◽  
Life Outcomes ◽  
Null Effect ◽  
Using Data ◽  
Representative Cohort

Despite a longstanding expert consensus about the importance of cognitive ability for life outcomes, contrary views continue to proliferate in scholarly and popular literature. This divergence of beliefs presents an obstacle for evidence-based policy and decision-making in a variety of settings. One commonly held idea is that greater cognitive ability does not matter or is actually harmful beyond a certain point (sometimes stated as greater than 100 or 120 IQ points). We empirically test these notions using data from four longitudinal, representative cohort studies comprising a total of 48,558 participants in the U.S. and U.K. from 1957 to the present. We find that ability measured in youth has a positive association with most occupational, educational, health, and social outcomes later in life. Most effects were characterized by a moderate-to-strong linear trend or a practically null effect (mean R^2 = .002 to .256). Nearly all nonlinear effects were practically insignificant in magnitude (mean incremental R^2 = .001) or did not replicate across cohorts or survey waves. We found no support for any downside to higher ability and no evidence for a threshold beyond which greater scores cease to be beneficial. Thus, greater cognitive ability is generally advantageous—and virtually never detrimental.

scholarly journals Can You Ever Be Too Smart for Your Own Good? Comparing Linear and Nonlinear Effects of Cognitive Ability on Life Outcomes

2021 ◽  
pp. 174569162096412
Author(s):  
Matt I. Brown ◽  
Jonathan Wai ◽  
Christopher F. Chabris
Keyword(s):  
Cognitive Ability ◽  
Linear Trend ◽  
Positive Association ◽  
Nonlinear Effects ◽  
Popular Literature ◽  
The United States ◽  
Life Outcomes ◽  
Null Effect ◽  
Using Data ◽  
Representative Cohort

Despite a long-standing expert consensus about the importance of cognitive ability for life outcomes, contrary views continue to proliferate in scholarly and popular literature. This divergence of beliefs presents an obstacle for evidence-based policymaking and decision-making in a variety of settings. One commonly held idea is that greater cognitive ability does not matter or is actually harmful beyond a certain point (sometimes stated as > 100 or 120 IQ points). We empirically tested these notions using data from four longitudinal, representative cohort studies comprising 48,558 participants in the United States and United Kingdom from 1957 to the present. We found that ability measured in youth has a positive association with most occupational, educational, health, and social outcomes later in life. Most effects were characterized by a moderate to strong linear trend or a practically null effect (mean R2 range = .002–.256). Nearly all nonlinear effects were practically insignificant in magnitude (mean incremental R2 = .001) or were not replicated across cohorts or survey waves. We found no support for any downside to higher ability and no evidence for a threshold beyond which greater scores cease to be beneficial. Thus, greater cognitive ability is generally advantageous—and virtually never detrimental.

Sign in / Sign up

Export Citation Format

Share Document