21,746 research outputs found
Bubbly and Buoyant Particle-Laden Turbulent Flows
Fluid turbulence is commonly associated with stronger drag, greater heat
transfer, and more efficient mixing than in laminar flows. In many natural and
industrial settings, turbulent liquid flows contain suspensions of dispersed
bubbles and light particles. Recently, much attention has been devoted to
understanding the behavior and underlying physics of such flows by use of both
experiments and high-resolution direct numerical simulations. This review
summarizes our present understanding of various phenomenological aspects of
bubbly and buoyant particle-laden turbulent flows. We begin by discussing
different dynamical regimes, including those of crossing trajectories and
wake-induced oscillations of rising particles, and regimes in which bubbles and
particles preferentially accumulate near walls or within vortical structures.
We then address how certain paradigmatic turbulent flows, such as homogeneous
isotropic turbulence, channel flow, Taylor-Couette turbulence, and thermally
driven turbulence, are modified by the presence of these dispersed bubbles and
buoyant particles. We end with a list of summary points and future research
questions.Comment: 29 pages, 14 figure
A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations
We prove a blow-up criterion in terms of the upper bound of the density for
the strong solution to the 3-D compressible Navier-Stokes equations. The
initial vacuum is allowed. The main ingredient of the proof is \textit{a
priori} estimate for an important quantity under the assumption that the
density is upper bounded, whose divergence can be viewed as the effective
viscous flux.Comment: 17 page
Horizon-unbiased Investment with Ambiguity
In the presence of ambiguity on the driving force of market randomness, we
consider the dynamic portfolio choice without any predetermined investment
horizon. The investment criteria is formulated as a robust forward performance
process, reflecting an investor's dynamic preference. We show that the market
risk premium and the utility risk premium jointly determine the investors'
trading direction and the worst-case scenarios of the risky asset's mean return
and volatility. The closed-form formulas for the optimal investment strategies
are given in the special settings of the CRRA preference
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