## Latest Research News on Fluid Dynamics: Jan 2021

**QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS**

This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty. [1]

**The Fluid Dynamics of Tornadoes
**

Because of the difficulty in making measurements under controlled conditions, most of what is known about the fluid dynamics of tornadoes comes from laboratory experiments that produce vortices with features similar to those observed in a tornado. Numerical simulation of laboratory experiments has become a valuable analytical tool owing to the greater ease of extracting data. The success of the numerical simulations has inspired better-defined numerical experiments capable of quantitatively describing the basic features of observed tornado vortices and has motivated simple fluid dynamical explanations. The present article reviews the state of knowledge concerning the fluid dynamics of tornadoes as found in laboratory and numerical analogs. [2]

**Nonlinear fluid dynamics from gravity
**

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of the coordinates on the boundary of AdS5—we use Einstein’s equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion. [3]

**Fluid Dynamics of Flow Driven by Nodal Cilia Precessing Non-circular Cones
**

Nodal cilia play an important role in the left-right symmetry breaking at the early stage of the mammal embryos and show an apparent rotational motion. This study is about the flow induced by cilia sweeping out circular/elliptical cones above a no-slip plane in the low Reynolds number regime. Using the regularized Stokeslet method, we examine the properties of flows generated by a single cilium and multiple cilia, especially two cilia, which are assumed to be anchored to the embryonic heart wall. For a short-term Lagrangian fluid tracer trajectory, epicycles are presented as a nodal cilium precesses in either a circular cone or a non-circular cone shape. For the long-term behavior, the trajectory is periodic around both the circular and elliptical cones. Compared to the circular cone cases, the vertical variances are enhanced in elliptical cone cases. Besides tracer trajectories, fluid velocity elds are presented to demonstrate the flow structure. When two cilia are considered in the system, the flow structure is analyzed for the dierent phase angles and relative orientation of the elliptical cones. [4]

**Charge Dynamics in Vegetable Oil-Based Ester Dielectric Fluid
**

Alkyl ester derivatives of palm kernel oil have been prepared for use as bio-dielectrics in oil filled HV electric equipment. Conduction and loss characteristics of the ester derivatives were studied to understand the behaviour of the material under electric field. Frequency response analyzer was used to study electrical conduction within the fluids since dielectric loss occurring at low frequencies under AC condition is dominated by mobile charge carriers. This is particularly important since power dissipation at power frequency, 50 Hz, may lead to dielectric heating. The dielectric response analysis of the samples with the range 10-3 – 104 Hz show a constant real relative permittivity at high frequency region. As the frequency drops below 101 Hz, there is interfacial polarization at the electrode-liquid interface, which results in a significant dielectric increment in the real part of the relative permittivity at low frequencies with a negative slope greater than 1 and a frequency independent conductance (εÊ¹ slope = -1). This is an indication of Maxwell-Wagner interfacial effect where electric double layer (EDL) is formed. The real part acquired a slope of about -1 around frequency of 103 Hz. This suggests that the establishment of the EDL may be tending towards steady state. This change in the low frequency dispersion could be due to the ionic species undergoing interfacial electrochemical processes, or ions of lower mobility may have contributed to the EDL formation within the frequency region. This may have limited the effect of the strongly divergent processes at the interface. [5]

**Reference**

[1] Roache, P.J., 1997. Quantification of uncertainty in computational fluid dynamics. Annual review of fluid Mechanics, 29(1), pp.123-160.

[2] Rotunno, R., 2013. The fluid dynamics of tornadoes. Annual review of fluid mechanics, 45.

[3] Bhattacharyya, S., Minwalla, S., Hubeny, V.E. and Rangamani, M., 2008. Nonlinear fluid dynamics from gravity. Journal of High Energy Physics, 2008(02), p.045.

[4] Zhao, L. (2015) “Fluid Dynamics of Flow Driven by Nodal Cilia Precessing Non-circular Cones”, Journal of Advances in Mathematics and Computer Science, 9(3), pp. 246-260. doi: 10.9734/BJMCS/2015/17290.

[5] Abdelmalik, A. A. (2013) “Charge Dynamics in Vegetable Oil-Based Ester Dielectric Fluid”, Current Journal of Applied Science and Technology, 4(2), pp. 371-386. doi: 10.9734/BJAST/2014/3627.