# FY2014 Annual Report

## Continuum Physics Unit

Professor Gustavo Gioia

### Abstract

The Continuum Physics Unit pursed theoretical and experimental research on turblent flows and tropical cyclones and granular materials, and continued to develop a joint fluid mechanics--continuum fluidics laboratory at OIST.

### 1. Staff

• Prof. Gustavo Gioia, Professor
• Dr. Tapan Sabuwala, Researcher
• Dr. Tinihau Meuel, Researcher
• Mr. Dongrong Zhang, Graduate Student
• Mr. Shohei Takaoka, Graduate Student (Research Rotation)
• Ms. Kaori Egashira, Research Administrator

### 2. Collaborations

• Theme: The spectral link in wall-bounded turbulent flows
• Type of collaboration: Scientific collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST

• Theme: Effect of rain in tropical cyclons
• Type of collaboration: Scientific collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST

• Theme: Impact cratering in granular beds
• Type of collaboration: Scientific collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST
• Professor Susan Kieffer, University of Illinois at Urbana-Champaign, USA

• Theme: Experiments on turbulent pipe flows
• Type of collaboration: Scientific collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST
• Professor Jun Sakakibara, Meiji University, Japan.

• Theme: Design of Taylor-Couette experiment
• Type of collaboration: Scientific collaboration
• Researchers:
• Dr. Yasuo Higashi, OIST
• Professor Pinaki Chakraborty, OIST

### 3. Activities and Findings

We have carried out theoretical research on the classic laws of the mean-velocity profiles (MVPs) of wall-bounded turbulent flows. Known as the law of the wall, the defect law and the log law, the classic laws are the fundamental laws of hydraulics and they inform the way in which MVPs are apprehended and conceptualized as macroscopic turbulent phenomena. What is more, Prandtl's theory of turbulent friction, a mainstay of hydraulic engineering, hydrology, meteorology and kindred disciplines, is but a corollary of the classic laws. And yet, for all that, the classic laws amount to little more than a sensible, if rather opaque, set of similarity assumptions as to the asymptotic behavior of the MVPs in the limits of vanishing viscosity and infinite turbulent domain. Thus, at present, the classic laws are solely related to, while furnishing scant physical insight into, the MVPs of wall-bounded turbulent flows, nor can any empirical data be harnessed in support of the classic laws unless it be data on the MVPs themselves. By combining two of our findings of prior years, the "spectral link" and the "spectral analogs", we have been able to show that the classic laws can be derived mathematically from an empirical property of the energetics of wall turbulence, namely that viscosity and finite turbulent domains have a depressive effect on the spectrum of turbulent energy. Our derivation has allowed us to draw support for the classic laws from empirical data on the spectrum of turbulent energy, which embodies the fabric of turbulent fluctuations in a flow, with no obvious ties to the mean-velocity profiles. From a broader perspective, our derivation indicates that, contrary to what might be inferred from the usual derivation of the classic laws, the mean-velocity profiles as well as the attendant phenomenon of turbulent friction are inextricably linked to, and can indeed be interpreted as macroscopic manifestations of, the spectrum of turbulent energy.

Other theoretical turbulent research carried out in 2014 has included work on the existence of multiple turbulent states in plane Couette flows (with results that are currently being readied for publication), work on scaling of the profiles of intensity of turbulent fluctuations (with results that show promise but remain inconclusive), and work on certain anomalies in the mean-velocity profiles of pipe flow (we have discovered the anomalies and are currently working on an explanation based on the spectral link, a leitmotif of our work on turbulence).

We have continued developing the turbulent pipe-flow facility in the joint fluid mechanics unit-continuum physics unit fluidics laboratory at OIST. During 2014 we were able to measure pressure drops via pressure transducers and velocity fields via stereoscopic particle image velocimetry (SPIV) in laminar, transitional, and fully-developed turbulent flows. We have successfully calibrated these measurements against benchmark data from state-of-the-art direct numerical simulations (DNS).

We have continued developing of a large Taylor-Couette experiment in the joint fluid mechanics unit-continuum physics unit fluidics laboratory. For the time being, measurements have been with air, but work is in progress that will allow us to use water as well. With air we have been able to measure energy spectra using hot-wire anemometry. We have discovered that multiple spectra can be triggered attendant on an invariant set of controlling parameters. This indicates that in Taylor-Couette flow there can be multiple turbulent states, a fact that has been know from measurements of the frictional drag and other variables. In contrast to those measurements, which spectra can be used to understand the differences and contrasts between states, a distinctive advantage that we are seeking to exploit.

We have continued work started last year on impact cratering in granular beds. Research on this topic has included more experiments carried out in the joint fluid mechanics unit-continuum physics unit granular-flow laboratory at OIST. The new experiments have allowed us to characterize the morphology of ejecta blankets; to understand the mechanism responsible for this morphology. we have started a series of large-scale three-dimensional computational simulations of impact cratering, using the granular-dynamics code LAMMPS.

We have continued work on the dynamical effect of the "rainpower" that is lost to turbulent friction as the raindrops fall through the air in a tropical cyclone (hurricane or typhoon).  Our conclusion from prior work with a semi-analytical model was that the effect of rainpower is to lessen the intensity of a typhoon by an estimated 20%. To test this conclusion under more realistic conditions than a semi-analytical model can provide, we have modified a state-of-the-art, multi-physics, multi-scale computer code (known as CM1'') for the simulation of typhoons, incorporating the rainpower and coupling it to the turbulence and the thermodynamics. Computational simulations with the modified CM1 have been in excellent accord with the predictions of the semi-analytical model. The general effect of rainpower on hurricane intensity--a 15% reduction as per our new estimate—-amounts to a systematic bias in the predictions of state-of-the-art typhoon models, which do not take the rainpower into account. Further, the computational simulations with the modified CM1 (which, unlike the semi-analytical model, can be used to simulate transients), indicate that rainpower increases hurricane intensity during rapid intensification'' (the short, early stage of hurricane evolution that poses the highest challenge in forecasting) and shortens the build-up time to the steady state.

We have continued work on two-phase fields in polyether-polyurethane foams, a solid-mechanics subject on which we had already carried out much research in previous years. Theoretical work carried out in 2014 has allowed us to improve a previous analytical explanation of force-penetration curves measured in extensive experiments in which foam specimens were subjected to punching with lengthscale-free (wedge-shaped and conical) punches. Experimental work carried out in 2014 involved the use of a digital-image correlation method to determine displacement fields on one of the lateral faces of a foam specimen during a punching test. The experimental results afforded direct empirical evidence of the presence of phases in the foam. With these new experimental and theoretical results, we have been able to complete a paper that was submitted for publication in the first half of 2015.

### 4. Publications

#### 4.1 Journals

1. C. Zuniga Zamalloa, H. C-H Ng, P. Chakraborty, and G. Gioia. 2014. Spectral analogues of the law of the wall, the defect law and the log law. Journal of Fluid Mechanics, vol. 757, pp. 498-513
2. T. Sabuwala, G. Gioia, and P. Chakraborty. 2015. Effect of rainpower on hurricane intensity. Geophysical Research Letters, vol. 42, doi:10.1002/2015GL063785

#### 4.2 Books and other one-time publications

• Nothing to report

#### 4.3 Oral and Poster Presentations

1. Gioia, G., The turbulent mean-velocity profile in pipeflow, Joint Seminar between OIST and JST mathematics program on vertex-boundary interactions and wall-bounded turbulent flows, Okinawa, Japan, May 26 (2014).
2. Cerbus, R., Samanta, D., Ingremeau, F., Tran, T., Goldburg, W., Chakraborty, P., The scaling of near-wall flows in quasi-two-dimensional turbulent channels, Frontiers of turbulence research, Kyoto, Japan, July 25 (2014).
3. Chakraborty, P., Zamalloa, C., Ng, H., Gioia, G., Spectral analogs of the law of the wall, the defect law, and the log law, Frontiers of turbulence research, Kyoto, Japan, July 25 (2014).
4. Liu, C., Gioia, G., Chakraborty, P., Frictional drag and mean-velocity profile in non-uniform, quasi-two-dimentional turbulent channels, Frontiers of turbulence research, Kyoto, Japan, July 25 (2014).
5. Sabuwala, T., Dai, X., Gioia, G., Mechanical Response of Elastic Open-cell Foams Under Punching, Insights From Experiments And Simulations, 11th World Congress on Computational Mechanics (WCCM 2014), Bercelona, Spain, July 27 (2014).
6. Sabuwala, T., Gioia, G., Chakraborty, P., Hurricane intensity modulation by rain-induced frictional dissipation, Asia Oceania Geosciences Society 11th Annual Meeting, Sapporo, Japan, July 28 (2014).
7. Gioia, G., Energy spectrum and mean-velocity profile in turbulent pipe and plane-couette flows, The 52th Meeting of the Society of Natural Philosophy, Rio De Janeiro, Brazil, October 24 (2014).
8. Sabuwala, T., Evaluating the effect of rainpower in a state-of-the-art dynamical typhoon model, Joint-seminar on physics of typhoons; theory and simulations, Okinawa, Japan, February 6 (2015).
9. Liu, C., Cerbus, R., Gioia, G., Chakraborty, P., Mutually independent cascades in anisotropic soap-film turbulence, APS March Meeting 2015, San Antonio, USA, March 4 (2015).
10. Zhang, D., Gioia, G., Chakraborty, P., The spectral link in mean-velocity profile of turbulent plane-couette flows, APS March Meeting 2015, San Antonio, USA, March 4 (2015).

### 5. Intellectual Property Rights and Other Specific Achievements

• Nothing to report

### 6. Meetings and Events

#### 6-1. Joint seminar

##### (1) Joint seminar between OIST and JST mathematics program on vortex-boundary interactions and wall-bounded turbulent flows
• Date: May 26, 2014
• Venue: OIST
• Co-organizer: Prof. Takashi Sakajo (Kyoto University)
• Speakers:
• Prof. Akio Nakahara (Nihon University)
• Prof. Pinaki Chakraborty (OIST)
• Prof. Gustavo Gioia (OIST)
• Prof. Takashi Sakajo (Kyoto University)
• Prof. Zin Arai (Hokkaido University)
• Prof. Takashi Ishihara (Nagoya University)
• Prof. Tomoo Yokoyama (Kyoto University of Education)
• Dr. Rhodri Nelson (Kyoto University)
##### (2) Joint seminar on physics of typhoons; theory and simulations
• Date: February 6, 2015
• Venue: OIST
• Speakers:
• Dr. Akiyoshi Wada (Meteorological Research Institute, Japan Meteorological Agency)
• Prof. Kosuke Ito (University of the Ryukyus)
• Prof. Pinaki Chakraborty (OIST)
• Dr. Tapan Sabuwala (OIST)

#### 6.2 Seminar

##### (1) Title: Influence of rain-related turbulent dissipation on the intensity of tropical cyclones (typhoons)
• Date: August 6, 2014
• Venue: Meiji University (Ikuta campus, Japan)
• Speaker:  Dr. Tapan Sabuwala (OIST)
##### (2) Title: The missing link in turbulence, or how to explain the "Moody Diagram"
• Date: October 30, 2014
• Venue: The Department of Mechanical Engineering, Federal University of Uberlandia (Brazil)
• Speaker: Prof. Gustavo Gioia (OIST)
##### (3) Title: Spectra and mean-velocity profiles in turbulent pipe flow
• Date: November 13, 2014
• Venue: CONICET, National Scientific and Technical Research Council (Argentina)
• Speaker: Prof. Gustavo Gioia (OIST)
##### (4) Title:  The challenges of tribology: contact mechanics, friction, and wear
• Date: March 9, 2015
• Venue: OIST
• Speaker: Prof. Sonia A.G. Oliveira (Federal University of Uberlandia, Brazil)

### 7. Other

• Nothing to report.