# Continuum Physics Unit

Professor Gustavo Gioia

### Abstract

The Continuum Physics Unit pursued research on turbulent flows and tropical cyclones, started a new experimental project of granular flow, and continued to develop a joint fluid mechanics--continuum physics laboratory at OIST.

### 1. Staff

• Dr. Gustavo Gioia, Professor
• Dr. Tapan Sabuwala, Researcher
• Dr. Henry Chi-Hin Ng, Researcher
• Dr. Devranjan Samanta, Researcher
• Mr. Dongrong Zhang, OIST PhD Student
• Ms. Kaori Egashira, Research Administrator

### 2. Collaborations

• Theme: Spectral scalings 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: Taylor-Couette apparatus
• Type of collaboration: Scientific collaboration
• Researchers:
• Dr. Yasuo Higashi, OIST
• Professor Pinaki Chakraborty, OIST
• Mr. H. Yamaoka, High Energy Accelerator Research Organization, Tsukuba, Japan

### 3. Activities and Findings

#### 3.1 Spectral scalings in wall-bounded turbulent flows

We have carried out more research on three novel scaling relations for the turbulent energy spectra of smooth wall-bounded, uniform turbulent flows: the spectral analog of the law of the wall, the spectral analog of the defect law, and the spectral analog of the log law (on which see last year's report). (The law of the wall, the defect law and the log law are the classical scaling relations for the turbulent mean-velocity profiles (MVPs)).

First, we have been able to show that the spectral analogs can be derived without invoking any specific model of wall turbulence. Thus, unlike prior scaling relations for the turbulent-energy spectra, which have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis, the spectral analogs can be said to be model-independent. By design, each spectral analog applies in the same spatial domain as the attendant scaling relation for the MVPs (the spectral analog of the law of the wall in the inner layer, the spectral analog of the defect law in the outer layer, and the spectral analog of the log law in the overlap layer). On the other hand, we have been able to establish, without additional assumptions, that each spectral  in a specific spectral domain (the spectral analog of the law of the wall in the high-wavenumber spectral domain where viscosity is active, the spectral analog of the defect law in the low-wavenumber spectral domain where viscosity is negligible, and the spectral analog of the log law in a transitional, intermediate-wavenumber spectral domain that may become sizable only at ultra-high Re). We have thus been able to conclude that there exist model-independent a one-to-one links between the spatial domains and the spectral domains, consistent with the well-known, incisive (but hitherto unsubstantiated) thesis of Tennekes and Lumley as to the existence of a close analogy between the spatial structure of turbulent boundary layer and the spectral structure of turbulence.''

Second, we have had recourse to direct-numerical-simulation data to verify that the spectral analogs apply to all components of the energy spectra, not just to the streamwise component (customarily denoted by E_uu). For some components, the spectral analogs turn out to apply well beyond their respective domains of application--a fitting reminder that these domains of application amount to sufficient, not necessary, conditions for the spectral analogs to apply.

Third, we have elucidated the relation between the spectral analog of the defect law and Kolmogorov scaling. In essence, we have been able to show that under the assumptions of Kolmogorov it is possible to derive a scaling relation which is a special case of the spectral analog of the defect law; further, at sufficiently high Reynolds number, the entire spectral domain of application of Kolmogorov scaling is subsumed under the sufficient condition for the spectral analog of the defect law to apply.

#### 3.2 Effect of rain in tropical cyclons

We have carried out more research with the objective of ascertaining the effect of the "rainpower" that is lost to turbulent friction as the raindrops fall through the air in a tropical cyclone (hurricane or typhoon). In prior research, we used a semi-analytical, heat-engine model of the thermodynamics of typhoons to show that, contrary to the prevalent notion that rain helps drive typhoon winds, the effect of rainpower is to lessen the intensity, or characteristic wind velocity, of a typhoon by an estimated 20%. To account for rainpower in the semi-analytical model, we employed a formulation which included a thickness of the boundary layer'' as a (somewhat ill-defined) parameter. We have come to the realization, however, that an alternative formulation is possible in which the thickness of the boundary layer can be ignored and the range of possible scenarios can be reduced to two maximally contrasting scenarios, namely the adiabatic scenario and the diabatic scenario.  In the adiabatic scenario, the turbulent wakes of the raindrops do not decay to heat within the eyewall (and the rainpower leaves the heat engine as output work). In the diabatic scenario, the turbulent wakes of the raindrops decay to heat within the eyewall and contribute locally to the production of entropy (and the rainpower feeds back into the heat engine). To each scenario there corresponds a specific form of the equation of energy balance and a specific form of the equation of entropy balance (the two fundamental equations of the model). Remarkably, for either scenario the conclusion turns out to be the same (and consistent with our prior conclusion): the effect of rainpower is to lessen the intensity of a typhoon by an estimated 20%.

#### 3.3 Impact cratering in granular beds

We have started an experimental project on impact cratering in granular beds. The focus has been on the morphology of ejecta blankets, and we are looking forward to possible applications in planetary science (thus our collaborator in this project, Prof. Susan Kieffer). With this project we have inaugurated a new, joint fluid mechanics unit-continuum physics unit granular-flow laboratory.

#### 3.4 Experiments on turbulent pipe flows

We have continued developing the pipe-flow experiment in the joint fluid mechanic unit-continuum physics unit laboratory. We have been able for the first time (in our lab, that is) to carry out reproducible measurements of frictional drag over a whole range of flows from laminar regime to fully turbulent regime. Further, we have been able to obtain high-precision, time-resolved stereoscopic Particle Image Velocimetry (PIV) data to study the cross-plane turbulent flow in the pipes.

#### 3.5 Taylor-Couette apparatus

We have completed the design, manufacturing, instrumentation, and setting up the smaller of two Taylor-Couette apparatuses in our laboratory. We are currently carrying out torque measurements for calibration purposes. This apparatus is a prototype for a larger Taylor-Couette apparatus for which the design and manufacturing has been completed.

### 4. Publications

#### 4.1 Journals

D. Samanta, F. Ingremeau, R. Cerbus, T. Tran, W. I. Goldburg, P. Chakraborty, and H. Kellay. Scaling of near-wall flows in quasi-two-dimensional turbulent channels. Physical Review Letters, vol 113, article 254502 (2014).

#### 4.2 Books and Other One-Time Publications

Nothing to report.

#### 4.3 Oral and Poster Presentations

1. Sabuwala, T., Dai, X. & Gioia, G.  Two-Phase Deformation of Low - Density Polyether - Polyurethane Foams Under Punching, in 16th International Conference on Advances in Materials & Processing Technologies, Taipei, Taiwan (2013).

2. Gioia, G., Perelet, A. & Sabuwala, T.  Two - Phase Compaction of Cohesive Granular Aggregates: Experimental Evidence from Punching Tests, in 16th International Conference on Advances in Materials & Processing Technologies, Taipei, Taiwan (2013).

3. Chakraborty, P., Gioia, G. & Kieffer, S.  Rotating volcanic plumes, in International Association of Volcanology and Chemistry of the Earth's Interior (IAVCEI) Scientific Assembly 2013, Kagoshima, Japan (2013).

4. Chakraborty, P. & Gioia, G.  A spectral theory of turbulent friction on rough and smooth walls, in Workshop on Larch scale fluid motion and turbulent fluctuation, Kyoto University, Kyoto (2014).

5. Gioia, G., Guttenberg, N., Goldenfeld, N. & Chakraborty, P.  A spectral theory of the mean-velocity profile in turbulent pipe flows, in Workshop on Large scale fluid motion and turbulent fluctuation, Kyoto University, Kyoto (2014).

6. Liu, C.-C., Gioia, G. & Chakraborty, P.  Local version of the spectral link in turbulent friction, in Workshop on Large scale fluid motion and turbulent fluctuation, Kyoto University, Kyoto (2014).

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

Nothing to report

### 6. Meetings and Events

#### 6.1 Seminar

1) Title: The onset of turbulence

• Date: July 29, 2013
• Venue: OIST Campus
• Speakers: Prof. Björn Hof (Institute of Science and Technology, Austria)

2) Title: Experimental study of pulmonary surfactant behavior during airway reopening: Application of μ-PIV to the complex multi-phase flow

• Date: August 5, 2013
• Venue: OIST Campus
• Speakers: Dr. Yamaguchi (Biomedical Engineering Department, Tulane University, New Orleans, LA)

3) Title:  Freeman Dyson was right - again: electrical polarization in sandstorms

• Date: January 15, 2014
• Venue: OIST Campus
• Speakers: Prof. Troy Shinbrot (Rutgers University, USA)

4) Title: Publishing in Nature: a step by step guide

• Date: January 16, 2014
• Venue: OIST Campus
• Speakers: Prof. Troy Shinbrot (Rutgers University, USA)

5) Title: A spectral theory of the mean-velocity profile in turbulent pipe flows

• Date: January 23, 2014
• Venue: Meiji University (Ikuta campus), Kanagawa
• Speakers: Gustavo Gioia (OIST)

6) Title: Hydrodynamics using soap films and soap bubbles

• Date: March 13, 2014
• Venue: OIST Campus
• Speakers: Prof. Hamid Kellay (University of Bordeaux, France)

7) Title: Information theory applied to fluid flow experiments

• Date: March 14, 2014
• Venue: OIST Campus
• Speakers: Prof. Walter Goldburg (Dept. of Physics and Astronomy, University of Pittsburgh)

#### 6.2 Short Course

Title:  A short course on Particle Image Velocimetry

• Date: August 16, 2013
• Venue: OIST Campus
• Speakers: Prof. Jun Sakakibara (Meiji University)