# FY2012 Annual Report

## Continuum Physics Unit

Professor Gustavo Gioia

### Abstract

Continuum Physics Unit pursued research on elastic foams, turbulence, and tropical cyclones.

### 1. Staff

• Dr. Gustavo Gioia, Professor
• Dr. Tapan Sabuwala, Researcher
• Dr. Devranjan Samanta, Researcher
• Dr. Henry Chi-Hin Ng, Researcher
• Ms. Kaori Egashira, Research Administrator

### 2. Collaborations

• Theme: Turbulent flows
• Type of collaboration: Scientific Collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST
• Professor Walter Goldburgh, University of Pittsburgh, USA
• Professor Hamid Kellay, University of Bordeaux, France
• Professor Nigel Goldenfeld, University of Illinois, USA

• Theme: Tropical cyclones
• Type of collaboration: Scientific Collaboration
• Researchers:
• Professor Pinaki Chakraborty, OIST

### 3. Activities and Findings

3.1 We have carried out extensive three-dimensional computational simulations of punching tests in polyether polyurethane elastic foams, using a constitutive model of foams that we published this academic year. These simulations have allowed us to relate the results of strain-field experimental measurements carried out (via a digital-image correlation technique) on the surface of a specimen to the strain field in the interior of the specimen. We have thus been able to test certain predictions of a two-phase theory of compressed polyether polyurethane elastic foams, which predictions apply only to the interior of a specimen.

3.2  Using dimensional analysis and similarity arguments, we have derived theoretically new scaling relations for the turbulent energy spectra of smooth wall-bounded, uniform turbulent flows. These new scaling relations are the spectral analogues of the law of the wall, the defect law, and the log law (the classical scaling relations for the turbulent mean-velocity profile).  To test the new scaling relations, we have carried out extensive analyses of experimental and direct-numerical-simulation data on both turbulent channel flow and turbulent pipe flow.

3.3 We have carried out a new set of frictional-drag measurements in a soap-film channel in which it is possible to realize turbulent soap-film flows with unambiguous spectral exponents of 5/3 (the spectral exponent that prevails in ordinary three-dimensional pipe flows) or 3 (a spectral exponent exclusively associated with two-dimensional turbulence). This new set of frictional-drag measurements was designed to test a specific prediction of the spectral theory of the frictional drag in turbulent flows on smooth walls (rough walls will be researched in future), namely that in non-uniform flows the frictional drag measured an any given point on the smooth wall is set by the spectral exponent that prevails locally in a neighborhood of that point.

3.4 Using a combination of theory and remote sensing, we have carried out the first computations of the entropic contribution of rain-induced dissipation in the eyewall of mature hurricanes, and showed that this contribution leads to substantial decrease in the maximum potential intensity of a hurricane.

3.5 In collaboration with the Fluid Mechanics unit, we have started a joint fluid mechanics--continuum physics laboratory at OIST.  To date, the laboratory includes a vertical soap-film tunnel and turbulent pipe flow setups, and state-of-the-art PIV and LDV flow-interrogation systems.

### 4. Publications

#### 4.1 Journals

1. Kellay, H., Tran, T., Goldburg, W., Goldenfeld, N., Gioia, G. & Chakraborty, P.  Testing a missing spectral link in turbulence. Physical Review Letters 109, (254502-1)~(254502-5), doi:10.1103/PhysRevLett.109.254502 (2012).

2. Sabuwala, T. & Gioia, G.  Skeleton-and-bubble model of polyether-polyurethane elastic open-cell foams for finite element analysis at large deformations. Journal of the Mechanics and Physics of Solids 61, 886-911 (2013).

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

Nothing to report

#### 4.3 Oral and Poster Presentations

1. Chakraborty, P., Kellay, H., Tran, T., Goldburg, W., Goldenfeld, N. & Gioia, G.  Experimental test of a missing spectral link in turbulence, in Annual Meeting of American Physical Society - Division of Fluid Dynamics (APS-DFD), San Diego, California, USA (2012).

2. Gioia, G., Zamalloa, C. Z. & Chakraborty, P.  Spectral analogue of the law of the wall, in Annual Meeting of American Physical Society - Division of Fluid Dynamics (APS-DFD), San Diego, California, USA (2012).

3. Liu, C.-C., Cerbus, R., Goldburg, W., Gioia, G. & Chakraborty, P.  The spectral link for frictional drag in non-uniform turbulent soap-film flows, in Annual Meeting of American Physical Society - Division of Fluid Dynamics (APS-DFD), San Diego, California, USA (2012).

4. Sabuwala, T., Gioia, G. & Chakraborty, P.  Rain-induced dissipation in hurricanes, in Annual Meeting of American Physical Society - Division of Fluid Dynamics (APS-DFD), San Diego, California, USA (2012).

5. Sabuwala, T., Gioia, G. & Chakraborty, P.  Rain-induced dissipation in hurricanes, in 25th Conference on Climate Variability and Change, 93rd AMS Annual Meeting, Austin, Texas, USA (2013).

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

Nothing to report

### 6. Meetings and Events

#### 6.1 Seminar

Title:  The missing spectral link'' in turbulence
Date:  November 26, 2012
Venue:  University of California at Davis, Department of Civil and Environmental Engineering, Davis, California, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.2 Seminar

Title: The spectral link in turbulence
Date:  August 30, 2012
Venue:  Schlumberger Ltd., Reservoir Completions Technology Center, Rosharon, Texas, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.3 Seminar

Title:  Linking energy spectra and mean-velocity profiles in wall-bounded turbulent flows
Date:  August 22, 2012
Venue:  Michigan Technological University, Department of Mechanical Engineering and Engineering Mechanics, Houghton, Michigan, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.4 Seminar

Title:  The spectral link in turbulence
Date:  August 15, 2012
Venue:  University of North Carolina, Department of Mechanical Engineering and Engineering Science, Charlotte, North Carolina, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.5 Seminar

Title:  The missing spectral link'' in turbulence
Date:  August 10,  2012
Venue:  University of Pittsburgh, Department of Physics, Pittsburgh, Pennsylvania, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.6 Seminar

Title:  Energy spectra and mean-velocity profiles in wall-bounded turbulent flows
Date:  August 6, 2012
Venue:  University of Minnesota, St. Anthony Falls Laboratoty, Minneapolis, Minnesota, USA
Speaker:  Prof. Gustavo Gioia (OIST)

#### 6.7 Seminar

Title:  Enceladus, the Moon of Saturn: Oasis or Ice Ball?
Date:  February 22, 2013
Venue:  OIST Campus Lab1
Speaker:  Prof. Susan Kieffer (The Walgeen-chair professor of Geology, Physics, and Center for Advanced Studies at the University of Illinois at Urbana-Champaign, USA)