{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"A new scaling law for K62 with applications to particle clustering in turbulent flow","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/78251"},{"label":"dc.language.iso","value":"en_US"},{"label":"dcterms.abstract","value":"There are two main results in this thesis. We develop a new scaling lawfor the turbulent dissipation rate, \u03f5, providing a quantitative extension tothe K62 lognormal postulate. We illustrate this scaling law through its application to subgrid scale (SGS) modeling in the large-eddy simulation (LES) of particle-laden turbulent flows. The second major contribution of this thesis examines the entire covariance matrix of \u03c7 = ln\u03f5 inwavenumber space and shows that it is approximately diagonal.  Prior turbulence studies of Kolmogorov and Obukhov have explored models for \u03f5 using lognormal random processes. We extend these ideas and establish a random field theory for \u03f5 enabling us to capture turbulentintensity fluctuations at scales smaller than the numerically resolved length scale. This particularly applicable in the LES framework in which only the large scales of the flow are resolved and the small scales are modeled. This theoretical foundation we present is verified by direct numerical simulation data from 3D forced, incompressible turbulence in a periodic domain, yields a new scaling law for the variance of \u03c7 in wavenumber space Var(\u03c7) \u223c k-2.61 \u00b1 0.03  The above scaling law is accurate for up to 1.72 decades in the inertial range for high Reynolds number numerical data. Also analyzed here are the strain, vorticity, and Reynolds stress, using the same simulation data. These results provide the foundation for modeling the turbulentdissipation rate in terms of random fields.  For application in particle-laden turbulence we note the clustering of particles in high strain regions, often in the interstitches between neighboring vortex tubes. The clustering is measured quantitatively via a radial distribution function. The clustering is sensitive to the relation between the particle relaxation time and the fluid relaxation times, down to the Kolmogorov length scale, thereby defining the Stokes number of the flow. However fluid time scales not adjacent to the particle time scales contribute little to the clustering, an important fact which governs the behavior of the clustering and the radial distribution, as a function of the Stokes number. The subgrid velocity fluctuations adds a new term (related to the subgrid fluid variance, and not to averaged subgrid properties) to the momentum equation."},{"label":"dcterms.available","value":"2018-06-21T13:38:43Z"},{"label":"dcterms.contributor","value":"Zingale, Michael"},{"label":"dcterms.creator","value":"Mahadeo, Vinay Preston"},{"label":"dcterms.dateAccepted","value":"2018-06-21T13:38:43Z"},{"label":"dcterms.dateSubmitted","value":"2018-06-21T13:38:43Z"},{"label":"dcterms.description","value":"Department of Applied Mathematics and Statistics"},{"label":"dcterms.extent","value":"92 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/78251"},{"label":"dcterms.issued","value":"2017-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2018-06-21T13:38:43Z (GMT). No. of bitstreams: 1\nMahadeo_grad.sunysb_0771E_13574.pdf: 4938109 bytes, checksum: 412f9b77e58435b6843d131ee3334c13 (MD5)\n  Previous issue date:   12"},{"label":"dcterms.subject","value":"Fluid mechanics"},{"label":"dcterms.title","value":"A new scaling law for K62 with applications to particle clustering in turbulent flow"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/14%2F60%2F78%2F146078921829620033398126638109083467004/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/14%2F60%2F78%2F146078921829620033398126638109083467004","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}