EAGER: Collaborative Research: Exploring the inverse cascade in two-dimensional turbulent soap films

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NON-TECHNICAL ABSTRACT: Turbulent flows past a wall experience frictional drag, the property of a flow that sets the cost of pumping oil through a pipeline, the draining capacity of a river in flood, and other quantities of practical interest. Much is known about the frictional drag, mostly from extensive experiments in which the frictional drag was measured in pipes or open channels, yet, there has been no known link between the frictional drag and the statistics of the turbulent eddies in the flow. The project' goal is to test experimentally a recently proposed theory that will allow us to predict the frictional drag from a knowledge of the statistics of the turbulent eddies. This will be achieved through measurements in a type of two-dimensional turbulent flow that may be realized in very thin soap films, where it is possible to create flows with different types of statistics. If confirmed, the theory could provide the key to understanding the drag-altering effects of polymeric additives used in oil pipelines, particulate suspensions found in rivers in flood, entrained bubbles found in water-treatment plants, and other agents known to affect the statistics of the flow. At Illinois and Pittsburgh, graduate and undergraduate students will be trained with a multidisciplinary focus encompassing engineering and fundamental condensed matter physics, introducing undergraduates and women to research in turbulence. The PIs will collaborate on outreach to grades 6-12, work with an all-girl's middle school to devise a unit on soap film physics, turbulence, chaos and optics, and participate in a teacher's workshop.TECHNICAL ABSTRACT: Turbulent flows past a wall experience frictional drag, the property of a flow that sets the cost of pumping oil through a pipeline, the draining capacity of a river in flood, and other quantities of practical interest. While much is known about the frictional drag, there has been no known link between the frictional drag and the turbulent spectrum (i.e., the statistics of turbulent fluctuations in the flow). The goal of this project is to test experimentally a recently proposed theory that would provide the missing "spectral link". If confirmed, the theory could prove key to understanding the drag-altering effects of polymeric additives used in oil pipelines, particulate suspensions found in rivers in flood, entrained bubbles found in water-treatment plants, and other agents known to affect the spectrum. The theory has been tested in two-dimensional soap-film turbulent flows with the type of spectrum known as the enstrophy cascade, but so far it has not been possible to create similar flows with the type of spectrum known as the inverse energy cascade. A method to create soap-film flows with the inverse energy cascade will be developed; it will then be used to measure the frictional drag of inverse cascade dominated 2D turbulence, completing the experimental verification of the spectral link. At Illinois and Pittsburgh, the PIs will train graduate and undergraduate students with a multidisciplinary focus encompassing engineering and fundamental condensed matter physics, introducing undergraduates and women to research in turbulence. The PIs will collaborate on outreach to grades 6-12, working with an all-girl's middle school to devise a unit on soap film physics, turbulence, chaos and optics, and participating in a teacher's workshop.