### Description

The motion of solid bodies through fluids is a complicated problem relevant to many different scientific disciplines ranging from the distribution of numerous environmental pollutants in the atmosphere and oceans to the feeding of the smallest micro-organism. The coupled interactions between the body and a

fluid are notoriously complex, with the body forcing the fluid through the no-slip boundary conditions, and the fluid forcing back on the body through the integration of the body surface integral of viscous stress tensor. The interactions may be further complicated by the flow enhanced mixing which may directly affect the net buoyancy forcing bodies in fluids through entrainment. Given the complexity of such systems, our proposal outlines a series of fundamental problems which

we will study using careful mathematical analysis, and experimental technique focussed upon deriving improved understanding of mixing, entrainment, and

ow properties in fluid systems. Specifically, we focus upon geometries for which new complete information may be computed analytically and asymptotically predicting the fluid flow structure, mixing, and entrainment. The tools we utilize involve a mixture of stochastic path integration, rigorous asymptotic analysis, and careful experimental measurement.

The environment in which we live and breathe is a complex coupled fluid system whose dynamics possess phenomena occurring on a vast range of space and time scales. From the smallest cilia in the lung which provide a hydrodynamic defense mechanism against inhaled contaminants to the atmosphere, oceans, and our climate, we interact directly with our fluid environment. The complete description of such a system remains beyond the computational scope of even the largest supercomputers, and a fundamental scientific endeavor is to characterize, and understand phenomena on different scales, and ultimately to integrate these phenomena to offer a grand picture of how this large scale system functions, as a whole.

fluid are notoriously complex, with the body forcing the fluid through the no-slip boundary conditions, and the fluid forcing back on the body through the integration of the body surface integral of viscous stress tensor. The interactions may be further complicated by the flow enhanced mixing which may directly affect the net buoyancy forcing bodies in fluids through entrainment. Given the complexity of such systems, our proposal outlines a series of fundamental problems which

we will study using careful mathematical analysis, and experimental technique focussed upon deriving improved understanding of mixing, entrainment, and

ow properties in fluid systems. Specifically, we focus upon geometries for which new complete information may be computed analytically and asymptotically predicting the fluid flow structure, mixing, and entrainment. The tools we utilize involve a mixture of stochastic path integration, rigorous asymptotic analysis, and careful experimental measurement.

The environment in which we live and breathe is a complex coupled fluid system whose dynamics possess phenomena occurring on a vast range of space and time scales. From the smallest cilia in the lung which provide a hydrodynamic defense mechanism against inhaled contaminants to the atmosphere, oceans, and our climate, we interact directly with our fluid environment. The complete description of such a system remains beyond the computational scope of even the largest supercomputers, and a fundamental scientific endeavor is to characterize, and understand phenomena on different scales, and ultimately to integrate these phenomena to offer a grand picture of how this large scale system functions, as a whole.

Status | Finished |
---|---|

Effective start/end date | 10/1/10 → 9/30/15 |

### Funding

- National Science Foundation (NSF)

### Fingerprint

fluid dynamics

fluid

entrainment

buoyancy forcing

mathematical analysis

defense mechanism

pollutant

atmosphere

flow structure

ocean

fluid flow

boundary condition

hydrodynamics

timescale

geometry

climate