Matthew J. Hancock

Wetting of textured surfaces

In collaboration with Prof. John Bush and graduate student Manu Prakash, we are studying the theory and design of optimally water repellent surfaces. Drawing on observations from nature, we hope to better understand the motion of microdrops on textured substrates, with application in microfluidics.

Water Waves / Environmental fluid mechanics

Wave generated sand bars on beaches

Theoretical modeling and experimental investigation of sand bar formation under ocean surface waves, including effects of suspended sediment (fine grains) and bed load transport on a sloping mean seabed, in water of intermediate depth. Model predictions compared with available laboratory and field data. Sediment sorting under surface waves studied experimentally with colored sands. In collaboration with Prof. Chiang C. Mei (Ph.D. thesis advisor) and Blake J. Landry.

Hancock, M. J., B. J. Landry, and C. C. Mei (2008), Sandbar formation under surface waves: Theory and experiments, J. Geophys. Res., 113, C07022, doi:10.1029/2007JC004374 [preprint]

Landry, B.J., M.J. Hancock and C. C. Mei. (2007) Note on sediment sorting in a sandy bed under standing water waves. Coast. Eng. 54, 694-699. [preprint]

Hancock, M. J. (2005) Generation of sand sand bars under surface waves. Ph.D. Thesis, Massachusetts Institute of Technology.

Wave propagation over a seabed with random roughness

We study the effects of multiple scattering of slowly modulated water waves by a weakly random bathymetry. The combined effects of weak nonlinearity, dispersion and random irregularities are treated together to yield a deterministic nonlinear Schrödinger equation with a complex damping term. Implications on localization and side-band instability are discussed. Transmission and nonlinear evolution of a wave packet past a finite strip of disorder is examined. In collaboration with Prof. Chiang C. Mei and Jørgen H. Pihl.

Mei, C. C. and M. J. Hancock. (2003) Weakly nonlinear surface waves over a random seabed. J. Fluid Mech. 475, 247-268. [preprint]

Pihl, J. H., C. C. Mei and M. J. Hancock. (2002) Surface gravity waves over a two-dimensional random seabed. Phys. Rev. E 66, 016611. [preprint]

Fundamental Fluid Dynamics

Fluid pipes: We present the results of a combined theoretical and experimental investigation of laminar vertical jets impinging on a deep fluid reservoir. We consider the parameter regime where, in a pure water system, the jet is characterized by a stationary field of capillary waves at its base. When the reservoir is contaminated by surfactant, the base of the jet is void of capillary waves, cylindrical and quiescent: water enters the reservoir as if through a rigid pipe. A theoretical description of the resulting fluid pipe is deduced by matching extensional plug flow upstream of the pipe onto entry pipe flow within it. Theoretical predictions for the pipe height are found to be in excellent accord with our experimental results. An analogous theoretical description of the planar fluid pipe expected to arise on a falling fluid sheet is presented. In collaboration with Prof. John Bush.

More pictures can be found here.

Hancock, M. J. and J. W. M. Bush. (2002) Fluid pipes. J. Fluid Mech., 466, 285-304. [preprint]

Biolocomotion: Part of my research involves topics in biolocomotion, in particular, the motion of creatures near near fluid interfaces. In collaboration with Prof. John Bush (MIT).

Past Research

Nonlinear Differential Equations

During my junior and senior years at the University of Waterloo, I worked with Prof. John Wainwright on a nonlinear dynamical system that modeled a class of cosmological models. My contribution was discovering a change of variable that allowed a five variable non-autonomous system with oscillating terms to be approximated by an autonomous "averaged" system. The averaged system was then analyzed using standard methods.

Horwood, J. T., M. J. Hancock, D. The and J. Wainwright. (2003) Late-time asymptotic dynamics of Bianchi VIII cosmologies. Class. Quantum Grav. 20, 1757-1777.

Nilsson, U. S., M. J. Hancock, and J. Wainwright. (2000) Non-tilted Bianchi VII0 models - the radiation fluid. Class. Quantum Grav. 17, 3119-34.

Wainwright, J., M. J. Hancock, and C. Uggla. (1999) Asymptotic self-similarity breaking at late times in cosmology. Class. Quantum Grav. 16, 2577-98.

Wainwright, J., A. A. Coley, G. F. R. Ellis and M. Hancock. (1998) On the isotropy of the Universe : do Bianchi VIIh cosmologies isotropize? Class. Quantum Grav. 15, 331-50.

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