Applied Mathematics Seminar

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Surface gravity waves transport mass through a process referred to as Stokes drift. Finite-sized particles of arbitrary shape exhibit additional Stokes drift-like phenomena. In this talk, I explore the effects of particle inertia and shape on particle behavior in waves. I demonstrate both an angular analogue of Stokes drift for non-spherical particles and a vertical Stokes drift for settling particles. Experimental observations are compared with these analytical results, and these behaviors are discussed in the context of microplastic transport in the ocean.

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Notes:

Zoom + In person projection

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Zoom + In person projection

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How weak is the weak turbulence? We analyze turbulence of weakly
interacting waves using the tools of information theory. It offers a
unique perspective for comparing thermal equilibrium and turbulence. The
mutual information between resonant modes in a finite box is shown to be
stationary and small in thermal equilibrium, yet to grow with time in
weak turbulence. We trace this growth to the concentration of
probability on the resonance surfaces, which can go all the way to a
singular measure. The surprising conclusion is that no matter how small
is the nonlinearity and how close to Gaussian is the statistics of any
single amplitude, a stationary phase-space measure is far from Gaussian,
as manifested by a large relative entropy. At the end I shall describe a
new class of the so-called Fibonacci models that describe resonantly
interacting waves and allow turbulence close to thermal equilibrium.
(0.1103/PhysRevLett.125.104501)

Synopsis:

Motivated by Enceladus cryovolcanism and possible shear heating along
its south pole fractures, we perform a theoretical and numerical study
of boundary-layer convection along a vertical heated wall in a bounded
ideal mushy region. By focusing on this simple model, we demonstrate the
existence of four regions with different regimes and scalings that are
studied asymptotically, showing a good agreement between the theory and
the numerical simulations. Close to the heated wall, the convection in
the mushy layer is similar to a rising buoyant plume abruptly stopped at
the top, leading to increased pressure and temperature in the upper
region, that could be the ignition of Enceladus' geysers.