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Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
Superfluid turbulence consisting of quantized vortices is called quantum turbulence (QT). Quantum turbulence and quantized vortices were discovered in superfluid $^4$He about 50 years ago, but innovation has occurred recently in this field.…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Magnetic helicity fluxes are investigated in a family of gauges in which the contribution from ideal magnetohydrodynamics takes the form of a purely advective flux. Numerical simulations of magnetohydrodynamic turbulence in this advective…
The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to…
The effect of a network of fixed rigid fibers on fluid flow is investigated by means of three-dimensional direct numerical simulations using an immersed boundary method for the fluid-structure coupling. Different flows are considered (i.e.,…
The dynamics of a spheroidal vesicle, bounded by an inextensible membrane, is analyzed in function of the enclosed fluid viscosity, and of the membrane mechanical properties. The two situations in which a bending rigidity and a shear…
Recent experiments on mucociliary clearance, an important defense against airborne pathogens, have raised questions about the topology of two-dimensional (2D) flows. We introduce a framework for studying ensembles of 2D time-invariant flow…
We develop a relativistic (quasi-)hydrodynamic framework, dubbed the gyrohydrodynamics, to describe fluid dynamics of many-body systems with spin under strong vorticity based on entropy-current analysis. This framework generalizes the…
Vortices are the fundamental units of turbulent flow. Understanding their stability properties therefore provides fundamental insights on the nature of turbulence itself. In this contribution I briefly review the phenomenological aspects of…
Turbulent flow restricted to two dimensions can spontaneously develop order on large scales, defying entropy expectations and in sharp contrast with turbulence in three dimensions where nonlinear turbulent processes act to destroy…
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…
Liquids flowing against solid surfaces experience friction. While solid friction is familiar to anyone with a sense of touch, liquid friction is much more exotic. At macroscopic scales indeed, the assumption of inifinite friction, i.e. that…
We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in \cite{ST}. We study the relationship of the existence of the flow and associated static metrics topological information on the…
The linear stability of a shear-thinning, viscoelastic fluid undergoing any of the canonical rectilinear shear flows, viz., plane Couette flow and pressure-driven flow through a channel or a tube is analyzed in the creeping-flow limit using…
Superfluid Turbulence is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, inter penetrating turbulent fluids: the first is inviscid with quantised vorticity, the second is viscous with continuous…
We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a…
We demonstrate that the condensed matter quantum systems encompassing two reservoirs connected by a junction permit a natural definition of flows of conserved measures, Renyi entropies. Such flows are similar to the flows of physical…
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity…
The phenomenon of stable persistent currents is central to the studies of superfluidity in a range of physical systems. While all of the previous theoretical studies of superfluid flows in annular geometries concentrated on conservative…