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An initial-value problem for arbitrary small 3D vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a…
Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the…
This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\to \infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C.…
The Rayleigh equation, which is the linearized Euler equations near a shear flow in vorticity formulation, is a key ingredient in the study of the long time behavior of solutions of linearized Euler equations, in the study of the linear…
In this paper, we are interested in the nonlinear Rayleigh-Taylor instability for the gravity-driven incompressible Navier-Stokes equations with Navier-slip boundary conditions around a smooth increasing density profile $\rho_0(x_2)$ in a…
We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…
Classical results from Sturm-Liouville theory state that the number of unstable eigenvalues of a scalar, second-order linear operator is equal to the number of associated conjugate points. Recent work has extended these results to a much…
The evolution of a small-amplitude localized vortex disturbance in an unbounded shear flow with the linear velocity profile is investigated. Based on the exact solution of the initial problem for basic flow, a revision is made of the…
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
The nonlinear development of finite amplitude disturbances in mixed convection flow in a heated vertical annulus is studied by direct numerical simulation. The unsteady Navier Stokes equations are solved numerically by a spectral method for…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
The Vertical Shear Instability is one of two known mechanisms potentially active in the so-called dead zones of protoplanetary accretion disks. A recent analysis indicates that a subset of unstable modes shows unbounded growth - both as…
Stationary longitudinal vortical rolls emerge in katabatic and anabatic Prandtl slope flows due to the dominance of the normal component of the buoyancy force over flow shear. Here, we further identify self pairing of these longitudinal…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
We introduce the longitudinal and transverse static surface modes and use them to solve the full-wave electromagnetic scattering problem from penetrable objects. The longitudinal static modes are the eigenmodes with zero surface curl of the…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…
The goal of this article is to present -- in a cohesive, and somewhat self-contained fashion -- several recent results revealing an experimentally, numerically, and mathematical analysis-supported \emph{geometric scenario} manifesting…