Related papers: Transient Growth in Shear Flows: Linearity vs Nonl…
Transient growth due to non-normality is investigated for the Taylor-Couette problem with counter-rotating cylinders as a function of aspect ratio eta and Reynolds number Re. For all Re < 500, transient growth is enhanced by curvature, i.e.…
A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings…
In this note, we critically discuss the issue of the possible finiteness of the turbulence lifetime in subcritical transition to turbulence in shear flows, which attracted a lot of interest recently. We briefly review recent experimental…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the disturbances, infinitesimal or finite, are ill-defined…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow focusing on a specific aerodynamic…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long standing puzzle. These flows are linearly stable. Here we explore the…
The entrainment of ambient fluid into a turbulent shear flow has been a topic of wide interest for several decades. To estimate the entrainment of ambient fluid into turbulent jet, it is essential to define the boundary of the jet. The…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in…
The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making…
The emergence of turbulence in shear flows is a well-investigated field. Yet, one of major issues is the apparent contradiction between linear stability analysis quoting a flow to be stable and results from experiments and simulations…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an…
This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. Under this formulation, resolvent analysis may extend to turbulent flows with non-stationary mean states; the…
We consider particle acceleration by large-scale incompressible turbulence with a lengthscale larger than the particle mean free path. We derive an ensemble-averaged transport equation of energetic charged particles from an extended…
Laminar as well as turbulent oscillatory pipe flows occur in many fields of biomedical science and engineering. Pulmonary air flow and vascular blood flow are usually laminar, because shear forces acting on the physiological system ought to…
Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…