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Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…

This paper extends the resolvent formalism for wall turbulence proposed by McKeon and Sharma(2010) to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier-Stokes equations are interpreted as a…

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

Using the previously developed model to describe laminar/turbulent states of a viscous fluid flow, which treats the flow as a collection of coherent structures of various size (Chekmarev, Chaos, 2013, 013144), the statistical temperature of…

The onset of turbulence in pipe flow has been a fundamental challenge in physics, applied mathematics, and engineering for over 140 years. To date, the precursor of this laminar-turbulent transition is recognized as transient turbulent…

A promising and cost-effective method for numerical simulation of high Re wall-bounded flows is wall-modeled large-eddy simulation. Most wall models are formulated from the Reynolds-averaged Navier-Stokes equations (RANS). These RANS-based…

The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…

It has been recently demonstrated, [3], that according to the principle of release of constraints, absence of shear stresses in the Euler equations must be compensated by additional degrees of freedom, and that led to a Reynolds-type…

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize…

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of…

Suspended particles can alter the properties of fluids and in particular also affect the transition from laminar to turbulent flow. In the present experimental study, we investigate the impact of neutrally buoyant, spherical inertial…

The simulation of turbulent flow requires many degrees of freedom to resolve all the relevant times and length scales. However, due to the dissipative nature of the Navier-Stokes equations, the long-term dynamics are expected to lie on a…

A new formulation of the Navier-Stokes equation, in terms of the gradient of the total mechanical energy, is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found.…

The study is devoted to the development of new effective tools and methods of ana-lytical hydrodynamics, including problems of existence, smoothness and structure of laminar and turbulent flows. The main problem is complex Navier-Stokes…

The transition from laminar to turbulent flow is an immensely important topic that is still being studied. Here we show that complex plasmas, i.e., microparticles immersed in a low temperature plasma, make it possible to study the…

Threshold amplitude of disturbance for transition to turbulence in a pipe Poiseuille flow is investigated. Based on the energy gradient theory, we argued that the transition to turbulence depends on magnitudes of the energy gradient of mean…

Modal stability analysis provides information about the long-time growth or decay of small-amplitude perturbations around a steady-state solution of a dynamical system. In fluid flows, exponentially growing perturbations can initiate…

Accurate prediction of the transition from laminar flow to turbulence remains an unresolved challenge despite its importance for understanding a variety of environmental, biological, and industrial phenomena. Well over a century of…

We introduce a novel toy model for shear flows, exploiting the spatial intermittency and the scale separation between large-scale flows and small-scale structures. The model is highly sparse, focusing exclusively on the most intense…

We study the Reynolds number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description…