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We examine the efficacy of streamwise traveling waves generated by a zero-net-mass-flux surface blowing and suction for controlling the onset of turbulence in a channel flow. For small amplitude actuation, we utilize weakly nonlinear…
Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely…
A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier-Stokes equations,…
The statistical evolution of ensembles of random, weakly-interacting waves is governed by wave kinetic equations. To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions…
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a…
Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The…
The purpose of this paper is to consider the application of the direct interaction approximation (DIA) developed by Kraichnan to generalized stochastic models in the turbulence problem. Previous developments were based on the…
Understanding how statistical equilibrium can occur in out-of-equilibrium systems is of paramount interest, as it would enable the use of statistical mechanics tools to these systems. Here, we report the first experimental evidence of…
Turbulence is a complex system exhibiting both universal statistical features and prominent coherent structures. We model turbulence using coherent vortices distributed within a multi-scale statistical framework, termed `woven turbulence'.…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…
Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest…
This paper constructs a rigorous mathematical framework for investigating laminar-turbulent transition induced by weak singularities of incompressible Navier-Stokes (NS) equations. By integrating the energy identity of Leray weak solutions…
For the first time weak turbulent theory was demonstrated for the surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis from kinetic equation.
The comprehension of stratified flows is important for geophysical and astrophysical applications. The Weak Wave Turbulence theory aims to provide a statistical description of internal gravity waves propagating in the bulk of such flows.…
In order to understand whether, and to what extent, spectral representation can effectively highlight the nonlinear interaction among different scales, it is necessary to consider the state that precedes the onset of instabilities and…
Turbulence of weakly interacting waves displays a great deal of universality: independence of the details of the interaction and of the pumping and dissipation scales. Here we study how inverse turbulent cascades (from small to large…
A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…