相关论文: Shell Model of Turbulence Perturbed by L\'{e}vy No…
This work is devoted to the proof of the existence of a martingale solution for a complex version of the stochastic Stefan problem. This particular formulation incorporates two important features: a mushy region and turbulent transport…
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-B\'enard (RB) convection as an example, we numerically…
The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to…
We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated…
A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found…
Unlike the power-law model, the Ellis model describes the apparent viscosity of a shear-thinning fluid with no singularity in the limit of a vanishingly small shear stress. In particular, this model matches the Newtonian behaviour when the…
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have…
In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…
The small scale statistics of homogeneous isotropic turbulence of dilute polymer solutions is investigated by means of direct numerical simulations of a simplified viscoelastic fluid model. It is found that polymers only partially suppress…
In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
A six-dimensional Navier-Stokes equation derived by one of the authors(ST) is solved for a turbulent mixing layer to demonstrate that it has a solitary wave solution. Turbulence intensities and Reynolds' stress are calculated using this…
We analyze the blowup (finite-time singularity) in inviscid shell models of convective turbulence. We show that the blowup exists and its internal structure undergoes a series of bifurcations under a change of shell model parameter. Various…
Turbulent flow remains a challenging subject, despite extensive efforts to find analytical descriptions. Modeling small scales of motion is crucial for saving time and resources in numerical simulations, particularly in industrial…
We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessary local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume…
This paper presents a rigorous theoretical extension of the Smagorinsky model for turbulence simulations. The author builds on its fundamental framework, addressing known limitations, and making new mathematical advances. Specifically, this…
A rigoros analytical justification of turbulence observed in active fluids and caused by self-propulsion is presented. We prove existence of unstable wave modes for the generalized Stokes and Navier-Stokes systems by developing an approach…
This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable…
We show that the intermittent dynamics observed in the inertial interval of Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection, the space-time scaling symmetries (like in…
Stationary solutions of a shell model of turbulence defined on a dyadic tree topology are studied. Each node's amplitude is expressed as the product of amplitude multipliers associated with its ancestors, providing a recursive…