Related papers: Navier--Stokes equations on the $\beta$-plane: det…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
We consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by time periodic inflow/outflow boundary conditions. We show that the problem admits a time periodic…
We formalise a systematic method of constructing forward self-similar solutions to the Navier-Stokes equations in order to characterise the late stage of decaying process of turbulent flows. (i) In view of critical scale-invariance of type…
In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that…
In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the…
Perturbed, helical trefoil vortex knots and a set of anti-parallel vortices are examined numerically to identify the scaling of their helicity and vorticity norms during reconnection. For the volume-integrated enstrophy $Z=\int\omega^2 dV$,…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We study the singular limit of a rotating compressible fluid described by a scaled barotropic Navier-Stokes system, where the Rossby number, the Mach number and the Froude number tend to 0 in a particular mutual rate while the Reynolds…
The old idea that an infinite dimensional dynamical system may have its high modes or frequencies slaved to low modes or frequencies is re-visited in the context of the $3D$ Navier-Stokes equations. A set of dimensionless frequencies…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of…
We study the stationary nonhomogeneous Navier--Stokes problem in a two dimensional symmetric domain with a semi-infinite outlet (for instance, either parabo-\\loidal or channel-like). Under the symmetry assumptions on the domain, boundary…
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to be a…
In this paper, we continue the discussion as done in \cite{CTZ15} on turbulent channel flow described by the Navier-Stokes model and the Navier-Stokes-alpha model. We study the non-stationary solutions for the Navier-Stokes equations and…
The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this…
We consider the incompressible 2D Navier-Stokes equations on the torus, driven by a deterministic time periodic force and a noise that is white in time and degenerate in Fourier space. The main result is twofold. Firstly, we establish a…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…
In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…
In the present technical note, we establish that the setting of the primitive variables of the unsteady incompressible fluid dynamics is ill-formulated in spatially periodic domains as the specification of the boundary velocity is too broad…