Note on the triad interactions of homogeneous turbulence

2014 ◽  
Vol 741 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Linear Problem ◽  
Flow Problem ◽  
Initial Conditions ◽  
Passive Scalar ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Marked Contrast ◽  
Scalar Type ◽  
Two Dimensional Flow ◽  
Triad Interactions

AbstractTriad interactions, involving a set of wave-vectors $\{\pm \boldsymbol {k}, \pm \boldsymbol {p}, \pm \boldsymbol {q}\}$, with $ \boldsymbol {k} + \boldsymbol {p}+ \boldsymbol {q}=0$, are considered, and the results of triad truncation are compared with the results of exact Euler evolution starting from the same initial conditions. The essential two-dimensionality of the triad interaction is used to separate the problem into two parts: a nonlinear two-dimensional flow problem in the triad plane, and a linear problem of ‘passive scalar’ type for the evolution of the component of velocity perpendicular to this plane. Several examples of triad evolution are presented in detail, and the marked contrast with Euler evolution is demonstrated. It is known that energy and helicity are conserved under triad truncation; it is shown that the ‘in-plane’ energy and enstrophy are also conserved. However, it is also shown that, in general, the evolution of the vorticity under triad truncation cannot be represented as transport by any divergence-free velocity field, with the consequence that the detailed topology of the vorticity field is not conserved under this truncation.

scholarly journals Three-Dimensional Mesoscale Dipole Frontal Collisions

2007 ◽  
Vol 37 (9) ◽  
pp. 2331-2344 ◽  
Author(s):  
Sara Dubosq ◽  
Álvaro Viúdez
Keyword(s):  
Numerical Model ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Vortex Interactions ◽  
Diffusion Effects ◽  
Two Dimensional Flow ◽  
Frontal Collisions ◽  
Bounce Back

Abstract Frontal collisions of mesoscale baroclinic dipoles are numerically investigated using a three-dimensional, Boussinesq, and f-plane numerical model that explicitly conserves potential vorticity on isopycnals. The initial conditions, obtained using the potential vorticity initialization approach, consist of twin baroclinic dipoles, balanced (void of waves) and static and inertially stable, moving in opposite directions. The dipoles may collide in a close-to-axial way (cyclone–anticyclone collisions) or nonaxially (cyclone–cyclone or anticyclone–anticyclone collisions). The results show that the interacting vortices may bounce back and interchange partners, may merge reaching a tripole state, or may squeeze between the outer vortices. The formation of a stable tripole from two colliding dipoles is possible but is dependent on diffusion effects. It is found that the nonaxial dipole collisions can be characterized by the interchange between the domain-averaged potential and kinetic energy. Dipole collisions in two-dimensional flow display also a variety of vortex interactions, qualitatively similar to the three-dimensional cases.

On the evolution and saturation of instabilities of two-dimensional isolated circular vortices

1999 ◽  
Vol 388 ◽  
pp. 217-257 ◽  
Author(s):  
R. C. KLOOSTERZIEL ◽  
G. F. CARNEVALE
Keyword(s):  
Dynamical System ◽  
Numerical Experiments ◽  
Finite Amplitude ◽  
Infinite Plane ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Wave Interactions ◽  
Geometrical Features ◽  
Two Dimensional Flow ◽  
Observed Behaviour

Laboratory observations and numerical experiments have shown that a variety of compound vortices can emerge in two-dimensional flow due to the instability of isolated circular vortices. The simple geometrical features of these compound vortices suggest that their description may take a simple form if an appropriately chosen set of functions is used. We employ a set which is complete on the infinite plane for vorticity distributions with finite total enstrophy. Through projection of the vorticity equation (Galerkin method) and subsequent truncation we derive a dynamical system which is used to model the observed behaviour in as simple as possible a fashion. It is found that at relatively low-order truncations the observed behaviour is qualitatively captured by the dynamical system. We determine what the necessary ingredients are for saturation of instabilities at finite amplitude in terms of wave–wave interactions and feedback between various azimuthal components of the vorticity field.

scholarly journals On the alignment dynamics of a passive scalar gradient in a two-dimensional flow

2005 ◽  
Vol 17 (11) ◽  
pp. 117102 ◽  
Author(s):  
A. Garcia ◽  
M. Gonzalez ◽  
P. Paranthoën
Keyword(s):  
Passive Scalar ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

scholarly journals On the late-time behaviour of a bounded, inviscid two-dimensional flow

2015 ◽  
Vol 783 ◽  
pp. 1-22 ◽  
Author(s):  
David G. Dritschel ◽  
Wanming Qi ◽  
J. B. Marston
Keyword(s):  
Large Scale ◽  
Point Vortex ◽  
Small Scale ◽  
Late Time ◽  
Two Dimensional ◽  
Time Behaviour ◽  
Vorticity Field ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Initial Vorticity

Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate-wavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point-vortex model characterising the interactions between the four main vortices which emerge.

On the Use of Two-Dimensional Incompressible Flow to Study Secondary Eyewall Formation in Tropical Cyclones

2010 ◽  
Vol 67 (12) ◽  
pp. 3765-3773 ◽  
Author(s):  
Yumin Moon ◽  
David S. Nolan ◽  
Mohamed Iskandarani
Keyword(s):  
Tropical Cyclone ◽  
Numerical Simulations ◽  
Tropical Cyclones ◽  
Incompressible Flow ◽  
Two Dimensional ◽  
Vorticity Field ◽  
The Core ◽  
Secondary Eyewall Formation ◽  
Two Dimensional Flow ◽  
Order Of Magnitude

Abstract Previous studies have offered hypotheses for the mechanisms that lead to secondary eyewall formation in tropical cyclones by using two-dimensional incompressible flow. Those studies represented the convection-induced vorticity field as either large but weak vortices that are the same sign as the tropical cyclone core or as purely asymmetric vorticity perturbations that are an order of magnitude weaker than the core. However, both observations and full-physics simulations of tropical cyclones indicate that the convection-induced vorticity field should also include clusters of small vorticity dipoles whose magnitude is comparable to that of the high-vorticity core. Results of numerical simulations indicate that the interaction between the tropical cyclone core vortex and the convection-induced small vorticity dipoles of considerable strength in two-dimensional flow does not lead to coherent concentric vorticity ring formation. The axisymmetrization process under the simplification of two-dimensional incompressible flow appears to be incomplete for describing secondary eyewall formation.

Two-Dimensional Flow of Polymer Solutions Through Porous Media

1999 ◽  
Vol 2 (3) ◽  
pp. 251-262
Author(s):  
P. Gestoso ◽  
A. J. Muller ◽  
A. E. Saez
Keyword(s):  
Porous Media ◽  
Polymer Solutions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow
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