Energy dissipation in spiral vortex layers wrapped around a straight vortex tube

Energy dissipation in spiral layers of high azimuthal vorticity around a straight vortex tube is investigated analytically. Asymptotic expressions of local and total viscous dissipation are obtained for the spiral vortex layers. When a vortex tube, which aligns with a uniform shear flow of a shear rate S, starts with a vortex filament of circulation Γ at an initial instant t=0, it wraps and stretches background vorticity lines around itself to form double spiral vortex layers of intense dissipation. The contribution of the spiral layers to total dissipation per unit axial length is evaluated to be 1.29πν2S2(Γ∕2πν)4∕3t at large vortex Reynolds numbers Γ∕ν⪢1, ν being the kinematic viscosity of fluid. There exists the critical time after which the contribution of the spirals to the total dissipation dominates that of the tube. If the tube is tilted at a small angle α in the direction of the uniform shear vorticity, the spirals around the tube are cross axially sheared into different shapes depending on the s...

[1]  A Survey on a Class of Exact Solutions of the Navier–Stokes Equations and a Model for Turbulence , 2004 .

[2]  P. Dimotakis.  The mixing transition in turbulent flows , 2000, Journal of Fluid Mechanics.

[3]  P. Sulem,et al.  Instability of strained vortex layers and vortex tube formation in homogeneous turbulence , 1995, Journal of Fluid Mechanics.

[4]  A. Vincent,et al.  The spatial structure and statistical properties of homogeneous turbulence , 1991, Journal of Fluid Mechanics.

[5]  A small‐scale turbulence model , 1993 .

[6]  H. K. Moffatt,et al.  Stretched vortices – the sinews of turbulence; large-Reynolds-number asymptotics , 1994, Journal of Fluid Mechanics.

[7]  H. Tennekes.  Simple Model for the Small‐Scale Structure of Turbulence , 1968 .

[8]  Javier Jiménez,et al.  Geometry and clustering of intense structures in isotropic turbulence , 2004, Journal of Fluid Mechanics.

[9]  The structure of intense vorticity in homogeneous isotropic turbulence , 1992 .

[10]  D. G. Crighton.  Instability of an elliptic jet , 1973 .

[11]  K. Horiuti,et al.  A classification method for vortex sheet and tube structures in turbulent flows , 2001 .

[12]  Javier Jiménez,et al.  The structure of intense vorticity in isotropic turbulence , 1993, Journal of Fluid Mechanics.

[13]  Roger E. A. Arndt,et al.  Advances in Turbulence , 1988, Lecture Notes in Mechanical Engineering.

[14]  Javier Jiménez,et al.  On the characteristics of vortex filaments in isotropic turbulence , 1998, Journal of Fluid Mechanics.

[15]  A. Vincent,et al.  The dynamics of vorticity tubes in homogeneous turbulence , 1994, Journal of Fluid Mechanics.

[16]  Fine Structure of a Directly Simulated Isotropic Turbulence , 1989 .

[17]  Javier Jiménez,et al.  Linear instability of a corrugated vortex sheet – a model for streak instability , 2003, Journal of Fluid Mechanics.

[18]  The interaction of a diffusing line vortex and an aligned shear flow , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[19]  Steven A. Orszag,et al.  Intermittent vortex structures in homogeneous isotropic turbulence , 1990, Nature.

[20]  T. Lundgren,et al.  Strained spiral vortex model for turbulent fine structure , 1982 .

[21]  Wrap, tilt and stretch of vorticity lines around a strong thin straight vortex tube in a simple shear flow , 1996 .

[22]  I. M. O T A K I S.  The mixing transition in turbulent flows , 2022 .

[23]  J. Jiménez,et al.  On steady columnar vortices under local compression , 1995, Journal of Fluid Mechanics.

[24]  Robert McDougall Kerr,et al.  Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence , 1983, Journal of Fluid Mechanics.

[25]  S. Corrsin.  Turbulent Dissipation Fluctuations , 1962 .

[26]  S. Kida,et al.  Dynamics of vortical structures in a homogeneous shear flow , 1994, Journal of Fluid Mechanics.

[27]  A. Gilbert.  A cascade interpretation of Lundgren’s stretched spiral vortex model for turbulent fine structure , 1993 .

[28]  Eric D. Siggia,et al.  Numerical study of small-scale intermittency in three-dimensional turbulence , 1981, Journal of Fluid Mechanics.

[29]  Martin R. Maxey,et al.  Small‐scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence , 1991 .

[30]  Martin R. Maxey,et al.  The evolution of small‐scale structures in homogeneous isotropic turbulence , 1992 .

[31]  T. Lundgren,et al.  Axial motion and scalar transport in stretched spiral vortices , 2001 .

[32]  Y. Couder,et al.  Direct observation of the intermittency of intense vorticity filaments in turbulence. , 1991, Physical review letters.

[33]  Fazle Hussain,et al.  Coherent structures near the wall in a turbulent channel flow , 1997, Journal of Fluid Mechanics.

[34]  Double Spirals around a Tubular Vortex in Turbulence , 2000 .

[35]  S. Kida,et al.  Spatiotemporal intermittency and instability of a forced turbulence , 1992 .

[36]  H. Miura,et al.  Identification of Tubular Vortices in Turbulence , 1997 .