Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains

Tadie. "Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains." Applications of Mathematics 44.1 (1999): 1-13. <http://eudml.org/doc/33023>.

@article{Tadie1999,
abstract = {In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ($r \le d$) where $ (r,\theta ,z)$ denotes the cylindrical co-ordinates in $\{\mathbb \{R\}\}^3$ is considered. The motion is with swirl (i.e. the $\theta $-component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ($f_q=0$ in (f)) in the whole space, as the flux constant $k$ tends to $\infty $, 1) $\mathrm \{dist\}(0z,\partial A)=O(k^\{1/2\})$; $\mathrm \{diam\}A = O(\exp (-c_0k^\{3/2\}))$; 2) $(k^\{1/2\} \Psi )_\{k \in \mathbb \{N\}\}$ converges to a vortex cylinder $U_m$ (see (1.2)). We show that for the problem with swirl, as $k\nearrow \infty $, 1) holds; if $m \le q+2$ then 2) holds and if $m> q+2$ it holds with $U_\{q+2\}$ instead of $U_m$. Moreover, these results are independent of $f_0$, $f_q$ and $d>0$.},
author = {Tadie},
journal = {Applications of Mathematics},
keywords = {vortex rings; potential theory; elliptic equations; vortex rings; swirl; exterior domain; potential theory; asymptotic behavior; elliptic equations},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains},
url = {http://eudml.org/doc/33023},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Tadie
TI - Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 1
SP - 1
EP - 13
AB - In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ($r \le d$) where $ (r,\theta ,z)$ denotes the cylindrical co-ordinates in ${\mathbb {R}}^3$ is considered. The motion is with swirl (i.e. the $\theta $-component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ($f_q=0$ in (f)) in the whole space, as the flux constant $k$ tends to $\infty $, 1) $\mathrm {dist}(0z,\partial A)=O(k^{1/2})$; $\mathrm {diam}A = O(\exp (-c_0k^{3/2}))$; 2) $(k^{1/2} \Psi )_{k \in \mathbb {N}}$ converges to a vortex cylinder $U_m$ (see (1.2)). We show that for the problem with swirl, as $k\nearrow \infty $, 1) holds; if $m \le q+2$ then 2) holds and if $m> q+2$ it holds with $U_{q+2}$ instead of $U_m$. Moreover, these results are independent of $f_0$, $f_q$ and $d>0$.
LA - eng
KW - vortex rings; potential theory; elliptic equations; vortex rings; swirl; exterior domain; potential theory; asymptotic behavior; elliptic equations
UR - http://eudml.org/doc/33023
ER -