Vinokurov D.   Tarunin E.L.  

Numerical study of convective vortex (dependencies of the integral characteristics on the boundary conditions)

Reporter: Vinokurov D.

G.P. Bogatyrev and his colleagues studied the laboratory model of typhoon-like vortex in
Perm since 1990 [1, 2]. This research was focused on formation and evolution of an intensive
convective vortex in rotating cylindrical vessel with local heating from a bottom. According to
the experiments, vortex velocity exceeded a solid-state rotation in about 10 times. After the
laboratory experiments several articles devoted to numerical modeling of similar phenomenon
were published [3, 4].
In this work we also use resources of numerical modeling to study dependencies which
were not investigated earlier. Our research focuses on integral characteristics, conditions of
intensive vortex formation and axial flow restructuring with changing of flow direction. The
axysimmetric problem, described by the heat convection equations (Boussinesq approximation),
was solved using finite differences in the variables of two-field method. Geometrical parameters
corresponded to the laboratory experiments [1]. Except geometrical parameters problem had
three dimensionless parameters – Grashof, Prandtl and Reynolds numbers.
Flow pictures for several flow types were obtained. Boundaries of intensive vortex formation
and axial flow restructuring were determined earlier [5]. In this work we investigate integral characteristics (kinetic energy, Nusselt number, integral angular momentum, global super-rotation [2]) dependencies on the boundary conditions (heat area, aspect ratio, side boundary type). Comparison with laboratory experiments results and tests on different grids were performed.

1. Bogatyrev G.P., Kolesnichenko I.V., Levina G.V. and Sukhanovsky A.N. Laboratory
Model of Generation of a Large-scale Spiral Vortex in a Convectively Unstable Rotating
Fluid // Izvestiya RAN. Fizika atmosfery i okeana, 2006, Vol. 42, Num. 4, pp. 460-466.
2. Batalov V., Sukhanovsky A., Frick P. Laboratory study of differential rotation in a con-
vective rotating layer // Geophysical and Astrophysical Fluid Dynamics. - 2010. - Vol.
104, no. 4. - Pp. 349–368.
3. Ivanov M.F., Povarnitsyn M.E. Numerical Simulation of the Evolution of Intensive Con-
vective Vortices of the Typhoon Type in a Rotating Fluid // Fluid Dynamics, 2003, Vol.
38, Num. 3, pp. 409-416.
4. Sukhanovsky A.N. Differential Rotation Formation in Cylindrical Fluid Layer // Vychis-
litelnaia mehanika sploshnyh sred, 2010, Vol. 3, Num. 2, pp. 103-115.
5. Vinokurov D.A., Tarunin E.L. Numerical investigation of convective vortex in locally heated rotating vessel // Vestnik Permskogo universiteta. Matematika. Mehanika. Informatika (in print)

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