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Title: Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field

Abstract

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound onmore » the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.« less

Authors:
 [1];  [2];  [3]
  1. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ (United Kingdom)
  2. School of Earth and Environment, University of Leeds, Leeds, LS2 9JT (United Kingdom)
  3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA (United Kingdom)
Publication Date:
OSTI Identifier:
21072383
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.75.026304; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-651X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; COMPUTERIZED SIMULATION; DIFFUSION; FLUID FLOW; FLUIDS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; VELOCITY; VORTICES

Citation Formats

Davidson, P A, Sreenivasan, Binod, and Aspden, A J. Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field. United States: N. p., 2007. Web. doi:10.1103/PHYSREVE.75.026304.
Davidson, P A, Sreenivasan, Binod, & Aspden, A J. Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field. United States. https://doi.org/10.1103/PHYSREVE.75.026304
Davidson, P A, Sreenivasan, Binod, and Aspden, A J. 2007. "Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field". United States. https://doi.org/10.1103/PHYSREVE.75.026304.
@article{osti_21072383,
title = {Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field},
author = {Davidson, P A and Sreenivasan, Binod and Aspden, A J},
abstractNote = {We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.},
doi = {10.1103/PHYSREVE.75.026304},
url = {https://www.osti.gov/biblio/21072383}, journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
issn = {1063-651X},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}