TY - JOUR

T1 - Variational inequalities for a body in a viscous shearing flow

AU - Nir, A.

AU - Weinberger, H. F.

AU - Acrivos, A.

PY - 1975/4

Y1 - 1975/4

N2 - The slow motion of a body in a viscous shearing field is examined. Variational principles are used to derive inequalities which approximate the elements of the shearing matrix M of a body of arbitrary shape, where M is the matrix relating the force, torque and stresslet exerted by the body on the fluid to the relative translational and rotational velocities of the body and the rate of deformation of the undisturbed linear field. An upper bound for the elements of M is obtained by showing that the quadratic form of M increases monotonically with B, the region occupied by the body, while a lower bound for this form is given in terms of the electrostatic properties of a conductor and a dielectric of the same shape as B. Particular attention is paid to bodies of revolution, for which certain more definitive results are obtained: for example, their resistance to a rotation with axial symmetry is always less than twice their resistance to a rotation perpendicular to their axis.

AB - The slow motion of a body in a viscous shearing field is examined. Variational principles are used to derive inequalities which approximate the elements of the shearing matrix M of a body of arbitrary shape, where M is the matrix relating the force, torque and stresslet exerted by the body on the fluid to the relative translational and rotational velocities of the body and the rate of deformation of the undisturbed linear field. An upper bound for the elements of M is obtained by showing that the quadratic form of M increases monotonically with B, the region occupied by the body, while a lower bound for this form is given in terms of the electrostatic properties of a conductor and a dielectric of the same shape as B. Particular attention is paid to bodies of revolution, for which certain more definitive results are obtained: for example, their resistance to a rotation with axial symmetry is always less than twice their resistance to a rotation perpendicular to their axis.

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U2 - 10.1017/S0022112075001206

DO - 10.1017/S0022112075001206

M3 - Article

AN - SCOPUS:0016496130

SN - 0022-1120

VL - 68

SP - 739

EP - 755

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

IS - 4

ER -