Generation of Two-Dimensional Unsteady Motion in a Viscous Incompressible Fluid of Finite Depth
P. Kundu1, B. N. Mandal2
1Department of Mathematics, Jadavpur University, Kolkata, 700032, India
2Indian Statistical Institute, Kolkata, 700108, India
Keywords: unsteady motion, viscous fluid, Laplace and Fourier transforms, method of steepest descent, free surface depression
Abstract
The problem of generation of two-dimensional unsteady motion in a viscous incompressible fluid of finite depth is investigated here. The motion is generated due to initial disturbances in the form of prescribed surface pressure or displacement at the free surface. The Fourier transform with respect to space and the Laplace transform with respect to time are used to obtain the form of the free surface in terms of multiple integrals. Finally, an asymptotic form of the free surface is obtained using the method of steepest descent.
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