1. How vortex filament are arrange in the vortex sheet?
a) Side by side
b) Front and back
c) Up and down
d) Left and right
Explanation: The flow in the planes perpendicular to the vortex filament at zero are identical to the flow induced by the point vortex of strength. An infinite number of straight vortex filaments side by side. Where the strength of each filament is infinite small. These vortex filament are arranged side by side from the vortex sheet.
2. Is vortex sheet is a term used in fluid mechanics?
a) False
b) True
Explanation: A vortex sheet is a term used in fluid mechanics for a surface across, which there is a discontinuity in fluid velocity. Such as in slippage of one layer of fluid over another .which the tangential components of the flow velocity are discontinuous across the vortex sheet, the normal components of the flow velocity is continuous
3. Is vortex sheet is unstable at high Reynolds number?
a) True
b) False
Explanation: The discontinuity in the tangential velocity means that the flow has infinite vorticity in a vortex sheet. At high Reynolds numbers vortex sheets tend to be unstable and they exhibit Kelvin-Helmholtz instability. The Kelvin-Helmholtz instability can occur when there is velocity shear in a single continuous fluid.
4. Is z=x+iy is the vortex sheet equation for complex coordinate?
a) False
b) True
Explanation: The formulation of the vortex sheet equation of motion is given in terms of a complex coordinates z=x+iy. The sheet is described parametrically by z(s, t), where s is the arc length between coordinate z and a reference point and t is the time left. This equation will give the vortex sheet for different complex coordinates.
5. At what point circulation between two material points in the sheet remains conserved.
a) Zero
b) One
c) Greater than zero
d) Less than zero
Explanation: Kelvin’s circulation theorem, is the absence of external forces on the sheet, the circulation between any two material points in the sheet remains conserved at zero. The equation of motion of the sheet can be rewritten in terms of circulation and by a change of variable.
6. Is flat vortex sheet with periodic boundaries can be used in high Reynolds number?
a) True
b) False
Explanation: A flat vortex sheet with periodic boundaries in the stream wise direction can be used to model a temporal free shear layer at high Reynolds number. Assume that the interval between the periodic boundaries is of length ‘1’, then the flat vortex sheet with periodic boundary can be used in a free shear layer at high Reynolds number.
7. Is zero is the initial condition for a flat vortex sheet?
a) True
b) False
Explanation: The integral form the Cauchy principal value integral. The initial condition for a flat vortex sheet with a constant strength is zero. The flat vortex sheet is an equilibrium solution. However, it is unstable to infinitesimal periodic disturbance. Hence, with a constant strength flat vortex sheet is used.
8. Is vortex sheet can go beyond the critical time?
a) True
b) False
Explanation: The vortex sheet solution as given by the birkoff-roff equation cannot go beyond the critical time. The spontaneous loss of analyticity in a vortex sheet is a consequence of mathematical modeling since a real fluid with viscosity, however, small will never develop singularity
9.Is viscosity is the smoothing parameter on the real fluid?
a) True
b) False
Explanation: Viscosity acts a smoothing parameter in areal fluid .these have been extensive studies on a vortex sheet, most of them by discrete or point vortex approximation with or without using a point vortex approximation and delta-regularization is obtained by smooth roll-up of a vortex sheet into a double branched spiral.
10. Is point vortices can control the growth of round-off errors?
a) True
b) False
Explanation: Point vortices are inherently chaotic, a Fourier filter is necessary to control the growth of round-off errors. Continuous approximation of a vortex sheet by vortex panels with are wise diffusion of circulation density also shows that the sheet rolls-up into a double branched spiral.