Kinematics of the transport of momentum by tilted troughs.

Abstract

It is shown that in x, y plane, while the direction of tangent to a tilted trough indicates whether the u-momentum flux is northwards or southwards, the curving or the concavity of the tilted trough indicates whether there is convergence or divergence of the momentum flux; Concavity of a trough towards east indicates divergence of flux and concavity towards west indicates convergence of momentum flux. The magnitude of this divergence for parabolically tilted trough is given by average value of (meridional velocity )²/(semi latus rectum of the parabola). Formulae are also given for momentum flux and its divergence when the tilted trough is a cubic curve. Qualitative pattern of the momentum flux and its divergence are given for various trough patterns to enable an analyst to infer the same from a mere look at the pattern on a chart.