An Investigation on the Effect of Prevailling Winds upon the Depth of Bays. (5th Paper)

[摘要] In the present paper, is made a theoretical discussion, based on W. Ekman's theory of drift current, on the direction of the general current near the bottom of shallow seas or bays produced by prevailing winds.Two special cases were fully discussed, viz.(I) The case of an enclosed sea of uniform depth, d'.Considering that a steady wind is blowing everywhere with the same strength horizontally along the positive direction of y-axis, the x- and y-components of the current produced thereby were formulated.The direction of the bottom current upon which the transport of sand particles on the bottom of the sea chiefly depends, is given by the expression tgα=A/B, in whichwhere α is the angle between the direction in which the prevailing wind is blowing and that of the bottom current, measured clockwise starting from the former to the latter, T is the tangential stress of the wind, D' is the depth of frictional _??_nfluence, a=π/D', γx and γy are the slope angles of the sea-surface in the directions of x and y respectively, ρ is the density of sea water, g the acceleration due to gravity.α was computed for va_??_ious values of depth, d', and it was found that α gradually increases with the depth, d', but that it does not exceed 45° so long as d' does not exceed the depth of frictional influence. Thus, it follows that the mathematical expression representing the effect of prevailing winds may be written in the form F (γ) cos (θ-θ0+α). Since, however, α is small and negligible if d' does not exceed half the depth of frictional influence, we may use the expression F (γ) cos (θ-θ0) introduced before by the present author, instead of F (γ) cos (θ-θ0+α), for most practical purposes at least for the first approximation.(II) The case of a sea of uniform depth, d', with a straight coast.Considering that a steady and uniform wind is blowing horizontally along the positive direction of y-axis, the x- and y- components of the current produced thereby were formulated.The direction of the bottom current was found to be given by the expression tg (2π-β)=A/B, in whichwhere β is the angle between the direction in which the wind is blowing and that of the bottom current, measured counterclockwise starting from the former to the latter.β was computed for various values of d' and θ-θ0, θ-θ0 being the angle between the direction of the prevailing winds and that of the coast line.Thus, the mathematical expression representing the effect of prevailing winds may be written in the form F (γ) cos (θ-θ0+π-β). Since, however, as in the case (I), (π-β) is not large if the depth of the sea is shallow and it is almost negligible if d' is less than half the depth of frictional influence, the value of F (γ) cos (θ-θ0+π-β) does not much differ from that of F (γ) cos (θ-θ0), and we may use the latter expression for practical purposes at least for the first approximation.It was further suggested that the above theory may be applied to some extent to the case of a peninsula. Some actual examples which seem to justify the above theory were found.A more detailed discussion will appear in a future number of the “Geophysical Magazine.”

[学科分类] 大气科学