Rotating Hydraulics: Nonlinear Topographic Effects in the by Lawrence L.J. Pratt, John A. Whitehead

By Lawrence L.J. Pratt, John A. Whitehead

This booklet completely covers the advance of the idea of rotating hydraulics, making common use of aiding laboratory versions and observational information. the necessity to comprehend rotating hydraulic phenomena is starting to be as basic curiosity in weather and international flow is continually expanding. The publication information state of the art study and comprises many workouts.

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Extra info for Rotating Hydraulics: Nonlinear Topographic Effects in the Ocean and Atmosphere (Atmospheric and Oceanographic Sciences Library)

Example text

The value of R− at p is that specified at y = y1 and t = 0. 6) More generally, the shapes of the characteristics are not known in advance and there is no immediate way of knowing the origin of the characteristic curves passing through p. In practice, this problem is dealt with by calculation of the initial slopes of the characteristics from the values of c− and c+ all along the y-axis. Straight-line approximations of the characteristic curves having these initial slopes are then projected forward a time increment t.

This fixes a point ˜ If the latter is > 3/2, two possible solutions for d˜ can be on the ordinate B˜ − h. found. One corresponds to the left-hand branch and the other to the right-hand branch of the curve. There is one solution for B˜ − h˜ = 3/2 corresponding to the minimum of the curve. 6) The quantity B-gh, sometimes called the specific energy, is the total energy minus the potential energy provided by the bottom elevation. It represents the intrinsic energy of the flow. Changing the bottom elevation alters the specific energy, forcing the depth to adjust to new values.

At the same time, interpretation of these effects almost always involves waves and wave propagation. We therefore preface our discussion of steady hydraulics with a conversation about wave propagation in shallow water. 2) 37 38 39 40 and 41 42 43 44 45 For a homogeneous fluid, g is the ordinary gravitational acceleration. In oceanic and atmospheric models, we often consider flow in a layer that has uniform density and that is overlain by a much thicker and inactive layer of slightly lower (but still uniform) density.

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