By Marius Ungarish
Gravity currents and intrusions are the ever present phenomena the place a fluid of 1 density flows horizontally right into a fluid of a unique density. For researchers and engineers, the facility to appreciate and expect those circulation fields is vital in wide-ranging purposes together with these concerned with atmospheric and ocean dynamics, the propagation of toxins, and the dispersion of volcanic clouds. even though many new theories, experimental info, simulation effects, and insights have surfaced lately, each one of these advancements stay scattered in journals and convention papers. A systematic and unified creation to the sector, which includes the hot effects and advancements, is sure to facilitate the applying of the to be had wisdom to either functional difficulties and additional investigations. Written via a well-known authority lively in fresh advancements in gravity present learn, An creation to Gravity Currents and Intrusions presents an updated, self-contained, and systematic creation to the learn, interpretation, and prediction of gravity present flows. the writer makes use of an easy mathematical framework to supply an obtainable and entire advent to the mathematical and actual points of this crucial subject. The textual content offers researchers and practitioners with the root required to formulate difficulties, interpret experimental effects and measurements info, receive uncomplicated and insightful analytical estimates and suggestions, and increase or enforce numerical codes for similar difficulties. The booklet additionally issues out gaps of data within the present figuring out that require additional learn. This obtainable reference calls for just a easy historical past in fluid mechanics and utilized arithmetic, making it a fantastic foundation for researchers and engineers new to the sector. it may additionally function a textbook for upper-level undergraduate and graduate point classes in fluid dynamics.
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Additional resources for An Introduction to Gravity Currents and Intrusions
52) and the relationships between the variables on these trajectories h−1/2 dh ± du = 0. 53) The initial conditions for the dam-break problem are: zero velocity and unit dimensionless height and length at t = 0. The boundary conditions are: at x = −1 the velocity is zero, and an additional condition for the velocity u at the nose x = xN (t) should be considered. In the classical hydraulic dam-break problem the nose height of the water (that propagates against the negligible resistance of the embedding air) decreases smoothly to zero at xN (t), and hence the velocity of the tip of the current follows straightforwardly from the internal solution.
A typical comparison between the analytical and numerical SW dam-break results is presented in Fig. 7. The agreement is, as expected, excellent, which provides a straightforward verification of both solutions. The backward-moving expansion wave reaches the wall at t = 1, which explains the discrepancy between the present analytical and finite-difference solutions at later times. A real laboratory saltwater Boussinesq current is shown in Fig. 1 for comparison. 75 (for the HS F r). Here we also use some Navier-Stokes simulations (which can be regarded as “numerical experiments”) to gain more insight into the initial behavior of the current.
64) is that at the position of the lock, x = 0, the height of the current is 4/9 and the speed is 2/3, independent of t and on the speed of the nose. It is easy to verify that c+ > c− in the LOM domain. Consequently, the “+” characteristics from the reservoir, which carry the value Γ+ = 2, cover the expansion fan domain and then proceed beyond the OM line, into the M ON domain. Finally, consider the characteristic region M ON where u = uN and h = hN . 65) provides (uniquely) the value of hN , and then of uN .
An Introduction to Gravity Currents and Intrusions by Marius Ungarish