The intermittent rising and descending movement of the bag induces the formation of a wave and an undertow. Terrier and co-workers used such bioreactors for plant cell cultures, but the technology may also be transferred to animal cell. The principle consists in producing wave and undertow in a semi-closed vessel. Possibly the simplest bioreactor to expose cells to dynamic and cyclic mechanical stimuli, bag bioreactors require minimum manipulations and adjustments. Vermette, in Comprehensive Biotechnology (Second Edition), 2011 2.28.3.1 Bag Bioreactors/Wave and Undertow Bioreactors However, due to the vertical structure of the forcing, shoreward flows are driven near the top of the water column and a balancing return flow, the undertow, occurs in the lower water column. Set-up, the upward slope of sea level against the shore, will balance the depth averaged wave forcing. The other consequence of the vertical dependence of the momentum transfer is that the shoreward thrust provided by wave breaking is concentrated near the surface. This time delay causes a shift of the forcing of longshore currents, such that a current jet will occur landward of the location expected from study of the breaking locations of incident waves. The transfer of momentum from wave motions to mean currents described by radiation stress gradients above does not account for the existence of an intermediate repository, the active turbulence of the roller, that decays slowly as it is carried with the progressing wave. Both processes originate at the surface but drive turbulence and bubbles into the upper part of the water column. When waves break, the organized orbital motions break down, either through the plunge of a curling jet of water thrown ahead of the advancing wave or as a turbulent foamy mass (called a roller) carried on the advancing crest. The primary cause of depth dependence arises from wave-breaking processes. Holman, in Encyclopedia of Ocean Sciences (Third Edition), 2019 Vertically Dependent Processesĭepth-independent models are successful in reproducing many nearshore fluid processes but cannot explain several important phenomena, for example undertow, offshore-directed currents that exist in the lower part of the water column under breaking waves. In reality, undertow is more complex on account of oblique wave approach and varying breaker positions ( Haines and Sallenger, 1994) however, now there are many field measurements of undertow on both barred ( Greenwood and Sherman, 1984 Davidson-Arnott and McDonald, 1989 Greenwood and Osborne, 1990 Masselink, 2004 Goodfellow and Stephenson, 2005 Houser et al., 2006) and nonbarred coasts ( Miles and Russell, 2004 Reniers et al., 2004 Aagaard and Vinther, 2008). Generally, the faster offshore speeds are found in the bottom half of the water column, close to the bed ( Figure 14). Setup and the generation of undertow are easily demonstrated within the 2D constraints of a wave tank, especially with regular waves ( Figure 14) and considerable progress has been made in modeling this based on the net drift velocity in unbroken waves and the mass transfer of water in the roller associated with breaking waves ( Dally and Dean, 1984, 1986 Svendsen, 1984a, 1984b Masselink and Black, 1995). Because flow occurs uniformly alongshore the current speeds are relatively low, usually on the order of a 3–10 cm s −1 under moderate wave conditions to perhaps 20–40 cm s −1 under large wave conditions. Ideally, undertow is a two-dimensional (2D) return flow that occurs uniformly alongshore and is manifested as an offshore-directed net flow below the level of the wave troughs ( Figure 14).
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