Is a suction cup at the bottom of a bathtub subject to an upward force from the surrounding water, even if there is no water under it? A student question, posted in a teacher facebook group on a Monday morning, led to a discussion involving 21 comments with 225 replies offered by 16 teachers during the next few days, including several simple experiments, as well as modeling, to evaluate different arguments. The discussions, summarized in this paper, provide an example of how social media can provide an ‘extended teacher room’ where teachers can explore and refine their understanding in a safe and mostly supportive environment, and also find ways to give more elaborate answers to challenging student questions.
The dynamics of small perturbations on a buoyant coastal current is investigated. The system is described using a one and a half-layer model where the active upper layer vanishes at a certain distance from the coast, forming a front. Perturbations are imposed on a steady basic state with no along-coast variation. Analytical solutions are discussed for two special configurations of the basic state: (i) constant along-shore velocity, i.e. a coastal current with triangular cross-section, and (ii) a constant potential vorticity current. Two wave modes are found in both cases: a slowly moving frontally trapped wave, and a coastally trapped wave that moves with approximately the internal Kelvin wave speed plus the speed of the current at the coast. However, these two wave modes are not sufficient to construct a generally shaped initial perturbation. The part of the initial perturbation not covered by the two wave modes will in case (i) split into an infinite number of higher wave modes all travelling faster than the frontal wave and in case (ii) be advected and slowly smeared out by the current. Under the assumption that the current is unidirectional we find that the perturbations always move in the direction of a Kelvin wave, i.e. in the same direction as the coastal current, for all physically relevant cases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.