Many Faces of Boussinesq Approximations
Vladimir A. Vladimirov, Nasser Al-Salti

TL;DR
This paper systematically analyzes the Boussinesq approximation equations using asymptotic theory, revealing an infinite variety of models classified by parameters that affect their accuracy and applicability.
Contribution
It introduces a classification of Boussinesq models based on two parameters, q and k, detailing their impact on model quality and scale variations.
Findings
Infinite set of asymptotic models classified by parameters q and k
Higher q improves approximation quality but reduces applicability
Scales of velocity, time, and viscosity can be varied independently
Abstract
The \emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters and , where and . Parameter is related to the `quality' of approximation, while gives us an infinite set of possible scales of velocity, time, viscosity, \emph{etc.} Increasing improves the quality of a model, but narrows the limits of its applicability. Parameter allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we…
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Taxonomy
TopicsNonlinear Waves and Solitons · Seismic Imaging and Inversion Techniques · Fluid Dynamics and Turbulent Flows
