  Residual and solution filtering procedures are studied with respect to
inhibiting the accumulation of small-scale (i.e., high wavenumber) content.
Assessing each method in terms of an ``equivalent residual equation" reveals
fundamental differences in their behaviors, such as how the underlying solution
can be constrained to a target filter width. The residual filtering (RF)
approach paired with a dissipative filter kernel is shown to restrict scale
generation in the fluid equations via dispersive effects; meanwhile, solution
filtering (SF) -- and artificial dissipation (AD), by extension -- operates
through dissipative mechanisms and actively attenuates high wavenumber content.
Discrete filters (i.e., the Top-hat and implicit Tangent schemes) are analyzed
in terms of their response characteristics and their associated effects on
reducing small-scale activity when paired with the RF versus SF approaches.
Linear theoretical assessments (e.g., von Neumann analysis) are shown to
successfully characterize the fundamental behaviors of the methods in
non-linear settings, as observed through canonical test cases based on 1D
viscous Burgers, 2D Euler, 3D Navier-Stokes equations.
