4 research outputs found
Acoustic Equation in a Lossy Medium
Here, the acoustic equation for a lossy medium is derived from the first
principle from the linearized compressible Navier-Stokes equation without
Stokes' hypothesis. The dispersion relation of the governing equation is
obtained, which exhibits both the dispersive and dissipative nature of the
acoustic perturbations traveling in a lossy medium, depending upon the length
scale. We specifically provide a theoretical cut-off wave number above which
the acoustic equation represents a diffusive nature. Such a behavior has not
been reported before, as per the knowledge of the authors
Perturbation Field in The Presence of Uniform Mean Flow: Doppler Effect for Flows and Acoustics
Having developed the perturbation equation for a dissipative quiescent medium
for planar propagation using the linearized compressible Navier-Stokes equation
without the Stokes' hypothesis \cite{arxiv2023}, here the same is extended
where a uniform mean flow is present in the ambiance to explore the propagation
properties for the Doppler effect.Comment: 15 pages, 6 figure
Bifurcation sequence of two-dimensional Taylor-Green vortex via vortex interactions: Evolution of energy spectrum
The vorticity dynamics of the two-dimensional (2D) Taylor-Green vortex (TGV)
problem is investigated in its multi-cellular configuration by solving the
incompressible Navier-Stokes equation for long time intervals using a
pseudo-spectral method. This helps follow the vorticity dynamics of periodic
free shear layer flows by solving an extremely accurate algorithm to explain
vortex interactions that lead to vortex stripping (forward cascade), merger,
and reconnection (inverse cascade) during various stages of evolution of
periodic arrangements of a large number of TGV vortical cells. This latter
aspect has been adopted so as not to be affected by the periodicity constraints
of a single periodic cell and the various imposed symmetries that attenuate
disturbance growth. The analytic solution of the TGV provides the initial
condition and the spatially accurate Fourier spectral method enables one to
track the first instability of the initial doubly periodic vortices. Despite a
plethora of studies following the primary instability to relate it with
transition to turbulence and the subsequent decay of turbulence in the
literature, the topic of bifurcation sequence for periodic TGV is rare, and
that is one of the main aims of the present research. Instead of restricting
one's attention on a single periodic TGV cell, here it is purposely reported
for multiple cells of the TGV in both directions, without invoking any
asymmetries extraneously. For such an ensemble, one can study various vortical
interactions giving rise to atypical energy spectra, a topic that has also been
seldom addressed to distinguish between successive instabilities that can upon
a conjecture, lead to transition and subsequent relaminarization, versus the
bifurcation sequences leading from one equilibrium state to subsequent ones.
The present study shows the dominance of the latter for 2D TGV at post-critical
Reynolds number
Evolution of Perturbation in Quiescent Medium
Here, the perturbation equation for a dissipative medium is derived from the
first principle from the linearized compressible Navier-Stokes equation without
Stokes's hypothesis. The dispersion relations of this generic governing
equation are obtained for one and three-dimensional perturbations, which
exhibit both the dispersive and dissipative nature of the perturbations
traveling in a dissipative medium, depending upon the length scale. We
specifically provide a theoretical cut-off wave number above which the
perturbation equation represents diffusive and dissipative nature. Such
behavior has not been reported before, as per the knowledge of the authors.Comment: 12 page 1 figure. arXiv admin note: substantial text overlap with
arXiv:2212.1379