Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formation and evolution of roll waves in a shallow free surface flow of
  a power-law fluid down an inclined plane   A laminar flow of a thin layer of mud down an inclined plane under the action
of gravity is considered. The instability of a film flow and the formation of
finite amplitude waves are studied in the framework of both two-dimensional
governing equations of a power-law fluid and its depth-averaged hyperbolic
simplification. Conditions of roll waves existence for these models are
formulated in terms of Whitham criterion. Numerical calculations of the free
surface evolution and the roll waves development are performed. It is shown
that the roll waves amplitude obtained by the 2D equations is slightly larger
than for the 1D model. Moreover, for certain flow parameters, small
perturbations of the basic solution grow for the 2D equations and decay for the
depth-averaged model. A two-parameter class of exact piecewise-smooth solutions
of the 1D model is obtained and a comparison with a numerical solution is made.
In the region of these parameters, diagrams of the roll waves existence are
constructed.

0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org