TY - JOUR

T1 - Nonlinear waves in a rivulet falling down a vertical plate

AU - Aktershev, S.P.

AU - Alekseenko, S.V.

N1 - Acknowledgment: Research was supported by the grant from the Russian Science Foundation No. 23-29-00254, https://rscf.ru/project/23-29-00254.

PY - 2023/11

Y1 - 2023/11

N2 - Nonlinear waves in a rectilinear rivulet flowing down a vertical plate are studied based on the developed theoretical model. The model equations are derived by the weighted residual method through projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. Stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. Nonlinear wave regimes of a rivulet flow are numerically studied within the framework of two different problems, namely, the problem of stationary traveling waves with a given wavelength and the problem of spatial development of forced waves with a given frequency. Characteristics of nonlinear quasi-two-dimensional stationary traveling waves are obtained, and spatial development of forced waves is studied. Waves of various families are identified. It is shown that in a certain narrow range of excitation frequency, there are no stationary traveling waves, but a pulsating regime of flow occurs.

AB - Nonlinear waves in a rectilinear rivulet flowing down a vertical plate are studied based on the developed theoretical model. The model equations are derived by the weighted residual method through projecting the Navier–Stokes equations onto the constructed system of basic orthogonal polynomials. Stability of the rivulet flow is analyzed and dispersion dependences for linear waves are obtained. Nonlinear wave regimes of a rivulet flow are numerically studied within the framework of two different problems, namely, the problem of stationary traveling waves with a given wavelength and the problem of spatial development of forced waves with a given frequency. Characteristics of nonlinear quasi-two-dimensional stationary traveling waves are obtained, and spatial development of forced waves is studied. Waves of various families are identified. It is shown that in a certain narrow range of excitation frequency, there are no stationary traveling waves, but a pulsating regime of flow occurs.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85166616188&origin=inward&txGid=ddaeee90f9b6f38d570a569b08e67ce7

UR - https://www.mendeley.com/catalogue/0ab3408f-9f5c-354a-a6ef-0d1ee0e80434/

U2 - 10.1016/j.ijnonlinmec.2023.104479

DO - 10.1016/j.ijnonlinmec.2023.104479

M3 - Article

VL - 156

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

M1 - 104479

ER -