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This paper mainly studied the evolution of liquid surface waves along an uneven wall. Considering the characteristic of the uneven wall changing over time, the perturbation equation for the surface waves is derived by using the small parameter perturbation method to solve the control equations under the given boundary conditions. The method of derivative expansion is used to find the solution to the equation and numerical research is then carried out for the wall shape of a simple harmonic. By studying the influence of different parameters on the wavy wall, it can be found that when the frequency of the wall is small, the wavelengths of static waves and traveling waves are close to each other, promoting the merger between the surface waves, and the surface wave amplitude is obviously increased when the wall frequency and wall depth or Re increase. By contrast of the two cases of wavy wall and uneven wall, the surface wave on uneven wall has a periodical change at the same location with the increase of time, while the surface wave on wavy wall has an almost periodic change with a longer wavelength. Although the decrease of the wall amplitude and the wall frequency both can cause surface wave amplitudes reduced, the surface waveforms are different, for the surface wave on the wavy wall can be regarded as the superposition of wavy wall waveform and surface waveform caused by uneven wall.
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Keywords:
- uneven wall /
- small parameter perturbation method /
- surface wave /
- liquid film
[1] Usha R, Uma B 2004 Int. J. Nonlin. Mech. 39 1589
[2] Yao W, Zhou Z W, Hu G H 2013 Acta Phys. Sin. 62 134701 (in Chinese) [姚祎, 周哲玮, 胡国辉 2013 62 134701]
[3] Li C X, Pei J Z, Ye X M 2013 Acta Phys. Sin. 62 214704 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 214704]
[4] Shi J S 2009 J. Eng. Thermophys-Rus. 30 1726 (in Chinese) [师晋生 2009 工程热 30 1726]
[5] Piao M R, Hu G H 2011 Chin. J. Comput. Phys. 28 843 (in Chinese) [朴明日, 胡国辉 2011 计算物理 28 843]
[6] Li C X 2013 J. Xi'an Jiaotong Univ. 47 40 (in Chinese) [李春曦 2013 西安交通大学学报 47 40]
[7] Shi J S 2013 J. Energy Power Eng. 7 899
[8] Wang Q C, Ma X H, Chen J B, Bo S S, Chen H X, Su F M 2007 J. Eng. Thermophys-Rus. 28 37 (in Chinese) [王群昌, 马学虎, 陈嘉宾, 薄守石, 陈宏霞, 苏凤民 2007 工程热 28 37]
[9] Zhang S G, Hu W X 2008 Chin. Phys. Lett. 25 4314
[10] Li Z, Hu G H, Zhou J J, Zhou Z W 2011 Acta Mech. Sinica. 43 699 (in Chinese) [李振, 胡国辉, 周继杰, 周哲玮 2011 力学学报 43 699]
[11] Matar O K, Kumar S 2007 J. Eng. Math. 57 145
[12] Matar O K, Craster R V, Kumar S 2007 Phys. Rev. E 76 056301
[13] Sisoev G M, Matar O K, Craster R V, Kumar S 2010 Chem. Eng. Sci. 65 950
[14] Eyov E, Klar A, Kadri U, Stiassine M 2013 Wave Motion. 50 929
[15] Howell P D, Robinson J, Stone H A 2013 J Fluid Mech. 732 190
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[1] Usha R, Uma B 2004 Int. J. Nonlin. Mech. 39 1589
[2] Yao W, Zhou Z W, Hu G H 2013 Acta Phys. Sin. 62 134701 (in Chinese) [姚祎, 周哲玮, 胡国辉 2013 62 134701]
[3] Li C X, Pei J Z, Ye X M 2013 Acta Phys. Sin. 62 214704 (in Chinese) [李春曦, 裴建军, 叶学民 2013 62 214704]
[4] Shi J S 2009 J. Eng. Thermophys-Rus. 30 1726 (in Chinese) [师晋生 2009 工程热 30 1726]
[5] Piao M R, Hu G H 2011 Chin. J. Comput. Phys. 28 843 (in Chinese) [朴明日, 胡国辉 2011 计算物理 28 843]
[6] Li C X 2013 J. Xi'an Jiaotong Univ. 47 40 (in Chinese) [李春曦 2013 西安交通大学学报 47 40]
[7] Shi J S 2013 J. Energy Power Eng. 7 899
[8] Wang Q C, Ma X H, Chen J B, Bo S S, Chen H X, Su F M 2007 J. Eng. Thermophys-Rus. 28 37 (in Chinese) [王群昌, 马学虎, 陈嘉宾, 薄守石, 陈宏霞, 苏凤民 2007 工程热 28 37]
[9] Zhang S G, Hu W X 2008 Chin. Phys. Lett. 25 4314
[10] Li Z, Hu G H, Zhou J J, Zhou Z W 2011 Acta Mech. Sinica. 43 699 (in Chinese) [李振, 胡国辉, 周继杰, 周哲玮 2011 力学学报 43 699]
[11] Matar O K, Kumar S 2007 J. Eng. Math. 57 145
[12] Matar O K, Craster R V, Kumar S 2007 Phys. Rev. E 76 056301
[13] Sisoev G M, Matar O K, Craster R V, Kumar S 2010 Chem. Eng. Sci. 65 950
[14] Eyov E, Klar A, Kadri U, Stiassine M 2013 Wave Motion. 50 929
[15] Howell P D, Robinson J, Stone H A 2013 J Fluid Mech. 732 190
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