Vorticity determination in a hydraulic jump by application of method of characteristics

Abstract

The method of characteristics for solving systems of partial differential equations coupled with jump conditions is used in analysing flow downstream of a hydraulic jump instead of the normal analytical approach adopted in Hornung [1]. It is shown that the method of characteristics together with the jump conditions can correctly be used as an alternative method to determine the mean vorticity downstream of the hydraulic jump as a function of the Froude number and height ratio. The mean vorticity does not increase from zero as a function of Froude number minus one but, however, it approaches a constant value at large Froude number. The present work extends the model of Hornung [1] to include non linear velocity profile used in calculating the torque with a view to determining the mean vorticity. The result obtained by this method generalizes that of [1].

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 239-248