Global Stability And Characteristics Of Intermittent Turbulence In Stokes Layer

Stokes layer(oscillating boundary layer)is one of the common unsteady viscous flows.The global instability problem,the laminar-turbulence transition and the characteristics of intermittent turbulence are investigated numerically.Analytic results are obtained as follows:1.The global instability of the semi-infinite Stokes layer,which generated by a flat plate oscillating synchronously in its own plane,is investigated by numerical simulation.The relation of the Floquet global instability with the instantaneous instability is discussed and detailed analysis is made for the relation of the disturbance evolution detected in the flow field with different growing stages.The difficulty of searching neutral curve for other range of wave numbers is revealed.The conception of the approximate Reynolds number is given,Thus,Neutral curve and the range of approximate Reynolds numbers are given for all streamwise wave numbers.According to the neutral curve obtained by instantaneous theory,the global instability characteristics in different range of wave numbers are as follows:For wave number belongs to 0.2 and 0.5,the solution of Floquet theory can be obtained as the same cycle as the base flow,the neutral curve can be predicted by the Floquet global instability.When wave number is less than 0.2 or belongs to 0.5 and 0.8,the cycle of disturbance displays half of the cycle of base flow,and there is no monotonic of these peaks of the disturbance.However,the approximate critical Reynolds number can be obtained where there is obvious growing or decaying disturbance in a small region near that Reynolds number.The neutral curve is obtained for the corresponding range of wave numbers.For wave number belongs to 0.8 and 1.5,the growth area is very small and the intermittent of disturbance is so strong that the results strongly rely on the initial condition and calculation method.The conception of neutral will failure.For wave number is greater than 1.5,it is indicated global stability for small disturbance.2.The process of laminar-turbulence transition of Stokes layer induced by roughness is as follows:A:In the earlier stage,when the two-dimensional disturbance(1,0)becomes quite large,the three-dimensional disturbance transforms into exponential growth from periodical evolution.Thus,more harmonics will be quickly increasing by nonlinear affection.Nevertheless,the two-dimensional disturbance still displays periodical evolution,because nonlinear affection is small this stage.B:when the harmonics grow large enough,such that the mean flow profiles is modified,the inflection point of mean flow profiles appears as a consequence,the flow field becomes so unstable that leading to the growing of more harmonics.The unstable zone of the neutral curve is enlarged quickly.The consequence is that the fluctuation energy and the fluctuation velocity gradient at the wall both reach to the maximum,leading the flow field into the transition process.C:In the latter stage of the transition,the interaction of the mean flow modification and the many harmonics,eventually lead to turbulence.3.The relations between the growth rate and the Fourier modes of spanwise harmonics are summarized as follows:The growth rate has little relation to streamwise wave number and displays linear relationship with spanwise wave number.There is selective enhancement of the transition with spanwise base wave number:when the base wave number is located in the centric position of the neutral curve,the harmonics will increase,owing to the growth rate by the integral of instantaneous growth rate in one cycle is large.This leads to transition as the amplitude of harmonics becomes large enough;when the base wave number is located in the edge of the neutral curve,the harmonics can't grow quickly,owing to the growth rate by the integral of instantaneous growth rate in one cycle is small.It will lead the flow into nonlinear equilibrium state.4.The subcritical nonlinear instability over two-dimensional roughness is studied,and response coefficient curve is given at different Reynolds numbers.It is shown that response coefficient become smaller as Reynolds number increases.Over the observation of evolution of the disturbance,it is found that,the disturbance experiences three stages as Reynolds number increases:A:The evolution displays ? as a cycle for low Reynolds numbers;B:There is variation of the peaks of the evolution,which is similar to the sub-harmonic wave as Reynolds number increases;C:As Reynolds number becomes larger,the evolution of the disturbance exhibits chaos.The critical roughness amplitude is defined in order to distinguish the transformation of stage B to stage C,the curve of subcritical instability over two-dimensional roughness is given.5.The influence on the disturbance of the factor,such as roughness amplitude,spanwise and streamwise wave number,is studied.It is shown that,transition occurs in specific condition and is related to the amplitude of two-dimensional wave.The amplitude 0.01 is considered to be necessary to triggering transition.6.The characteristics of the intermittent turbulence at different Reynolds number are as follow:Variation of skin friction coefficient with Reynolds number is given.When Reynolds number is smaller than 300,the flow is laminar.From Reynolds number of 300,the coefficient curve lift,which means the flow is transitional.It agrees with the experimental results,which shows the transition Reynolds number is around 275.Variation of velocity gradient at wall with Reynolds number is studied.It is indicated that the difference between velocity gradient at Reynolds number 300 and laminar results is small.As Reynolds number increases,the magnitude of velocity gradient increases during the acceleration phase with the profile peaking at the beginning of the deceleration phase,the peak seems to be more advanced as Reynolds number increases.While the flow is transitional,the phase position of the zero point of velocity gradient at wall doesn't change with Reynolds number,but is more delay than laminar condition.The near-wall velocity profile is described by the steady state relation of linear law,but doesn't follow the logarithmic region at most phases.When Reynolds number is relatively large,such as R>400,the velocity profile agrees well with the logarithmic region at few phases.It can be attributed to the strong non-equilibrium behavior of the intermittent turbulence.As the flow accelerates,the magnitude of kinetic energy and Reynolds shear stress increases and the peak is close to the wall,as Reynolds number increases,the peak displays closer;as the flow decelerates,the kinetic energy dissipate and Reynolds shear stress decreases,meanwhile,the peak of Reynolds shear stress gradually moves away from the wall.The streamwise vortexes is found to exist near the wall,it shows less and weak vortexes during the acceleration phase,more and stronger vortexes produces during the deceleration phase.