Session Q04: Flow Instability: General II

Numerical investigation of stratified anabatic flows in idealized valleys

Due to the diurnal cycle of heating and cooling, the atmospheric boundary layer in areas of complex terrain is dominated by downslope, or katabatic, flows during the evening cooling, and upslope, or anabatic, flows during the morning heating. In valleys, katabatic flows during the evening lead to the formation of a stably stratified layer at the base of the valley, whereas upslope flows in the morning lead to the destruction of the stable stratification. This study investigates the dynamics of anabatic flows in a stably stratified idealized valley through direct numerical simulations (DNS). We establish a novel set of dimensionless parameters controlling the dynamics of stratified valley flows. We identify new flow regimes within the valley, including regimes in which the symmetry of the problem breaks down and asymmetric flow profiles emerge. We also identify unique three-dimensional instabilities as functions of the dimensionless parameter space.   

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

The analysis of time-dependent flows is notoriously challenging for linear stability methods. The Optimally Time-Dependent (OTD) modes is a recent linear framework to construct an orthonormal basis of the instantaneously most unstable directions of the tangent space. The resulting subspace can be used to extract information about the time-asymptotic and transient stability of the trajectory. We analyse the corresponding instantaneous OTD modes for pulsating Poiseuille flow, an archetypal non-autonomous fluid system, to explore the potential of the method for the transient linear stability analysis of general time-dependent flows. The time-asymptotic results of Floquet theory are confirmed by computing the Finite-Time Lyapunov exponents for a large parameter range. The comparison between the OTD modes in the limit cycle and the eigenmodes of the Orr-Sommerfeld operator for Poiseuille flow reveals the dominant intracyclic instability mechanism corresponding to modulated Tollmien-Schlichting waves as well as the transient disappearance of these structures during part of the cycle. The full non-normal growth potential of the OTD subspace is found to be nearly identical to that of Poiseuille flow. The OTD spectrum exhibits subharmonic eigenvalue orbits that are due to the presence of exceptional points in the instantaneous Orr-Sommerfeld spectrum.   

Dynamical Collapse of Interacting Two-Dimensional Buoyant Plumes

Buoyant plumes often exhibit pulsatile motion with a "puffing" frequency that depends on the Richardson number. This behavior has been well documented in both non-reacting plumes and pool fires. In this study, we investigate how this dynamical behavior is affected in two dimensions by the introduction of an adjacent plume. We expect that, at large spacing, the puffing frequency should be independent of the adjacent plume and, at small spacing, the frequency should approach the same frequency as if the two plumes were combined into one. The dynamical behavior between these two limits, however, depends on the competing effects of entrainment and vortex interaction along the inner shear layers. To investigate this regime, two-dimensional high-fidelity numerical simulations using adaptive mesh refinement are used to model the isothermal injection of helium into air from two adjacent plumes. Our results show that, as the spacing between the two plumes decreases, the plume interactions cause the puffing frequency to first increase, before decreasing to the expected combined frequency, comparable to reacting plume data. Further analysis is performed to extract phase information and to examine the collapse of the data using non-dimensional numbers.   

Helical instability in pulsatile and oscillatory pipe flows

Pulsatile pipe flows in the presence of geometric distortions (e.g. bent, constriction) have recently been show to exhibit a nonlinear instability consisting of helical vortices [1]. The instability appears during the deceleration phase, breaks down into turbulence, and eventually returns to the laminar state when the flow accelerates. We track the instability in Reynolds number-Womersley number parameter space, and towards purely oscillatory flows, i.e. flows without mean component. We find that intermediate values of pulsation amplitude 1~<A~<1000 have a stabilizing effect, i.e. the instability threshold Re_δ increases with increasing A. Else Re_δ remains nearly constant.  Here, Re_δ is the Reynolds number based on Stokes layer thickness and A=U_o/U_m; U_o and U_m are oscillatory and mean components of the flow speed, respectively. Increasing Womersley number (i.e. pulsation frequency) on the other hand the instability threshold moves to lower Re_δ. Moreover, we find that streamwise location of the instability in the pipe shifts towards the distortion site (bent section in our case) with increasing Womersley number.  

                       

 

Sensitivity of merging and mixing to initial perturbations in Holmboe instabilities

The effects of different initial perturbations on the evolution of Holmboe instabilities in stratified shear flows have been investigated through direct numerical simulations. The phase difference and amplitude of the primary and subharmonic Holmboe modes determine the development of Holmboe instabilities, which, in turn, influence diapycnal mixing in stratified flows. The amplitude has a more significant effect on the merging of primary Holmboe modes compared to the initial phase difference. For a given amplitude of the primary perturbation, a larger amplitude of subharmonic perturbation results in an earlier merging event. In three-dimensional simulations, the subharmonic mode is incited if the subharmonic perturbation is imposed, increasing the amplitude of Holmboe waves by a factor of 2. Although this Holmboe instability grows slower initially, the growing period is longer and the accumulated amount of mixing is also larger.   

Longitudinal instability and turbulent transition observed in Taylor-Couette flow

The characterization of time varying flows within the Taylor Couette system has received some attention to date, for example with modulations of cylinder rotation, as well with impulsive starts or stops. Here we briefly present observations where the outer cylinder motion is unsteady, undergoing both positive and negative acceleration, while the inner cylinder remains at rest. Longitudinal streaks (i.e. along the rotation axis) develop during the period of deceleration. These waves become increasingly corrugated before merging with the developed turbulence emanating from both end-cap boundaries. The flow altogether then further relaxes to a wavy vortex state. Given the narrow gap width and velocimetry measurements, these longitudinal modes likely represent a boundary layer instability. Similar structures were observed in passing by Coles (1965), but they remain to be characterized in the context of Taylor Couette flow.  

    

Analysis of a Non-Equilibrium Vortex Pair as Aircraft Trailing Vortices

Shortly after the roll-up evolution of the vortex sheet behind the wings of an aircraft, a coherent counter-rotating vortex pair emerges. Presence of this vortex pair in the downstream of an aircraft, creates unsafe conditions for other aircraft. This study uses non-equilibrium pressure theory to develop an accurate model describing the physical behavior of the vortex pair created by an aircraft in the early to mid-field vortex regime.  An isolated aircraft vortex is first modeled and compared using several vortex models. Eddy viscosity to kinematic viscosity ratio correlation for aircraft trailing vortices has been introduced to satisfy the turbulent energy embedded in the vortex cores. Subsequently, the counter-rotating vortex pair is considered, and detailed derivation of the non-equilibrium vortex pair model is introduced. Existence of a vortex pair with non-equilibrium cores embedded in an inviscid fluid medium is discussed. Vortex pairs are characterized by an accompanying isolating “atmosphere”, commonly known as “Kelvin oval”. When aircraft vortex pair are close to merger or the vortex cores increasingly dilate, the non-equilibrium vortex pair model predicts instability. Non-equilibrium oval size changes drastically from the potential oval size.   

An Experimental Study on Vortex-Induced Vibrations of a Cylinder in Shear-Thinning Flow

Traditional vortex-induced vibration (VIV) experiments subject a flexible or flexibly-mounted cylinder to Newtonian flow. In this work, we present experimental results on VIV of a one-degree-of-freedom cylinder placed in shear-thinning flows. These experiments were conducted in a water channel using a cylinder with a diameter of 2 mm. In each series of experiments, we kept the characteristic Reynolds number, defined based on the characteristic viscosity using the Carreau model, constant and varied the reduced velocity. For experiments at constant characteristic Reynolds numbers, we observed a lock-in region in a reduced velocity range of approximately 6 to 9 with a maximum amplitude of oscillations of approximately 0.3D. The amplitude of oscillations and the width of the lock-in region decreased with decreasing characteristic Reynolds number and at characteristic Reynolds numbers lower than 18, VIV was completely suppressed.   

Three-dimensional, short-wavelength instabilities in idealized models of aircraft wake vortices

Aircraft wakes are known to comprise of counter-rotating vortex pairs, and their instability characteristics have significant implications on aircraft performance and safety. Three-dimensional short-wavelength instabilities on idealized aircraft wake vortex pair are investigated using a local stability analysis. Two strategies are used to generate the base flow; the first involves approximating the base flow as a combination of two counter rotating Lamb-Oseen vortices and in the second strategy, the base flow is generated by performing a 2D numerical simulation. The vortex pair is found to be susceptible to elliptic and tripolar instabilities, and the corresponding growth rates are calculated for a wide range of vortex core size to vortex separation distance ratios. The local stability results are compared against relevant previous studies based on both local and global stability analyses. Finally, to represent aircraft wake vortices more faithfully, an axial flow is added to the aforementioned 2D base flow, and the effects of the axial flow are systematically investigated.