Evolution Of Finite-amplitude Disturbances Research Articles

Effect of purely elastic flow instability on molecular conformation and drag

Linear stability analysis has shown that viscoelastic creeping flow of an Oldroyd-B liquid through a sinusoidal channel is unstable to stationary, wall-localized and short wavelength perturbations [B. Sadanandan, R. Sureshkumar, Global linear stability analysis of non-separated viscoelastic flow through a periodically constricted channel, J. Non-Newtonian Fluid Mech. 122 (2004) 55]. In this work, time-dependent simulations are performed to determine the nonlinear evolution of finite amplitude disturbances in the post-critical flow regime. It is shown that a nonlinear transition, which is facilitated by a supercritical pitchfork bifurcation, establishes a finite amplitude state (FAS) in which the average polymer stretch is highly modulated. The maximum normal stress, observed at the channel nip, can increase by up to approximately 100% when the Weissenberg number, defined as the ratio of the fluid relaxation time to an inverse characteristic shear rate, is increased by only 10% beyond its critical value. This is attributed to the amplification of configurational perturbations by the base flow shear rate, which attains its maximum at the channel nip. The effect of finite chain extensibility on the critical condition and nonlinear instability is investigated using the FENE-CR model. The stabilizing effect of finite extensibility can be expressed through a renormalization of the Weissenberg number by accounting for the screening effect of the nonlinear force law on the transmission of configurational perturbations to polymeric stress. The principal features of the FAS are qualitatively model-independent. The FAS exhibits a small, but numerically perceptible increase in the friction factor as compared to the base flow. The implication of the findings on the experimentally observed flow resistance enhancement phenomenon in viscoelastic creeping flows through converging/diverging geometries is discussed.

Nonlinear stability analysis of viscoelastic Taylor–Couette flow in the presence of viscous heating

Recently, based on a linear stability analysis we demonstrated the existence of a new thermoelastic mode of instability in the viscoelastic Taylor–Couette flow [Al-Mubaiyedh et al., Phys. Fluids 11, 3217 (1999); J. Rheol. 44, 1121 (2000)]. In this work, we use direct time-dependent simulations to examine the nonlinear evolution of finite amplitude disturbances arising as a result of this new mode of instability in the postcritical regime of purely elastic (i.e., Re=0), nonisothermal Taylor–Couette flow. Based on these simulations, it is shown that over a wide range of parameter space that includes the experimental conditions of White and Muller [Phys. Rev. Lett. 84, 5130 (2000)], the primary bifurcation is supercritical and leads to a stationary and axisymmetric toroidal flow pattern. Moreover, the onset time associated with the evolution of finite amplitude disturbances to the final state is comparable to the thermal diffusion time. These simulations are consistent with the experimental findings.

On the evolution of finite-amplitude disturbance to the barotropic and baroclinic quasigeostrophic flows

Some new results on the evolution of finite-amplitude disturbances to the nonlinearly stable and unstable quasigeostrophic flows are presented. Both barotropic and multilayer baroclinic problems are investigated. The upper (lower) bounds on the energy and potential enstrophy of disturbances to the nonlinearly stable(unstable) basic flows are established.

The wavefront shape, position, and evolution of a great solitary wave of translation

Doppler radar mapped the evolution of a pair of atmospheric solitary waves emanating from a thunderstorm complex. The 100-km-long curved wavefront and position of these few-kilometer-wide waves are hypothesized to be a result of an amplitude-dependent wave speed. The observed unfolding is compared with a solution of the nonlinear integro-differential equation governing the evolution of finite amplitude disturbances in stratified media.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hetonic Explosions: The Breakup and Spread of Warm Pools as Explained by Baroclinic Point Vortices

As an alternative to small amplitude continuous theories we study the disintegration of warm pools of fluid on a rotating earth using clouds of baroclinic point vortices, or hetons. The equations describing the motion of the hetons are relatively simple ordinary differential equations whose numerical integration makes it possible to physically interpret the temporal evolution of finite amplitude disturbances. Using experience with small numbers of hetons as a guide, a heuristic model is proposed. This predicts that the number of baroclinic vortices forming at the rim of a circular warm pool is given by the radius of the pool divided by 1.27 times the Rossby radius, while these vortices should expand outward at a rate given by 1.65 times the Rossby radius times the vorticity density of the pool. The first prediction is in agreement with previous laboratory experiments while the second has not previously been reported.