Nonmodal energy growth and optimal perturbations in compressible plane Couette flow

Nonmodal transient growth studies and estimation of optimal perturbations have been made for the compressible plane Couette flow with three-dimensional disturbances. The maximum amplification of perturbation energy over time, $G_{\max}$, is found to increase with increasing Reynolds number ${\it Re}$, but decreases with increasing Mach number $M$. More specifically, the optimal energy amplification $G_{\rm opt}$ (the supremum of $G_{\max}$ over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as $M$ increases. The corresponding optimal streamwise wavenumber, $\alpha_{\rm opt}$, is non-zero at M=0, increases with increasing $M$, reaching a maximum for some value of $M$ and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers, the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law $G(t/{\it Re}) \sim {\it Re}^2$, the reasons for which are shown to be tied to the dominance of some terms in the linear stability operator. Based on a detailed nonmodal energy analysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid {\it algebraic} instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow ($\dot{\mathcal E}_1$) in the same limit

Sea Control in the Arctic: A Soviet Perspective

In the Punic Wars, Hannibal surprised and strategically dislocated the Roman legions by attacking them with his war elephants as he made his way across what had been considered to be an insurmountable geographical barrier, the Alps. In a similar fashion, recent developments in Soviet Arctic mobility and logistics give the Soviets the capability to inflict strategic surprise on the West. Although there is no evidence that the Soviets intend to implement the strategic plans or concepts of operations discussed here, they do possess substantial capabilities in the Arctic which could threaten the United States and Canada. U.S. and Canadian strategists must consider these capabilities in determining our territorial defense plans and our Arctic defense forces

Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space

This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's procedure (1938) to the initial-value problem allowed us to find the region of the wavenumber-Reynolds number map where the enstrophy of any initial disturbance cannot grow. This region is wider than the kinetic energy's one. We also show that the parameters space is split in two regions with clearly distinct propagation and dispersion properties

Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow

Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow with {\it stratified} viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the critical Reynolds number ($Re$) is significantly smaller for the uniform shear flow than its non-uniform shear counterpart. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for ``mode I'' instability, whereas it occurs in the bulk of the flow domain for ``mode II''. For the non-modal analysis, it is shown that the maximum amplification of perturbation energy, $G_{\max}$, is significantly larger for the uniform shear case compared to its non-uniform counterpart. For $\alpha=0$, the linear stability operator can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the $Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim {\it Re}^2$. A reduced inviscid model has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, it is shown that the {\it viscosity-stratification} of the underlying mean flow would lead to a delayed transition in compressible Couette flow

A combined molecular‐beam epitaxy and scanning tunneling microscopy system

A combined molecular‐beam epitaxy and scanning tunneling microscopy system has been constructed. The design has been optimized for the study of III‐V semiconductors with the goal of examining the surface with both in situ scanning tunneling microscopy (STM) and reflection high‐energy electron diffraction (RHEED). Using this system, it is possible to quench the growth and produce real‐space images of the surface as it appeared during deposition. Measurements obtained with both RHEED and STM are presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70399/2/RSINAK-62-6-1400-1.pd

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

Making space for embedded knowledge in global mental health: a role for social work

The ‘Global Mental Health’ (GMH) movement, an influential driver of transnational knowledge transfer in the field of mental health, advocates evidence-based strategies to ‘scale up’ services in low- and middle-income countries. As with debates on global and local frameworks for social work, there are concerns about marginalisation of knowledge that does not neatly fit the GMH discourse. This article analyses the professional and disciplinary structures that shape knowledge transfer in GMH and the implications for social work's engagement with the movement. Analysis of key documents and secondary literature identifies three key issues for GMH: its potentially negative impact on ‘local’ knowledge production; the challenges of accounting for culture and context; and the selective forms of evidence that are ‘allowed’ to contribute to GMH. Finding ways to encompass more ‘situated’ perspectives could reshape GMH in accord with its aspirations for participation by a wider range of stakeholders. Social work's values-based commitment to rights and empowerment, emphasis on embedded knowledge emerging from close links with practice, and theoretical engagement with social, cultural and political context, enable the profession to contribute significantly to this task. Such engagement would bring improvements in care for those suffering from mental health disorders, their families and communities

Growth mode evolution during homoepitaxy of GaAs (001)

Scanning tunneling microscopy studies have been performed on GaAs homoepitaxial films grown by molecular‐beam epitaxy. After an initial transient regime, indicated by reflection high‐energy electron diffraction oscillations, the system evolves to a dynamical steady state. This state is characterized by a constant step density and as such the growth mode can be termed generalized step flow.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70664/2/APPLAB-64-4-484-1.pd

Probing Electroweak Top Quark Couplings at Hadron Colliders

We consider QCD t\bar{t}\gamma and t\bar{t}Z production at hadron colliders as a tool to measure the tt\gamma and ttZ couplings. At the Tevatron it may be possible to perform a first, albeit not very precise, test of the tt\gamma vector and axial vector couplings in t\bar{t}\gamma production, provided that more than 5 fb^{-1} of integrated luminosity are accumulated. The t\bar{t}Z cross section at the Tevatron is too small to be observable. At the CERN Large Hadron Collider (LHC) it will be possible to probe the tt\gamma couplings at the few percent level, which approaches the precision which one hopes to achieve with a next-generation e^+e^- linear collider. The LHC's capability of associated QCD t\bar{t}V (V=\gamma, Z) production has the added advantage that the tt\gamma and ttZ couplings are not entangled. For an integrated luminosity of 300 fb^{-1}, the ttZ vector (axial vector) coupling can be determined with an uncertainty of 45-85% (15-20%), whereas the dimension-five dipole form factors can be measured with a precision of 50-55%. The achievable limits improve typically by a factor of 2-3 for the luminosity-upgraded (3 ab^{-1}) LHC.Comment: Revtex3, 30 pages, 9 Figures, 6 Table

A Versatile, Portable Intravital Microscopy Platform for Studying Beta-cell Biology In Vivo

The pancreatic islet is a complex micro-organ containing numerous cell types, including endocrine, immune, and endothelial cells. The communication of these systems is lost upon isolation of the islets, and therefore the pathogenesis of diabetes can only be fully understood by studying this organized, multicellular environment in vivo. We have developed several adaptable tools to create a versatile platform to interrogate β-cell function in vivo. Specifically, we developed β-cell-selective virally-encoded fluorescent protein biosensors that can be rapidly and easily introduced into any mouse. We then coupled the use of these biosensors with intravital microscopy, a powerful tool that can be used to collect cellular and subcellular data from living tissues. Together, these approaches allowed the observation of in vivo β-cell-specific ROS dynamics using the Grx1-roGFP2 biosensor and calcium signaling using the GcAMP6s biosensor. Next, we utilized abdominal imaging windows (AIW) to extend our in vivo observations beyond single-point terminal measurements to collect longitudinal physiological and biosensor data through repeated imaging of the same mice over time. This platform represents a significant advancement in our ability to study β-cell structure and signaling in vivo, and its portability for use in virtually any mouse model will enable meaningful studies of β-cell physiology in the endogenous islet niche