Disk Boundary Layer Research Articles

Innovative Turbine Stator Well Design Using a Kriging-Assisted Optimization Method

At present, it is a common practice to expose engine components to main annulus air temperatures exceeding the thermal material limit in order to increase the overall engine performance and to minimize the engine specific fuel consumption. To prevent overheating of the materials and thus the reduction of component life, an internal flow system is required to cool and protect the critical engine parts. Previous studies have shown that the insertion of a deflector plate in turbine cavities leads to a more effective use of reduced cooling air, since the coolant is fed more effectively into the disk boundary layer. This paper describes a flexible design parameterization of an engine representative turbine stator well geometry with stationary deflector plate and its implementation within an automated design optimization process using automatic meshing and steady-state computational fluid dynamics (CFD). Special attention and effort is turned to the flexibility of the parameterization method in order to reduce the number of design variables to a minimum on the one hand, but increasing the design space flexibility and generality on the other. Finally, the optimized design is evaluated using a previously validated conjugate heat transfer method (by coupling a finite element analysis (FEA) to CFD) and compared against both the nonoptimized deflector design and a reference baseline design without a deflector plate.

QPO frequency derivative–frequency correlation indicates non-Keplerian boundary layer with a maximum in rotation rate

Abstract The correlation between the frequency and the absolute value of the frequency derivative of the kilohertz quasi-periodic oscillations (QPOs) observed for the first time from 4U 1636-53 is a simple consequence and indicator of the existence of a non-Keplerian rotation rate in the accretion disc boundary layer. This Letter interprets the observed correlation, showing that the observations provide strong evidence in support of the fundamental assumption of disc accretion models around slow rotators, that the boundary layer matches the Keplerian disc to the neutron star magnetosphere.

RX GEMINORUM: PHOTOMETRIC SOLUTIONS, (NEARLY UNIFORM) GAINER ROTATION, DONOR RADIAL VELOCITY SOLUTION, NON-LTE ACCRETION DISK MODELS OF HαEMISSION PROFILES, AND SECULAR LIGHT CURVE CHANGES IN THE 20TH CENTURY

We obtained full-orbit Iybvu intermediate-band photometry and CCD spectroscopy of the long-period Algol eclipsing binary RX Geminorum. Photometric solutions using the Wilson–Devinney code give a gainer rotation (hotter, mass-accreting component) about 15 times the synchronous rate. We describe a simple technique to detect departures from uniform rotation of the hotter component. These binaries radiate double-peaked Hα emission from a low-mass accretion disk around the gainer. We used an approximate non-LTE disk code to predict models in fair agreement with observations, except in the far wings of the emission profile, where the star–inner disk boundary layer emits extra radiation. Variations in Hα emission derive from modulations in the transfer rate. A study of times of minima during the 20th century suggests that a perturbing third body is present near RX Gem.

A Note on the Correspondence Between Certain Nanofluid Flows and Standard Fluid Flows

This note introduces a rescaling approach that greatly simplifies the evaluation of flow and physical parameters such as skin friction and heat transfer rate in recent single phase nanofluids research for which the nanofluids begin to create a non-Newtonian fluid after 5–6% volumetric concentration of nanoparticles. Much of the task is hence reduced to a particular case for a chosen fluid. By the help of specified transformations, the nanofluid results can be obtained from known properties of regular fluid. Such rescaling is shown to work well for the rotating disk boundary layer flow in nanofluid, and thus sheds light upon the future studies of this kind when further physical mechanism are taken into account.

The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer

A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.

Angular Momentum Transport in Accretion Disk Boundary Layers Around Weakly Magnetized Stars

The standard model for turbulent shear viscosity in accretion disks is based on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. This implies that the turbulent stress must be negative and thus transport angular momentum inwards, in the boundary layer where the accretion disk meets the surface of a weakly magnetized star. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability (MRI) is inefficient in disk regions where, as expected in boundary layers, the angular frequency increases with radius. Motivated by the need of a deeper understanding of the behavior of an MHD fluid in a differentially rotating background that deviates from a Keplerian profile, we study the dynamics of MHD waves in configurations that are stable to the standard MRI. Employing the shearing-sheet framework, we show that transient amplification of shearing MHD waves can generate magnetic energy without leading to a substantial generation of hydromagnetic stresses. While these results are in agreement with numerical simulations, they emphasize the need to better understand the mechanism for angular momentum transport in the inner disk regions on more solid grounds.

On magnetohydrodynamic turbulence and angular momentum transport in accretion disk boundary layers

AbstractThe physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations and suggests that the detailed structure of turbulent MHD boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.

ON HYDROMAGNETIC STRESSES IN ACCRETION DISK BOUNDARY LAYERS

Detailed calculations of the physical structure of accretion disk boundary layers, and thus their inferred observational properties, rely on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability (MRI) is inefficient in disk regions where, as expected in boundary layers, the angular frequency increases with radius. In order to shed light into physically viable mechanisms for angular momentum transport in this inner disk region, we examine the generation of hydromagnetic stresses and energy density in differentially rotating backgrounds with angular frequencies that increase outward in the shearing-sheet framework. We isolate the modes that are unrelated to the standard MRI and provide analytic solutions for the long-term evolution of the resulting shearing MHD waves. We show that, although the energy density of these waves can be amplified significantly, their associated stresses oscillate around zero, rendering them an inefficient mechanism to transport significant angular momentum (inward). These findings are consistent with the results obtained in numerical simulations of MHD accretion disk boundary layers and challenge the standard assumption of efficient angular momentum transport in the inner disk regions. This suggests that the detailed structure of turbulent MHD accretion disk boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.

Response to rotating forcing of the von-Kármán disk boundary layer

In the present experimental investigation of the three-dimensional boundary layer due to a disk rotating in otherwise still air, the aim is to study the response to a radially localized perturbation applied with a prescribed relative frequency with respect to the disk.The response to localized rotating forcing is measured with a hot-wire probe. The rotation rate of the forcing element is controlled independently of the disk rotation rate, and the dynamics of the spatial response is studied as a function of the ratio between the two rotation rates. The theoretically expected disturbance trajectories are derived from an instability analysis based on the exact local dispersion relations computed from the complete linearized Navier-Stokes equations. Theoretical predictions and experimental measurements are shown to be in good agreement.

X-RAY AND ULTRAVIOLET EMISSION FROM THE RECURRENT NOVA RS OPHIUCHI IN QUIESCENCE: SIGNATURES OF ACCRETION AND SHOCKED GAS

RS Ophiuchi is a recurrent nova system that experiences outbursts every ~20 years, implying accretion at a high rate onto a massive white dwarf. However, previous X-ray observations of the system in quiescence have detected only faint emission that is difficult to reconcile with the high accretion rate predicted by nova theory for such frequent outbursts. Here, we use new Chandra and XMM-Newton observations obtained 537 and 744 days after the 2006 outburst to constrain both the accretion rate onto the white dwarf and the properties of the nova ejecta at these times. We detect low level UV variability with the XMM-Newton Optical Monitor on day 744 that is consistent with accretion disk flickering, and use this to place a lower limit on the accretion rate. The X-ray spectra in both observations are well described by a two component thermal plasma model. The first component originates in the nova shell, which can emit X-rays for up to a decade after the outburst. The other component likely arises in the accretion disk boundary layer, and can be equally well fit by a single temperature plasma or a cooling flow model. Although the flux of the single temperature model implies an accretion rate that is 40 times lower than theoretical predictions for RS Oph, the best fit cooling flow model implies Mdot < 1.2x10^-8 M_sol/yr 537 days after the outburst, which is within a factor of 2 of the theoretical accretion rate required to power an outburst every 20 years. Furthermore, we place an upper limit on the accretion rate through an optically thick region of the boundary layer of 2.0x10^-8 M_sol/yr. Thus, the X-ray emission in quiescence is consistent with the accretion rate expectations of nova theory. Finally, we discuss the possible origins of the low temperature associated with the accretion component, which is a factor of 10 lower than in T CrB, an otherwise similar recurrent nova.

Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform vertical magnetic field

The present paper is concerned with the analytical solution of the boundary layer flow of a steady, laminar, incompressible, viscous and electrically conducting fluid due to a rotating disk. Within this purpose, the recently popular homotopy analysis method is employed, making it possible to obtain explicitly analytic expressions for Lighthill’s coordinate straining parameter c in terms of the magnetic field parameter m, first used in Ackroyd (J Eng Phys 12:207–220, 1978) for the nonmagnetic case and recently studied to get the small perturbation and large asymptotic representations in Ariel (Z Angew Math Mech 82:235–246, 2001) for the magnetic case. Making use of the outlined approach, the mean velocity profiles corresponding to a wide range of magnetic strength parameters are computed, and also explicit formulas are derived for several quantities of physical significance.

Origins of the H, He i and Ca ii line emission in classical T Tauri stars

We perform local excitation calculations to obtain line opacities and emissivity ratios, and compare them with observed properties of H, He i, O i, Ca ii and Na i lines to determine the requisite conditions of density, temperature and photon ionization rate. We find that ultraviolet photoionization is the most probable excitation mechanism for generating the He iλ10830 opacities that produce all the associated absorption features. We also calculate the specific line flux at an observed velocity of vobs=±150 km s−1 for both radial wind and infall models. All the model results, together with observed correlations between absorption and emission features and between narrow and broad emission components, are used to deduce the origins of the strong H, He i and Ca ii broad line emission. We conclude that the first two arise primarily in a radial outflow that is highly clumpy. The bulk of the wind volume is filled by gas at a density ∼109 cm−3 and optically thick to He iλ10830 and Hα, but optically thin to He iλ5876, Paγ and the Ca ii infrared triplet. The optically thick He iλ5876 emission occurs mostly in regions of density ≥1011 cm−3 and temperature ≥1.5 × 104 K, while the optically thick Hα and Paγ emission occurs mostly in regions of density around 1011 cm−3 and temperature between 8750 and 1.25 × 104 K. In producing the observed line fluxes at a given vobs, the covering factor of these emission clumps is sufficiently small to not incur significant absorption of the stellar and veiling continua in either He i or H lines. The strong Ca ii broad line emission likely arises in both the magnetospheric accretion flow and the disc boundary layer where the gases dissipate part of their rotational energies before infalling along magnetic field lines. The needed density and temperature are ∼1012 cm−3 and ≤7500 K, respectively.

Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection

The present paper is devoted to the study of derivation of analytical expressions for the solution of steady, laminar, incompressible, viscous fluid of the boundary layer flow due to a rotating disk in the presence of a uniform suction or injection. Within this aim, the recently popular homotopy analysis method is employed to obtain the exact solutions, in contrast to the full numerically or perturbative/asymptotically evaluated ones in the literature. It is shown here that such a technique is extremely powerful in gaining solutions in terms of the purely exponential and decaying functions if the proposed approach introduced here is carefully pursued. The homotopy technique makes it possible to obtain explicitly analytic expressions for Lighthill's coordinate straining parameter c in terms of the suction/blowing parameter s, first used in [1]. Using the outlined approach, not only the mean velocity profiles corresponding to a wide range suction/blowing parameter are computed non-iteratively and analytically, but also explicit formulas are derived for some quantities of physical significance. The notion of optimal convergence control parameter is made use to accelerate the rate of convergence of the homotopy series, whose convergence is later proven via a convergence theorem.

Crossflow instability of finite Bödewadt flows: Transients and spiral waves

The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primarily present in the boundary layers on the rotating top and sidewalls and the stationary bottom wall, with a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows on the top and bottom. The top end wall boundary layer has a profile that very closely matches the von Kármán solution for a rotating disk boundary layer; it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer on the stationary bottom end wall has a profile that agrees with the Bödewadt solution for a stationary disk with an ambient flow in solid-body rotation. This boundary layer is not robust, suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most inflectional. In the absence of any external forcing, the circular waves are transitory, but low amplitude forcing can sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing.

Primary instability mechanisms on the magnetohydrodynamic boundary layer flow over a rotating disk subject to a uniform radial flow

This paper is devoted to the investigation of three primary linear instability mechanisms due to the resonating disturbance waves present in the three-dimensional incompressible viscous/inviscid rotating disk boundary layer flow, extending our earlier still outer fluid work [M. Turkyilmazoglu, “Resonance instabilities on the boundary layer flow over a rotating-disk under the influence of a uniform magnetic field,” J. Eng. Math. 59, 337 (2007)] to a uniform nonzero radial flow. A spatiotemporal linear stability analysis is conducted to search for the influences of physical parameters on the possible important mechanisms of resonances leading to, respectively, the absolute instability, the direct spatial instability, and the direct temporal instability. The radial flow is shown to act in the way of stabilizing all the possible mechanisms considered, more pronouncedly as the magnetic field gets strengthened. The onset of absolute instability and convective temporal instability is found to be more sensitive to the variations in the radial flow than is the onset of convective direct spatial instability. Although a considerable delay of the onset of absolute instability as well as temporal instability can be achieved by increasing the magnitude of the radial flow, the direct spatial resonance instability mechanism persists to occur for low Reynolds numbers, while the flow is still in the laminar regime, which is expected to trigger nonlinearity just prior to transition to turbulence.

APEX-CHAMP+high-JCO observations of low-mass young stellar objects

AIMS Our aim is to characterize the size, mass, density and temperature profiles of the protostellar envelope of HH~46 IRS 1 and its surrounding cloud material as well as the effect the outflow has on its environment.METHODS The CHAMP+ and LABOCA arrays on the APEX telescope, combined with lower frequency line receivers, are used to obtain a large continuum map and smaller heterodyne maps in various isotopologues of CO and HCO+. The high-J lines of CO (6--5 and 7--6) and its isotopologues together with [C I] 2--1, observed with CHAMP+, are used to probe the warm molecular gas in the inner few hundred AU and in the outflowing gas. The data are interpreted with continuum and line radiative transfer models. RESULTS Broad outflow wings are seen in CO low- and high-J lines at several positions, constraining the gas temperatures to a constant value of ~100 K along the red outflow axis and to ~60 K for the blue outflow. The derived outflow mass is of order 0.4--0.8 M_sol, significantly higher than previously found. The bulk of the strong high-J CO line emission has a surprisingly narrow width, however, even at outflow positions. These lines cannot be fit by a passively heated model of the HH 46 IRS envelope. We propose that it originates from photon heating of the outflow cavity walls by ultraviolet photons originating in outflow shocks and the accretion disk boundary layers. At the position of the bow shock itself, the UV photons are energetic enough to dissociate CO. The envelope mass of ~5 M_sol is strongly concentrated towards HH 46 IRS with a density power law of -1.8.

Interface modes and their instabilities in accretion disc boundary layers

We study global non-axisymmetric oscillation modes trapped near the inner boundary of an accretion disc. Observations indicate that some of the quasi-periodic oscillations (QPOs) observed in the luminosities of accreting compact objects (neutron stars, black holes and white dwarfs) are produced in the innermost regions of accretion discs or boundary layers. Two simple models are considered in this paper. The magnetosphere–disc model consists of a thin Keplerian disc in contact with a uniformly rotating magnetosphere with and low plasma density, while the star–disc model involves a Keplerian disc terminated at the stellar atmosphere with high density and small density scaleheight. We find that the interface modes at the magnetosphere–disc boundary are generally unstable due to Rayleigh–Taylor and/or Kelvin–Helmholtz instabilities. However, differential rotation of the disc tends to suppress Rayleigh–Taylor instability, and a sufficiently high disc sound speed (or temperature) is needed to overcome this suppression and to attain net mode growth. On the other hand, Kelvin–Helmholtz instability may be active at low disc sound speeds. We also find that the interface modes trapped at the boundary between a thin disc and an unmagnetized star do not suffer Rayleigh–Taylor or Kelvin–Helmholtz instability, but can become unstable due to wave leakage to large disc radii and, for sufficiently steep disc density distributions, due to wave absorption at the corotation resonance in the disc. The non-axisymmetric interface modes studied in this paper may be relevant to the high-frequency QPOs observed in some X-ray binaries and in cataclysmic variables.

Influence of suction/blowing on the finite amplitude disturbances having non-stationary modes of a compressible boundary layer flow

In this paper, a weakly non-linear stability analysis is pursued to explore the effects of suction and blowing on a compressible mode of instability of the three-dimensional boundary layer flow induced by a rotating disk. The main thrust of the research is to extend the stationary work of Seddougui and Bassom (1996) to cover for the non-stationary mode so that it is targeted to determine whether the major role in finite amplitude destabilization of the boundary layer is played by the stationary mode of Seddougui and Bassom (1996) or the non-stationary mode as calculated from the present study. Within this perspective, the basic compressible flow obtained in the large Reynolds number limit, together with a suction parameter entering into the wall with normal velocity at the wall, is perturbed by disturbances which are constituted as the non-linear interaction of fundamental modes and harmonics. The effects of non-linearity are then explored by deriving a finite amplitude equation governing the evolution of the non-linear lower branch modes and also allowing the finite amplitude growth of a disturbance close to the neutral location determined from a prior stability analysis. Although the form of the amplitude equation is not at all surprising (given a similar result for the stationary vortices in Seddougui and Bassom (1996)), the dependence of the coefficients of the Landau-type modulated vortex amplitude equation on the frequency parameter is established here. A close examination of the coefficients of this evolution equation indicates strongly that the non-linearity has a destabilizing effect for both suction and blowing through the surface of the disk, the effect of which is much more stronger for a suction. Also the impact of non-linearity is higher for the non-stationary compressible modes than for the stationary waves of Seddougui (1990) and Seddougui and Bassom (1996). Moreover, in the case of suction, there occurs a regime of non-stationary modes that cover not only the positive frequency waves, but also waves having negative frequencies, and these modes are always unstable no matter whether the wall is insulated or isothermal. The solution of the asymptotic amplitude equation further demonstrates that as the local Mach number increases, compressibility has the influence of stabilization by requiring smaller initial amplitude of the disturbance for the laminar rotating disk boundary layer flow to become unstable whenever fluid injection is applied. Unlike this, suction makes the underlying flow more convectively unstable as far as the compressibility is concerned, particulary for the modes generated as a consequence of an isothermal wall. Both for the suction and injection cases, disturbances having positive frequency are always shown to cause an instantaneous non-linear amplification prior to the negative frequency waves.

Large eddy simulation and measurements of turbulent enclosed rotor-stator flows

Turbulent flows are studied in an actual enclosed rotor-stator configuration with a rotating hub and a stationary shroud. Besides its fundamental importance—the disk boundary layer is one of the simplest platforms for investigating the underlying structure of three-dimensional boundary layers—this cavity models more complex configurations relevant to rotating machinery. Large eddy simulation is performed using a spectral vanishing viscosity technique that is shown leading to stable discretizations without sacrificing the formal accuracy of the spectral approximation. Numerical results and velocity measurements have been favorably compared for a large range of rotational Reynolds numbers (105⩽Re=Ωb2∕ν⩽106) in an annular cavity of curvature parameter Rm=(b+a)∕(b−a)=1.8 and of aspect ratio G=(b−a)∕h=5, where a and b are, respectively, the inner and outer radii of the rotating disk and h is the interdisk spacing. In the detailed picture of the flow structure that emerges, the turbulence is confined mainly in the boundary layers including in the Stewartson layer along the external cylinder. For Reynolds numbers Re⩾105, the stator boundary layer is turbulent over most of the cavity. On the other hand, the rotor layer becomes progressively turbulent from the outer radial locations, although the rotating hub is shown to destabilize the inner part of the boundary layers. The isosurface maps of the Q-criterion reveal that the three-dimensional spiral arms observed in the unstable laminar regime evolve to more axisymmetric structures when turbulence occurs. At Re=106, the flow is fully turbulent and the anisotropy invariant map highlights turbulence structuring, which can be either a “cigar-shaped” structuring aligned on the tangential direction or a “pancake-shaped” structuring depending on the axial location. The reduction of the structural parameter a1 (the ratio of the magnitude of the shear stress vector to twice the turbulence kinetic energy) under the typical limit 0.15, as well as the misalignment between the shear stress vector and the mean velocity gradient vector, highlight the three-dimensional nature of both rotor and stator boundary layers with a degree of three-dimensionality much higher than in the idealized system studied by Lygren and Andersson [J. Fluid Mech. 426, 297 (2001); ZAMP 55, 268 (2004); and Int. J. Heat Fluid Flow 27, 551 (2006)].

Influence of Finite Amplitude Disturbances on the Nonstationary Modes of a Compressible Boundary Layer Flow

A weakly nonlinear stability analysis is performed to search for the effects of compressibility on a mode of instability of the three‐dimensional boundary layer flow due to a rotating disk. The motivation is to extend the stationary work of [1] (hereafter referred to as S90) to incorporate into the nonstationary mode so that it will be investigated whether the finite amplitude destabilization of the boundary layer is owing to this mode or the mode of S90. Therefore, the basic compressible flow obtained in the large Reynolds number limit is perturbed by disturbances that are nonlinear and also time dependent. In this connection, the effects of nonlinearity are explored allowing the finite amplitude growth of a disturbance close to the neutral location and thus, a finite amplitude equation governing the evolution of the nonlinear lower branch modes is obtained. The coefficients of this evolution equation clearly demonstrate that the nonlinearity is destabilizing for all the modes, the effect of which is higher for the nonstationary waves as compared to the stationary waves. Some modes particularly having positive frequency, regardless of the adiabatic or wall heating/cooling conditions, are always found to be unstable, which are apparently more important than those stationary modes determined in S90. The solution of the asymptotic amplitude equation reveals that compressibility as the local Mach number increases, has the influence of stabilization by requiring smaller initial amplitude of the disturbance for the laminar rotating disk boundary layer flow to become unstable. Apart from the already unstable positive frequency waves, perturbations with positive frequency are always seen to compete to lead the solution to unstable state before the negative frequency waves do. Also, cooling the surface of the disk will be apparently ineffective to suppress the instability mechanisms operating in this boundary layer flow.