On the Stability of Ekman Boundary Layer Flow with Thermally Unstable Stratification

Asai, Tomio; Nakasuji, Isao

doi:10.2151/jmsj1965.51.1_29

Cited by 25 publications

(4 citation statements)

References 22 publications

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“…The application of the convective instability findings to geophysical secondary flows using the eddy viscosity analogy was immediately evident for convective cloud streets such as those in Figure 1. Kuo [1963], Asai and Nakasuji [1973], and Deardorff [1972] found linear vortices in their solutions for unstably stratified PBL flow. Pioneering work on finite amplitude cellular convection was done by Malkus and Veronis [1958], using the nonlinear techniques described by Stuart [1958Stuart [ , 1971.…”

Section: The Results Show That Inflection Point Instabilities Occur Atmentioning

confidence: 99%

Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

Brown¹

1980

Reviews of Geophysics

255

149

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Within the past decade, satellite pictures have shown persistent cloud patterns which indicate that the flow in the atmospheric planetary boundary layer is often organized into helical secondary circulations aligned parallel to the mean flow. Theory and observation agree that both convection in the presence of shear and the dynamic inflection point instabilities of the Ekman layer lead to these flow patterns. The observatio•ns and theory are reviewed with emphasis on the dynamics-dominated flow. cal flows developed slowlye:marked by two perceptive and diligent observers, Langmuir and Woodcock, and then grew rapidly as a result of the remote sensing technology developed in the past 20 years. Langmuir [1938] had inferred the existence of helical flow in the top layer of the ocean from observations of long rows of floating seaweed parallel to the wind. His experiments on Lake George, using oil slicks, leaves, cork, and submerged umbrellas buoyed wit h lamp bulbs, established quantitative values for the scale and velocities in these circulations which stand today. The term 'windrows' was applied early by mariners to the long lines of flotsam or suppressed capillary waves appearing along the wind direction. Garbage dumped by the state of New York has been observed drifting back toward New York in the sea breeze in neat rows. In all of these cases the rows are nearly parallel to the wind and, by virtue of characteristic wavelength, appear to be related to the Langmuir circulations in the water. However, the question of the generating mechanism has not been resolved and has been discussed by Welander [1963], Faller [1964], Scott et al. [1969], Craik and Leibovich [1976], and Faller and Caponi [1978]. Woodcock [1942] used seagull soaring patterns correlated with wind and temperature measurements to suggest cellular and lineal convective patterns in the atmosphere. The banded cloud regions appear in broad scale views of the earth obtained from satellites (Figure 1). Lineal cloud bands occur in hurricanes and consistently in the arctic regions, where cold Pape•r number 80R0121. 683 684 BROWN: LONGITUDINAL INSTABILITIES AND SECONDARY FLOWS IN THE PBL

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Section: The Results Show That Inflection Point Instabilities Occur Atmentioning

confidence: 99%

Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

Brown¹

1980

Reviews of Geophysics

255

149

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“…In this configuration they found that convective rolls may be aligned north-south or east-west, depending on the parameter values characterizing the system. The interaction of Ekman instabilities and convection or stable stratification is also important in the planetary boundary layer (see Etling 1971;Brown 1972;Asai & Nakasuji 1973;Wipperman, Etling & Kirstein 1978; also the review Etling & Brown 1993). …”

Section: Introductionmentioning

confidence: 99%

The onset of thermal convection in EkmanCouette shear flow with oblique rotation

2003

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The onset of convection of a Boussinesq fluid in a horizontal plane layer is studied. The system rotates with constant angular velocity Ω Ω Ω, which is inclined at an angle ϑ to the vertical. The layer is sheared by keeping the upper boundary fixed, while the lower boundary moves parallel to itself with constant velocity U 0 normal to the plane containing the rotation vector and gravity g (i.e. U 0 g × Ω Ω Ω). The system is characterized by five dimensionless parameters: the Rayleigh number Ra, the Taylor number τ 2 , the Reynolds number Re (based on U 0 ), the Prandtl number Pr and the angle ϑ. The basic equilibrium state consists of a linear temperature profile and an Ekman-Couette flow, both dependent only on the vertical coordinate z. Our linear stability study involves determining the critical Rayleigh number Ra c as a function of τ and Re for representative values of ϑ and Pr.Our main results relate to the case of large Reynolds number, for which there is the possibility of hydrodynamic instability. When the rotation is vertical ϑ = 0 and τ 1, so-called type I and type II Ekman layer instabilities are possible. With the inclusion of buoyancy Ra = 0 mode competition occurs. On increasing τ from zero, with fixed large Re, we identify four types of mode: a convective mode stabilized by the strong shear for moderate τ , hydrodynamic type I and II modes either assisted (Ra > 0) or suppressed (Ra < 0) by buoyancy forces at numerically large τ , and a convective mode for very large τ that is largely uninfluenced by the thin Ekman shear layer, except in that it provides a selection mechanism for roll orientation which would otherwise be arbitrary. Significantly, in the case of oblique rotation ϑ = 0, the symmetry associated with U 0 ↔ −U 0 for the vertical rotation is broken and so the cases of positive and negative Re exhibit distinct stability characteristics, which we consider separately. Detailed numerical results were obtained for the representative case ϑ = π/4. Though the overall features of the stability results are broadly similar to the case of vertical rotation, their detailed structure possesses a surprising variety of subtle differences.

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“…Previous studies have investigated the structures of the thermal-shear instability for constant values of the vertical wind shear and 2 (< 0) (Hill 1968;Asai 1970), or an unstably stratified Ekman boundary layer (Asai and Nakasuji 1973). These approaches agreed on roll-shaped and shear-parallel structures as the fastest-growing mode.…”

Section: Linear Stability Analysesmentioning

confidence: 99%

On the formation mechanism of cirrus banding: radiosonde observations, numerical simulations, and stability analyses

Yamazaki

Miura

2021

Journal of the Atmospheric Sciences

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The structures and formation mechanisms of cirrus banding are investigated by analyzing radiosonde observations, conducting high-resolution numerical experiments, and performing linear stability analyses. In all 29 cases of cirrus bands that were analyzed, radiosonde observational data indicate that statically unstable layers exist. The detected banding clouds were aligned nearly parallel to the vertical shear vector in the unstable layer. In high-resolution numerical experiments using the cloud-resolving model SCALE-RM, cirrus bands forming in the outflow layer of a tropical cyclone are explicitly simulated. The existence of statically unstable layers and band-parallel background vertical wind shear are commonly identified in the simulations. Sensitivity experiments and heat budget analyses demonstrated that the unstable stratification within the cirrus clouds was maintained by the cloud-radiation interactions. To reveal the behavior of fluid instabilities in the cirrus bands, linear stability analyses in a basic state constructed from the radiosonde observations were performed. The fastest-growing disturbance is highly similar to that of the previously known thermal-shear instability in a uniform and isolated unstable layer and the results obtained by radiosonde observations and numerical simulations. All of the results consistently indicate that thermal-shear instability is responsible for the formation of cirrus banding. Our results not only follow previous modeling studies but also provide observational support, quantification of the destabilization by the cloud-radiation interactions, as well as a theoretical basis of the thermal-shear instability in a complex environment near cirrus bands.

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On the Stability of Ekman Boundary Layer Flow with Thermally Unstable Stratification

Cited by 25 publications

References 22 publications

Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

The onset of thermal convection in EkmanCouette shear flow with oblique rotation

On the formation mechanism of cirrus banding: radiosonde observations, numerical simulations, and stability analyses

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