Boundary-layer growth near a rear stagnation point

1962 ◽  
Vol 12 (02) ◽  
pp. 161 ◽  
Author(s):  
Ian Proudman ◽  
Kathleen Johnson
1973 ◽  
Vol 59 (4) ◽  
pp. 769-773 ◽  
Author(s):  
J. A. Howarth

This paper presents the analysis and numerical solution for the axisymmetric analogue of the problem considered by Proudman & Johnson (1962) and Robins & Howarth (1972).


The work presented here is an extension of that of Blasius (1908) on boundary-layer growth at a cylinder started from rest. It is shown that if an infinite plane moves in its own plane in a viscous fluid, the velocity distributions are similar at different times if the velocity V{t) of the plane is of the form V(t) = Atα or V(t) = A ect, where t is the time. These cases are then applied to the theory of boundary-layer growth and the second approximation to the velocity in the boundary layer is calculated. From this we find a first approximation for the distance travelled by the cylinder before separation starts. The second approximation to the separation distance was calculated by Blasius for α = 1, by Goldstein & Rosenhead (1936) for α = 0, and is found here for the case V(t) — A ect. Another approximate method for finding the separation distance, when separation starts at the rear stagnation point, is developed and applied to the impulsive start. The method is based on the momentum equation and assumes that the velocity profile near the rear stagnation point will always be similar to an initial profile. The numerical results are presented in the tables, and include the variation with a of the separation distance (according to the first approximation). It is hoped to use the method of Gortler (1944) to evaluate the drag on a circular cylinder and thus to discuss the initial motion of such a cylinder.


1975 ◽  
Vol 67 (2) ◽  
pp. 289-297 ◽  
Author(s):  
J. A. Howarth

The theory of boundary-layer growth at a rear stagnation point, first presented by Proudman & Johnson, is here extended to cover fully three-dimensional rear stagnation points. Supporting numerical solutions of the full initial-value problem establish the relevance of the in viscid similarity solutions obtained.


1947 ◽  
Vol 14 (3) ◽  
pp. A213-A216
Author(s):  
R. C. Binder

Abstract A method is presented for calculating the efficiency of a diffuser for two-dimensional, steady, incompressible flow without separation. The method involves a combination of organized boundary-layer data and frictionless potential-flow relations. The potential velocity and pressure are found after the boundary-layer growth is determined by a trial-and-check calculation.


2016 ◽  
Vol 16 (9) ◽  
pp. 5811-5839 ◽  
Author(s):  
Jan Kazil ◽  
Graham Feingold ◽  
Takanobu Yamaguchi

Abstract. Observed and projected trends in large-scale wind speed over the oceans prompt the question: how do marine stratocumulus clouds and their radiative properties respond to changes in large-scale wind speed? Wind speed drives the surface fluxes of sensible heat, moisture, and momentum and thereby acts on cloud liquid water path (LWP) and cloud radiative properties. We present an investigation of the dynamical response of non-precipitating, overcast marine stratocumulus clouds to different wind speeds over the course of a diurnal cycle, all else equal. In cloud-system resolving simulations, we find that higher wind speed leads to faster boundary layer growth and stronger entrainment. The dynamical driver is enhanced buoyant production of turbulence kinetic energy (TKE) from latent heat release in cloud updrafts. LWP is enhanced during the night and in the morning at higher wind speed, and more strongly suppressed later in the day. Wind speed hence accentuates the diurnal LWP cycle by expanding the morning–afternoon contrast. The higher LWP at higher wind speed does not, however, enhance cloud top cooling because in clouds with LWP ⪆ 50 g m−2, longwave emissions are insensitive to LWP. This leads to the general conclusion that in sufficiently thick stratocumulus clouds, additional boundary layer growth and entrainment due to a boundary layer moistening arises by stronger production of TKE from latent heat release in cloud updrafts, rather than from enhanced longwave cooling. We find that large-scale wind modulates boundary layer decoupling. At nighttime and at low wind speed during daytime, it enhances decoupling in part by faster boundary layer growth and stronger entrainment and in part because shear from large-scale wind in the sub-cloud layer hinders vertical moisture transport between the surface and cloud base. With increasing wind speed, however, in decoupled daytime conditions, shear-driven circulation due to large-scale wind takes over from buoyancy-driven circulation in transporting moisture from the surface to cloud base and thereby reduces decoupling and helps maintain LWP. The total (shortwave + longwave) cloud radiative effect (CRE) responds to changes in LWP and cloud fraction, and higher wind speed translates to a stronger diurnally averaged total CRE. However, the sensitivity of the diurnally averaged total CRE to wind speed decreases with increasing wind speed.


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