Abstract A two-dimensional version of the Pennsylvania State University mesoscale model has been applied to Winter Monsoon Experiment data in order to simulate the diurnally occurring convection observed over the South China Sea. The domain includes a representation of part of Borneo as well as the sea so that the model can simulate the initiation of convection. Also included in the model are parameterizations of mesoscale ice phase and moisture processes and longwave and shortwave radiation with a diurnal cycle. This allows use of the model to test the relative importance of various heating mechanisms to the stratiform cloud deck, which typically occupies several hundred kilometers of the domain. Frank and Cohen's cumulus parameterization scheme is employed to represent vital unresolved vertical transports in the convective area. The major conclusions are: Ice phase processes are important in determining the level of maximum large-scale heating and vertical motion because there is a strong anvil componen...

Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model [presentation]

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

/pdf/evidence-of-very-long-meandering-features-in-the-logarithmic-2m2f4f0daq.pdf

Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

The present study explores the effects of Reynolds number, over three orders of magnitude, in the viscous wall region of a turbulent boundary layer. Complementary experiments were conducted both in the boundary layer wind tunnel at the University of Utah and in the atmospheric surface layer which flows over the salt flats of the Great Salt Lake Desert in western Utah. The Reynolds numbers, based on momentum deficit thickness, of the two flows were Rθ=2×103 and Rθ≈5×106, respectively. High-resolution velocity measurements were obtained from a five-element vertical rake of hot-wires spanning the buffer region. In both the low and high Rθ flows, the length of the hot-wires measured less than 6 viscous units. To facilitate reliable comparisons, both the laboratory and field experiments employed the same instrumentation and procedures. Data indicate that, even in the immediate vicinity of the surface, strong influences from low-frequency motions at high Rθ produce noticeable Reynolds number differences in the ...

A comparative study of near-wall turbulence in high and low Reynolds number boundary layers

Simultaneous streamwise velocity measurements across the vertical direction obtained in the atmospheric surface layer (Re_τ ≃ 5 × 10^5) under near thermally neutral conditions are used to outline and quantify interactions between the scales of turbulence, from the very-large-scale motions to the dissipative scales. Results from conditioned spectra, joint probability density functions and conditional averages show that the signature of very-large-scale oscillations can be found across the whole wall region and that these scales interact with the near-wall turbulence from the energy-containing eddies to the dissipative scales, most strongly in a layer close to the wall, z^+ ≲ 10^3. The scale separation achievable in the atmospheric surface layer appears to be a key difference from the low-Reynolds-number picture, in which structures attached to the wall are known to extend through the full wall-normal extent of the boundary layer. A phenomenological picture of very-large-scale motions coexisting and interacting with structures from the hairpin paradigm is provided here for the high-Reynolds-number case. In particular, it is inferred that the hairpin-packet conceptual model may not be exhaustively representative of the whole wall region, but only of a near-wall layer of z^+ = O(10^3), where scale interactions are mostly confined.

/pdf/interactions-within-the-turbulent-boundary-layer-at-high-5a5psuns1q.pdf

Interactions within the turbulent boundary layer at high Reynolds number

The neutrally stable atmospheric surface layer is used as a physical model of a very high
Reynolds number, canonical turbulent boundary layer. Challenges and limitations with
this model are addressed in detail, including the inherent thermal stratification, surface
roughness and non-stationarity of the atmosphere. Concurrent hot-wire and sonic
anemometry data acquired in Utah’s western desert provide insight to Reynolds number
trends in the axial velocity statistics and spectra.

The near-neutral atmospheric surface layer: turbulence and non-stationarity

Based upon high resolution LDA measurements over a range of momentum deficit thickness Reynolds numbers (Rθ=U∞θ/ν) from 1430 to 31 000, DeGraaff and Eaton [J. Fluid Mech. 422, 319 (2000)] propose a new mixed scaling for the near-wall region profile of the axial turbulent stress, u2¯. The present results support the validity of this scaling over an extended Reynolds number range 1000⩽Rθ⩽5×106.

Scaling the near-wall axial turbulent stress in the zero pressure gradient boundary layer

The fluctuating wall pressure and its gradients in the plane of the surface were measured beneath the turbulent boundary layer that forms over the salt playa of Utah's west desert. Measurements were acquired under the condition of near-neutral thermal stability to best mimic the canonical zero-pressure-gradient boundary-layer flow. The Reynolds number (based on surface-layer thickness, δ, and the friction velocity, uτ) was estimated to be 1 × 106 ± 2 × 105. The equivalent sandgrain surface roughness was estimated to be in the range 15≤ks+≤85. Pressure measurements acquired simultaneously from an array of up to ten microphones were analysed. A compact array of four microphones was used to estimate the instantaneous streamwise and spanwise gradients of the surface pressure. Owing to the large length scales and low flow speeds, attaining accurate pressure statistics in the present flow required sensors capable of measuring unusually low frequencies. The effects of imperfect spatial and temporal resolution on the present measurements were also explored. Relative to pressure, pressure gradients exhibit an enhanced sensitivity to spatial resolution. Their accurate measurement does not, however, require fully capturing the low frequencies that are inherent and significant in the pressure itself. The present pressure spectra convincingly exhibit over three decades of approximately −1 slope. Comparisons with low-Reynolds-number data support previous predictions that the inner normalized wall pressure variance increases logarithmically with Reynolds number. The wall pressure autocorrelation exhibits its first zero-crossing at an advected length that is between one tenth and one fifth of the surface-layer thickness. Under any of the normalizations investigated, the present surface vorticity flux intensity values are difficult to reconcile with low-Reynolds-number data trends. Inner variables, however, do yield normalized flux intensity values that are of the same order of magnitude at low and high Reynolds number. Spectra reveal that even at high Reynolds number, the primary contributions to the pressure gradient intensities occur over a relatively narrow frequency range. This frequency range is shown to be consistent with the scale of the sublayer pocket motions. In accord with low-Reynolds-number data, the streamwise pressure gradient signals at high Reynolds number are also characterized by statistically significant pairings of opposing sign fluctuations.

Meredith Metzger

Papers

A comparative study of near-wall turbulence in high and low Reynolds number boundary layers

Interactions within the turbulent boundary layer at high Reynolds number

The near-neutral atmospheric surface layer: turbulence and non-stationarity

Scaling the near-wall axial turbulent stress in the zero pressure gradient boundary layer

Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number