On robust estimation of the location parameter

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

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

/pdf/the-phenomenology-of-small-scale-turbulence-3a5uzrupts.pdf

The phenomenology of small-scale turbulence

This review discusses the use of the combination of surface roughness and hydrophobicity for engineering large slip at the fluid-solid interface. These superhydrophobic surfaces were initially inspired by the unique water-repellent properties of the lotus leaf and can be employed to produce drag reduction in both laminar and turbulent flows, enhance mixing in laminar flows, and amplify diffusion-osmotic flows. We review the current state of experiments, simulations, and theory of flow past superhydrophobic surfaces. In addition, the designs and limitations of these surfaces are discussed, with an eye toward implementing these surfaces in a wide range of applications.

Slip on Superhydrophobic Surfaces

Phase‐conjugate mirrors are used in optics to compensate for aberrations caused by inhomogeneities in the propagation medium and by imperfections in optical components. In acoustics, analogous behavior can be achieved by a time‐reversed retransmission of signals received by an array. Compensation for multipath propagation and array imperfections is automatic and does not require knowledge of the detailed properties of either the medium or the array. The behavior of acoustic phase‐conjugate arrays is illustrated in several examples, some highly idealized and some more realistic. The effects of aperture size and inhomogeneities in the propagation medium are treated for both the near‐field and far‐field regions. It is concluded that phase‐conjugate arrays offer an attractive approach to some long‐standing problems in underwater acoustics.

Phase conjugation in underwater acoustics

This work is an experimental investigation of the turbulent concentration field formed when the nozzle gas from a round, momentum-driven, free turbulent jet mixes with gas entrained from a quiescent reservoir. The measurements, which were made with a non-intrusive laser-Rayleigh scattering diagnostic at Reynolds numbers of 5000, 16000, and 40000, cover the axial range from 20 to 90 jet exit diameters and resolve the full range of temporal and spatial concentration scales. Reynolds-number-independent and Reynolds-number-dependent similarities are investigated. The mean and r.m.s. values of the concentration are found to be consistent with jet similarity laws. Concentration fluctuation power spectra are found to be self-similar along rays emanating from the virtual origin of the jet. The probability density function for the concentration is also found to be self-similar along rays. Near the centreline of the jet, the scaled probability density function of jet fluid concentration is found to be nearly independent of the Reynolds number.

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Similarity of the concentration field of gas-phase turbulent jets

A new method for coherent underwater acoustic communication called passive phase conjugation is evaluated. The method is so named because of conceptual similarities to active phase conjugation methods that have been demonstrated in the ocean. In contrast to active techniques, however, the array in passive phase conjugation needs only receive. The procedure begins with a source transmitting a single probe pulse. After waiting for the multipathed arrivals to clear, the source then transmits the data stream. At each element in the distant receiving array, the received probe is cross-correlated with the received data stream. This cross-correlation is done in parallel at each array element and the results are summed across the array to achieve the final communication signal suitable for demodulation. As the ocean changes, it becomes necessary to break up the data stream and insert new probe pulses. Results from an experiment conducted in Puget Sound near Seattle are reported. Measurements were made at multiple ranges and water depths in range-dependent environments.

Underwater acoustic communication by passive-phase conjugation: theory and experimental results

Turbulent boundary layer skin friction in liquid flows may be reduced when bubbles are present near the surface on which the boundary layer forms. Prior experimental studies of this phenomenon reached downstream-distance-based Reynolds numbers (m. At the lowest test speed and highest air injection rate, buoyancy pushed the air bubbles to the plate surface where they coalesced to form a nearly continuous gas film that persisted to the end of the plate with near-100% skin-friction drag reduction. At the higher two flow speeds, the bubbles generally remained distinct and skin-friction drag reduction was observed when the bubbly mixture was closer to the plate surface than 300 wall units of the boundary-layer flow without air injection, even when the bubble diameter was more than 100 of these wall units. Skin-friction drag reduction was lost when the near-wall shear induced the bubbles to migrate from the plate surface. This bubble-migration phenomenon limited the persistence of bubble-induced skin-friction drag reduction to the first few metres downstream of the air injector in the current experiments.

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

A review of existing literature is made to determine typical values for the physical properties cirrus clouds. The properties examined (with typical values and measured ranges) are cloud-center altitude (9 km, 4 to 20 km), cloud thickness (1.5 km, 0.1 to 8 km), crystal number density (30 L−1, 10−4 to 10−4 L−1), condensed water content (0.025 g m −3, 10−4 to 1.2 g m −3), and crystal size (250 μm, 1 to 8000 μm). A typical crystal size distribution is also reported.

David R. Dowling

Papers

Phase conjugation in underwater acoustics

Similarity of the concentration field of gas-phase turbulent jets

Underwater acoustic communication by passive-phase conjugation: theory and experimental results

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

A Summary of the Physical Properties of Cirrus Clouds