The Three-Dimensional Evolution of Oblique Waves in Plane Wakes

1993 ◽  
pp. 325-332 ◽  
Author(s):  
Eckart Meiburg
Keyword(s):  
Three Dimensional ◽  
Oblique Waves

Three-dimensional mode growth in boundary layers with tuned and detuned subharmonic resonance

1995 ◽  
Vol 352 (1700) ◽  
pp. 453-471 ◽  
Keyword(s):  
Three Dimensional ◽  
Low Frequency ◽  
Phase Speed ◽  
Subharmonic Resonance ◽  
Oblique Waves ◽  
Periodic Disturbances ◽  
Wave Numbers ◽  
Interaction Order ◽  
Tollmien Schlichting ◽  
Low Amplitude

This work involves the use of controlled periodic disturbances to excite a plane Tollmien-Schlichting (TS) wave at one frequency ( f 2D) along with pairs of oblique waves with equal but opposite wave angles at a different frequency ( f 3D) in order to study the resonant growth of 3D modes in a Blasius boundary layer. In our earlier work (Corke & Mangano 1989; Corke 1990), the frequency of the oblique modes was exactly the subharmonic of the plane Tollmien-Schlichting (TS) mode. These modes were also phase-speed locked so that in terms of their streamwise wave numbers, α2D=1/2 α3D. This so-called ‘tuned’ subharmonic resonance leads to the enhanced growth of the otherwise linearly damped oblique waves, as well as the growth of higher harmonic 3D modes with frequencies and wave numbers: (3/2 f2d, 3/2 α2D, ±β3D), (5/2 f2d, 5/2 α2D, ±β3D), (f2d, α2D, ±2β3D) and (0, 0, ±2β3D). Even when the initial 3D oblique waves have frequencies which are close to the TS subharmonic frequency, a ‘detuned’ subharmonic resonance leads to the enhanced growth of the 3D mode. In addition, it promotes the growth of numerous discrete modes produced by successive sum and difference interactions. These interacted modes are also three dimensional, with higher amplification rates that increase with the interaction order. The growth of these modes accounts for the rapid spectral filling, and low-frequency modulation commonly observed in natural subharmonic transition. Starting from a ‘tuned' resonance, this scenario then provides a mechanism for the generation of a broad spectrum at the later stages of subharmonic mode transition. However, the results also suggest that with ‘natural’ transition, starting from low-amplitude broadband disturbances, the most likely 2D/3D resonance will be ‘detuned’.

Calculation of Horizontal Sectional Loads and Torsional Moment

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Vladimir Shigunov ◽  
Alexander von Graefe ◽  
Ould el Moctar
Keyword(s):  
Free Surface ◽  
Shear Force ◽  
Three Dimensional ◽  
Bending Moment ◽  
Green Functions ◽  
Container Ship ◽  
Horizontal Shear ◽  
Torsional Moment ◽  
Oblique Waves ◽  
Rankine Source

Horizontal sectional loads (horizontal shear force and horizontal bending moment) and torsional moment are more difficult to predict with potential flow methods than vertical loads, especially in stern-quartering waves. Accurate computation of torsional moment is especially important for large modern container ships. The three-dimensional (3D) seakeeping code GL Rankine has been applied previously to the computation of vertical loads in head, following and oblique waves; this paper addresses horizontal loads and torsional moment in oblique waves at various forward speeds for a modern container ship. The results obtained with the Rankine source-patch method are compared with the computations using zero-speed free-surface Green functions and with model experiments.

scholarly journals Oblique instability of a stratified oscillatory boundary layer

2021 ◽  
Vol 933 ◽  
Author(s):  
Jason Yalim ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Boundary Layers ◽  
Oscillation Frequency ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Buoyancy Frequency ◽  
Oblique Waves ◽  
Oscillatory Shear Flow ◽  
Oscillatory Boundary Layer

The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.

Effects of surface corrugation on the stability of a zero-pressure-gradient boundary layer

2014 ◽  
Vol 741 ◽  
pp. 228-251 ◽  
Author(s):  
Mochamad Dady Ma’mun ◽  
Masahito Asai ◽  
Ayumu Inasawa
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Two Dimensional ◽  
S Wave ◽  
Flow Distortion ◽  
Oblique Waves ◽  
Surface Corrugation ◽  
S Waves ◽  
Displacement Thickness

AbstractThe effects of surface corrugation with small amplitude on the growth of Tollmien–Schlichting (T–S) waves were examined experimentally in a zero-pressure-gradient boundary layer. Two- and three-dimensional corrugations of sinusoidal geometry with wavelengths of the same order as that of the two-dimensional T–S wave were considered. The corrugation amplitudes were one order of magnitude smaller than the boundary-layer displacement thickness. Streamwise growth of T–S waves on the corrugated walls was compared with that in the boundary layer on the smooth surface. A distinct difference was found in the destabilizing effect between the two- and three-dimensional corrugations. The two-dimensional corrugation significantly enhanced the growth of two-dimensional T–S waves even when the corrugation amplitude was only ∼10% of the displacement thickness. On decreasing the corrugation amplitude, the growth rate of two-dimensional T–S waves asymptotically approached that in the smooth-wall case. On the other hand, the three-dimensional corrugation had only a small influence on the growth of two-dimensional T–S waves even when the corrugation amplitude was as large as 20% of the displacement thickness. For three-dimensional corrugations, however, a pair of oblique waves was generated and developed by an interaction between the two-dimensional T–S wave and the corrugation-induced mean-flow distortion for the corrugation wavelength considered. On increasing the corrugation amplitude, the oblique waves generated were increased in amplitude and thus significantly influenced the secondary instability process.

Resonant growth of three-dimensional modes in trnsitioning Blasius boundary layers

1989 ◽  
Vol 209 ◽  
pp. 93-150 ◽  
Author(s):  
T. C. Corke ◽  
R. A. Mangano
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Local Heating ◽  
Rapid Development ◽  
Plane Waves ◽  
Three Dimensional ◽  
Heating Time ◽  
Transition To Turbulence ◽  
Special Focus ◽  
Oblique Waves

By carefully controlled phase-coupled input of simultaneous two- and three-dimensional disturbances, the nonlinear evolution and breakdown of the laminar flow in a boundary layer was examined. This involved the generation of plane Tollmien–Schlichting waves and pairs of oblique waves so as to promote nearresonance conditions which have been theoretically shown to lead to the rapid development of three-dimensionality in unstble boundary layers. Special emphasis is placed on the two prominent mechanisms, namely resonant-triads of Orr–Sommerfeld modes and the secondary instability of the streamwise periodic flow to spanwise periodic three-dimensional disturbances. The sensitivity of these mechanisms on the amplitudes and wavenumbers of the input disturbances was of special focus.The simultaneous two- and three-dimensional wave generation was accomplished using a spanwise array of line heaters suspended just above the wall at the approximate height of the critical layer in the laminar boundary layer. These were operated to produce, through local heating, time-periodic spanwise-phase-varying velocity perturbations. Of primary emphasis in this paper are conditions obtained by the combined forcing of fundamental plane waves with wavenumbers (α, 0) and pairs of subharmonic oblique waves (½α, ± β). The reslults document resonant growth of energy in the subharmonic modes, the formation of staggered lambda vortex patterns with a cross-stream scale commensurate with the seeded ± β condition, and their subsequet transition to turbulence. Complete documentation of the flow field at these various stages is presented using smoke-wire flow visualization and through phase-conditioned hot-wire surveys measuring all three velocity components in three space dimensions.

scholarly journals Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field

2007 ◽  
Vol 574 ◽  
pp. 131-154 ◽  
Author(s):  
A. VOROBEV ◽  
O. ZIKANOV
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Transition To Turbulence ◽  
Free Shear Layer ◽  
Parallel Magnetic Field ◽  
Oblique Waves ◽  
Electrically Conducting

Instability and transition to turbulence in a temporally evolving free shear layer of an electrically conducting fluid affected by an imposed parallel magnetic field is investigated numerically. The case of low magnetic Reynolds number is considered. It has long been known that the neutral disturbances of the linear problem are three-dimensional at sufficiently strong magnetic fields. We analyse the details of this instability solving the generalized Orr–Sommerfeld equation to determine the wavenumbers, growth rates and spatial shapes of the eigenmodes. The three-dimensional perturbations are identified as oblique waves and their properties are described. In particular, we find that at high hydrodynamic Reynolds number, the effect of the strength of the magnetic field on the fastest growing perturbations is limited to an increase of their oblique angle. The dimensions and spatial shape of the waves remain unchanged. The transition to turbulence triggered by the growing oblique waves is investigated in direct numerical simulations. It is shown that initial perturbations in the form of superposition of two symmetric waves are particularly effective in inducing three-dimensionality and turbulence in the flow.

Dynamic Behaviour of a Container Ship Using Two- and Three-Dimensional Hydroelasticity Analyses

2008 ◽  
Author(s):  
I. Basaran ◽  
O. Belik ◽  
P. Temarel
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Behaviour ◽  
Three Dimensional ◽  
Structural Models ◽  
Container Ship ◽  
Oblique Waves ◽  
Wave Induced

The symmetric (vertical bending) and antisymmetric (coupled horizontal bending and twisting) dynamic behaviours of a feeder container ship travelling in regular oblique waves are investigated using two- and three-dimensional hydroelasticity theories. Different three-dimensional FE structural models are generated in order to investigate the influence of hatch coamings and on-deck container cargo. Corresponding beam structural idealizations are obtained from these models. Comparisons are carried out between the dynamic characteristics and wave-induced loads predicted by both methods.

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