Results are reported of a computational study investigating the responses of flat plate boundary layers and wakes to horizontal wave outer flows. Solutions are obtained for temporal, spatial, and traveling waves using Navier Stokes, boundary layer, and perturbation expansion equations. A wide range of parameters are considered for all the three waves. The results are presented in terms of Stokes-layer overshoots, phase leads (lags), and streaming. The response to the temporal wave showed all the previously reported features. The magnitude and nature of the response are small and simple such that it is essentially a small disturbance on the steady solution. Results are explainable in terms of one parameter ξ (the frequency of oscillation). For the spatial wave, the magnitude and the nature of the response are significantly increased and complex such that it cannot be considered simply a small disturbance on the without-wave solution. The results are explainable in terms of the two parameters λ−1 and x/λ (where λ is the wavelength). A clear asymmetry is observed in the wake response for the spatial wave. An examination of components of the perturbation expansion equations indicates that the asymmetry is a first-order effect due to nonlinear interaction between the steady and first-harmonic velocity components. For the traveling wave, the responses are more complex and an additional parameter, c (the wave speed), is required to explain the results. In general, for small wave speeds the results are similar to a spatial wave, whereas for higher wave speeds the response approaches the temporal wave response. The boundary layer and perturbation expansion solutions compares well with the Navier Stokes solution in their range of validity.

1.
Chen, H. C., and Patel, V. C., 1989, “The Flow around Wing-Body Junctions,” Proc. Symposium on Numerical and Physical Aerodynamic Flows, Vol. 4.
2.
Chen, H. C., and Patel, V. C., 1990, “Solutions of Reynolds-Averaged Navier-Stokes Equations for Three-Dimensional Incompressible Flows,” Journal of Computational Physics, Vol. 88, No. 2.
3.
Choi, J. E., 1993, “Role of Free-Surface Boundary Layer Conditions and Nonlinearities in Wave/Boundary-Layer and Wake Interaction,” Ph.D. thesis, The University of Iowa.
4.
Choi, J. E., and Stern, F., 1993, “Solid-Fluid Juncture Boundary Layer and Wake with Waves,” Proceedings Sixth International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa.
5.
Graham, M., 1993, private communication.
6.
Hanjalic, K., Jakirlic, S., and Hadzic, I., 1993, “Computation of Oscillating Turbulent Flows at Transitional Re-numbers,” Turbulent Shear Flows, Vol. 9, J. C. Andre et al., eds. Springer-Verlag, pp. 324–342.
7.
Hill, P. G., and Stenning A. H., 1960, “Laminar Boundary Layers in Oscillating Flow,” ASME Journal of Basic Engineering, pp. 593–608.
8.
Horlock, J., 1968, “Fluctuating Lift Forces on a Airfoils moving through Transverse and Chordwise Gusts,” ASME Journal of Basic Engineering, pp. 494–500.
9.
Lurie, E. H., 1993, “Unsteady Response of a Two-Dimensional Hydrofoil Subject to High Reduced Frequency Gust Loading,” M. S. thesis, Dept. of Ocean Engg., MIT, Cambridge, MA.
10.
Paterson, E., and Stern, F., 1993, “Computation of Unsteady Viscous Flow with Application to the MIT Flapping-Foil Experiment,” Proceedings Sixth International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa.
11.
Patel
M. H.
,
1975
, “
On Laminar Boundary Layers in Oscillatory Flow
,”
Proceedings of the Royal Society of London
, Series A, Vol.
347
, pp.
99
123
.
12.
Patel
M. H.
,
1977
, “
On Turbulent Boundary Layers in Oscillatory Flow
,”
Proceedings of the Royal Society of London
, Series A, Vol.
353
, pp.
121
143
.
13.
Poling
D.
, and
Telionis
D.
,
1986
, “
The Response of Airfoils to Periodic Disturbances-The Unsteady Kutta Condition
,”
AIAA Journal
, Vol.
24
, No.
2
, pp.
193
199
.
14.
Spalart, P. R., and Baldwin, B. S., 1989, “Direct Simulation of a Turbulent Oscillating Boundary Layer,” Turbulent Shear Flows, 6, J. C. Andre et al., eds., Springer-Verlag, 417–440.
15.
Stern
F.
,
1986
, “
Effects of Waves on the Boundary Layer of a Surface-Piercing Body
,”
Journal of Ship Research
, Vol.
30
, pp.
256
274
.
16.
Stern
F.
,
Hwang
W. S.
, and
Jaw
S. Y.
,
1989
, “
Effects of Waves on the Boundary Layer of a Surface-Piercing Flat Plate: Experiment and Theory
,”
Journal of Ship Research
, Vol.
33
, pp.
63
80
.
17.
Stern
F.
,
Choi
J. E.
, and
Hwang
W. S.
,
1993
, “
Effects of Waves on the Wake of a Surface-Piercing Flat Plate: Experiment and Theory
,”
Journal of Ship Research
, Vol.
37
, pp.
102
118
.
18.
Stern
F.
,
Kim
H. T.
,
Zhang
D. H.
,
Toda
Y.
,
Kerwin
J.
, and
Jessup
S.
,
1994
, “
Computation of Viscous Flow Around Propeller-Body Configurations: Series 60 CB = 0.6 Ship Model
,”
Journal of Ship Research
, Vol.
38
, pp.
137
157
.
19.
Telionis, D. P., 1981, Unsteady Viscous Flow, Springer-Verlag, New York.
This content is only available via PDF.
You do not currently have access to this content.