Techniques for measuring bulge–scar pattern of free surface deformation and related velocity distribution in shallow water flow over a bump
Lichuan Gui • Hyunse Yoon • Frederick Stern
Received: 23 July 2013 / Revised: 30 March 2014 / Accepted: 2 April 2014 / Published online: 16 April 2014 Springer-Verlag Berlin Heidelberg 2014
Abstract One of the unsteady features of shallow water free surface waves over a bump is the bulge–scar pattern of the free surface deformation. An imaging technique is developed to measure the duration, displacement and size of the bulge–scar pattern from the bump top to the primary wave crest. A unique configuration of particle image velocimetry is used to measure the velocity distribution under the visualized free surface bulge at the primary wave trough. Test results indicate that the bulge–scar pattern of the free surface deformation is related to a stream-wise vortex pair in the secondary flow over the bump. The new measurement techniques may work together with the conventional measurement techniques to obtain a complete database for the shallow water free surface instability over the bump. 1 Introduction
Open-channel flows over a bump are investigated in a shallow water flume at the Iowa Institute of Hydraulic
Research (IIHR) in order to understand the physics of the free surface instability, verify relevant instability theories, and provide data for CFD validation (Gui et al. 2014).
Since unstable free surface flows are complicated, a complete database for the shallow water free surface instability over the bump cannot be achieved by only using conventional wave gauges and standard particle image velocimetry (PIV) systems to individually measure free surface elevations and flow velocity distributions. Appropriate measurement systems need to be developed to acquire more details of the unstable free surface and to correlate the free surface instability with flow instabilities, which is the main focus of the presented paper.
According to one of the theoretical solutions of potential free surface flows past submerged obstacles (Dias and
Vanden-Broeck 2002, 2004), a free surface flow over a bump may contain a train of steady waves downstream. In the deep water cases, the Kelvin–Helmholtz instability can occur because of the velocity difference across the free surface between water and air (e.g. Funada and Joseph 2001). When the flow boundary layer separates from the bump surface to form a free shear layer downstream, the Kelvin–Helmholtz instability appears in the shear layer behind the bump with high water velocity above and stagnant flow area underneath and the shear layer flaps with an overall oscillation (Scha¨fer et al. 2009). The numerical simulations by Marquillie and
Ehrenstein (2002, 2003) indicate that the flow in the boundary layer separation bubble behind a bump has only low-frequency velocity fluctuations close to the bump, but it has both low- and high-frequency velocity fluctuations away from the bump. In the cases of shallow water, the span-wise vortex structures shed behind submerged obstacles may rise up and interact with the free surface waves (Iafrati et al. 2001). In addition, the stream-wise vortex structures result from the centrifugal instabilities of curved flows, i.e., the
Go¨rtler instability over the convex bump surface (Floryan 1986; Saric 1994; Wernz et al. 2005) and the Taylor/TaylorDean instability of circular flow at the wave trough (Chen and Chang 1992) may also interact with the free surface.
Therefore, the shallow water free surface instability is a complicated phenomenon related to multiple sources of flow instabilities.
Due to the flow instability, the free surface becomes unstable and deforms from the ideal wave profile. In the
L. Gui H. Yoon F. Stern (&)
IIHR-Hydroscience and Engineering, The University of Iowa,
Iowa City, IA 52242, USA e-mail: firstname.lastname@example.org 123
Exp Fluids (2014) 55:1721
DOI 10.1007/s00348-014-1721-9 cases of shallow water, two typical free surface deformation patterns can be seen on the waves over the bump. The first type is referred as free surface turbulence pattern, i.e., the free surface is deformed stochastically without a traceable shape and duration. The second type of free surface deformation is the bulge–scar pattern that has a traceable shape and duration, i.e. a free surface bulge starts around the bump top, extends downstream to the first wave trough, and then bifurcates to form a scar at the first wave crest. It can be visually observed that the bulge–scar pattern of free surface deformation appears and disappears randomly in time and location with duration up to a few seconds, and it moves in the cross-stream direction with a noticeable speed. In many cases, multiple bulge–scar patterns appear at the same time with distance from close to very far. A quantitative determination of the bulge location and scar width in its duration and of the distances among multiple bulges is very important to understand the physics of the shallow water free surface instability over a bump. And even more importantly is to determine the relation between the bulge–scar pattern and the known structure of flow instability.
Free surface velocity distributions and free surface deformations were measured using imaging techniques similar to the particle image velocimetry, e.g., large-scale
PIV described by Fujita et al. (1998) and Muste et al. (2000), and stereo-correlation suggested by Jarny et al. (2008). Atsavapranee et al. (2005) applied a global laser rangefinder profilometry (GLRP) to determine 3D wave profile with multiple laser beams. Fouras et al. (2006) applied a background-oriented topographic technique to determine local free surface angles according to distortion of the reference image. Sanada and Toda (2008) used the similar method by replacing the background with a reflected light image to measured free surface waves. The large-scale PIV technique requires floating materials to visualize the free surface flows that are basically steady, and the spatial resolution is limited because of relatively low seeding density of the floating markers. The stereo-correlation method uses particles to visualize the free surface with high marker density, but the fluid should not be transparent so that only particles on the surface are visible. The GLRP does not provide a continuous distribution of the wave elevation, so the fine structure of the free surface deformation may not be resolved. The background-oriented topographic techniques are not able to resolve small free surface structures as bulges and scars on the free surface. Shadowgraph and Schlieren methods (e.g.,