Data Assimilation Seminar
Prof. John C. Wells (Jun. 28, 2018, 15:30-)
|Affiliation||Department of Civil Engineering, Ritsumeikan University|
|Title||Towards nowcasting in Lake Biwa: field tests of acoustic tomography, and discussion of some theorems relating the flow at a water surface to that below|
I will discuss two topics that are motivated by my lab's objective to establish a nowcasting system that can track the current and temperature fields in Lake Biwa, Japan.
First, I will present results from a test of Coastal Acoustic Tomography (CAT) in Lake Biwa in November 2017. Three 5 kHz transducers were deployed along a 10.2 km line from the West Shore of the lake to Takeshima. Acoustic travel times between transducers are computed from correlograms of the emitted "M11" quasi-random code with the received signal. Small but consistent differences in travel times between reciprocal paths were observed, whence we estimate path-averaged currents along the dominant acoustic path on the order of 5 cm/s, which is not inconsistent with expected magnitudes at this site. For the temperature profile in November, ray paths pass almost entirely below the thermocline. To my knowledge this is the first reported estimate of currents by Acoustic Tomography in a lake.
Second I will consider how to estimate subsurface flow from the fluctuating velocities and height at the surface of a river or sea, supposed to be accessible from high resolution, high-speed video recordings, perhaps by a stereo pair of bank-mounted cameras. Restricting attention to constant-density flow, a kinematic relation will first be derived that can be considered to extend the classical Biot-Savart law between vorticity and velocity. Next, the Navier-Stokes equations for constant-density liquid lead to dynamical relations between quantities at the surface with the flow field below. Empirical relations might also be used to estimate subsurface flow. For example, Large Eddy Simulation (LES) permits statistical correlations between the surface and subsurface flow to be estimated. Some relevant results by my laboratory, based on the Proper Orthogonal Decomposition, have been presented in Nguyen et al. (2011). A weakness of such empirical estimation methods is that if the actual flow includes events are not "spanned" by samples in the LES database, the predictions will fail. Thus it is important to have other tools available, such as the kinematic and dynamical relations derived here.
|Link to PDF file|