DISCUSSION. GRADUALLY VARIED SURFACE PROFILES IN HORIZONTAL AND ADVERSELY SLOPING CHANNELS.

Gradually Varied Surfaces and Gradually Varied Functions

The gradually varied surface was introduced and studied in digital and discrete spaces by Chen. The basic idea of introducing gradually varied surfaces is to employ a purely discrete interpolation algorithm to fit a discrete surface when the desired surface is not required to be “smooth.” In this paper, we generalize the concept of gradually varied surfaces. A digital surface is defined as a ma...

Gradually-varied Flows in Open-channel Networks

− Reported here are some results obtained, from a calculus algorithm application that, based on known equation analytical solutions of water flow profiles, allows the study of steady-state, gradually varied flow in open channel networks. The procedure allows to calculate, in the case of slow water flow into gradually downward slope channels, in the direction of motion, the florates and water le...

A Study of the Turbulent Flows in Sloping and Adversely Sloping Rectangular Culverts

In this paper, an experimental investigation was carried out to study the turbulent flows and flow characteristics through sloping and adversely sloping rectangular culverts in a rectangular channel of constant width using Laser Doppler Velocimetry (LDV). Also, experimental study was carried out to investigate the characteristics of the hydraulic jump occurring in a sloping and adversely slopin...

Spatially Varied Flow Profiles in a V-Shaped Side-Channel

A Note on Gradually Varied Functions and Harmonic Functions

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for σ−-net might be very small. Keeping the original discretization (square or triangulation), can we get some interesting properties related to gradual variation? In this note, we try to prove that many harmonic functions are gradually varied or near gradually var...