Inhomogeneity Generated Waves: Harbingers for Turbulence Generation

TL;DR

This paper introduces a new class of inhomogeneity generated waves in Navier-Stokes equations, demonstrating their existence, analytical solutions, and potential role in turbulence and energy transfer.

Contribution

It provides the first analytical demonstration of inhomogeneity generated waves in Navier-Stokes equations and explores their properties and implications.

Findings

Existence of inhomogeneity generated waves with amplitudes increasing over time

Change in volumetric viscous heating due to shear flow

Early stage of wave steepening observed in linear regime

Abstract

The Navier-Stokes equations describe fluid flow in many everyday life situations. Newton's second law of motion describes changes in the object's speed when a force applied. The Navier-Stokes equations are equivalent to Newton's Law when many objects such as microscopic particles in the air or water are considered as a group. Ocean currents, motion of smoke, dynamics of hurricane or weather patterns, air/fluid flow when the detonated device goes and many other interesting phenomena are all examples of situations when the Navier-Stokes equations govern temporal evolution. Despite its long history as a mathematical problem and simplicity of the equations, the time evolution of their solutions is not obvious. In this letter, I describe waves discovered some time ago that have received little attention in the neutral fluid physics community. Because of their properties these waves play an important role in processes like energy transfer, turbulence generation, heating, etc. Here, my intention is to demonstrate an existence of inhomogeneity generated waves in Navier-Stokes equations in the simplest possible case, give analytical solutions and provide some insight about them. We show (a) an existence of this new type of waves, which in our simple case considered here have amplitudes that increase with time, and (b) change in volumetric viscous heating when there is a shear flow present. Later process and accumulation of the kinetic energy in inhomogeneity generated waves shows an early stage of wave steepening in the linear regime.