Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

An Anisotropic SubgridScale Parameterization for LargeEddy Simulations of Stratified Turbulence
(AMS, 20201001)Subgridscale (SGS) parameterizations in atmosphere and ocean models are often defined independently in the horizontal and vertical directions because the grid spacing is not the same in these directions (anisotropic ... 
Resolution Dependence and SubfilterScale Motions in Idealized SquallLine Simulations
(AMS, 20200708)In this paper, the sensitivity of idealized squallline simulations to horizontal resolution, subgrid turbulence mixing scheme, and subfilterscale motion is discussed. Inconsistent results from numerical simulations ... 
Normal Mode Spectra of Idealized Baroclinic Waves
(AMS, 20200201)Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra ... 
Realizing SurfaceDriven Flows in the Primitive Equations
(AMS, 20150501)The surface quasigeostrophic (SQG) model describes flows with surface buoyancy perturbations with no interior quasigeostrophic potential vorticity at small Rossby number Ro and O(1) Burger number, where quasigeostrophic ... 
Dependence of Model Energy Spectra on Vertical Resolution
(AMS, 20160401)Many highresolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a powerlaw slope of −3 at large horizontal scales that shallows to approximately −5/3 in ... 
Topographically generated internal waves and boundary layer instabilities
(AIP, 20150106)Flow over topography has been shown to generate finite amplitude internal waves upstream, over the topography and downstream. Such waves can interact with the viscous bottom boundary layer to produce vigorous instabilities. ... 
Random forcing of geostrophic motion in rotating stratified turbulence
(AIP, 20171229)Random forcing of geostrophic motion is a common approach in idealized simulations of rotating stratified turbulence. Such forcing represents the injection of energy into largescale balanced motion, and the resulting ... 
Wall turbulence response to surface cooling and formation of strongly stable stratified boundary layers
(AIP, 20190820)This paper investigates the processes by which stable boundary layers are formed through strong surface cooling imposed on neutrally stratified wallbounded turbulence using highresolution direct numerical simulation at ... 
Synchronization of ComplexValued Dynamical Networks
(University of Waterloo, 20210927)Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, ... 
Backscatter in stratified turbulence
(Elsevier, 201611)In this paper, kinetic and potential energy transfers around a spectral test fil ter scale in direct numerical simulations of decaying stratified turbulence are studied in both physical and spectral domains. It is shown ... 
Prandtl number dependence of stratified turbulence
(Cambridge, 20200921)Stratified turbulence has a horizontally layered structure with quasitwodimensional vortices due to buoyancy forces that suppress vertical motion. The Prandtl number Pr quantifies the relative strengths of viscosity ... 
Coupled models of structured contagion processes in humanenvironment systems
(University of Waterloo, 20210915)Models of infectious processes are a common feature in the landscape of applied mathematics. It is rare that these processes are isolated from other significant dynamics in nature, and therefore we can incorporate some of ... 
Universe Beyond Inflation and ΛCDM
(University of Waterloo, 20210909)The current paradigm of universe, $\Lambda CDM$ model with an early phase of inflation, has been quite successful in describing our universe in a simple manner, yet matching well with the observational evidence. This model ... 
Effects of a Geostrophic Current on the Propagation and Generation of Internal Tides
(University of Waterloo, 20210830)Internal tides (ITs) are ubiquitous in a stratified ocean where they are generated in response to tidal flows incident upon bottom topography. Alongshelf currents or boundary currents are ocean currents commonly observed ... 
Mathematical modelling of supraglacial meltwater production and drainage
(University of Waterloo, 20210830)Mountain glaciers and the polar ice sheets exert a critical control on water resource availability, drive sea level change, and impact global ocean circulation. These and other impacts are controlled by surface meltwater ... 
A Comparative and Exploratory Study of Homogeneous and Inhomogeneous Stratified Turbulence
(University of Waterloo, 20210825)The study of turbulence in the oceans and atmosphere is farflung and everreaching in the academic world with research being done theoretically, experimentally and numerically. With great strides in the increasing power ... 
Spectrum of Cuscuton Bounce and Cosmological Parameter Inference Using Dark Sirens
(University of Waterloo, 20210825)Over the last couple of decades, cosmology has become an exciting area to study. Technological developments in both the computational and observational fronts have propelled cosmology into the limelight of modern physics. ... 
UnderIce Fluid Dynamics in Freshwater Lakes: Implications for Ecology in a Changing Climate
(University of Waterloo, 20210824)An abundance of evidence exists to support the notion of annual winter blooms of phytoplankton, particularly diatoms, persistent in the surface waters of freshwater lakes located in temperate and boreal climatic zones. ... 
A Floating Ball and Two Asymptotic Problems in Capillarity
(University of Waterloo, 20210602)The study of capillary phenomena can be traced back to the age of Aristotle. In this thesis, a floating ball and two asymptotic problems in capillarity are considered, all of which include surface tension and gravity. The ... 
On Realistic Errors in Quantum Computers
(University of Waterloo, 20210527)In this thesis, we are concerned with the problem of characterizing noise associated with implementations of quantum circuits. We first explore the notion of error rates of quantum circuits and argue that the semantic ...